![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 |
The article claims that we use decimal numbering because humans have 10 fingers. I find this claim highly suspect: 10 fingers is sufficent to count in base 11 (just as one finger is sufficent to count in base 2). Does someone have a good citation for this? -- Gmaxwell 20:33, 22 May 2005 (UTC)
Zero is an artificial mathematical symbol, unnatural for human perception. "Decimal" does not *necesarily* imply that 10 is spelled using two symbols. When you start counting fingers, 10 ranks the same as each of the 1 to 9 numerals. So, why ten and not eleven? Try to quickly show the number 30 by flashing your fingers. It's as natural as... 123. Now, try with 33. Still think that base eleven suits your fingers? Luciand 15:50, 29 December 2005 (UTC)
I am not really happy with the current TOC:
Contents * 1 Decimal notation o 1.1 Alternative notations o 1.2 Decimal fractions o 1.3 Other rational numbers o 1.4 Real numbers * 2 History o 2.1 Decimal writers * 3 See also * 4 External links
The article is about decimal notation, so it does not make sense (to me) to have a section titled "decimal notation". And even if it is there, I don't see why one should have a subsection called "Alternative notation". That should be its own section, preferably at the bottom, as it is a related topic to decimal notation, but not the focus of the article. Comments? Oleg Alexandrov ( talk) 00:54, 22 February 2006 (UTC)
I failed the article for two reasons:
After that is done, feel free to renominate it at any time. Titoxd( ?!? - cool stuff) 18:40, 27 April 2007 (UTC)
One should note that Multiplication and Division take part in different parts of the brain (see Butterworth "The Mathematical Brain". and by separate processes. Multiplication is closer to animate numbers (such as other animals recognise), division more distant.
While a single method of counting is reckoned (a count of batches), there are many different division systems. The simple representation of numbers can be shown on a stone-board, where N stones in one column becomes 1 stone in the right. The most common form of number is the alternating system, where one replaces M stones for a single stone in the row above, and D stones in the top row for a single stone in the bottom row, one to the right. M is usually a number of count (eg 5, 10), where D is usually a division number (2, 4, 6, 8, 12). The chinese abacus is D=2 over M=5.
A precusros for an alternating system is a system of stand-alone fractions in D. This is known of the sumerians, and of the romans, but not elsewhere. However, the roman uncia is probably not the source of the germanic 100 of vi score.
One sees that many different systems become apparant eg 20 = 4*5 or 2*10, 40=4*10, 60=6*10, 120=12*10 are all historically known. The inherent 'decimal' system is seen, except that some have '5' at that point. To some extent, these arise by "making things bigger". The prehistory of 60 is 3*20. [O. Neugebauer - the exact sciences in ancient times]
Fractions are more complex. One has the Greek system (also mayan), where one makes ratio, eg 1944 parts where 2000 make the English foot, or the Roman weight-fractions (an uncia of weight, length and time, and number = 1/2, whence ounce and inch). One sees from their measurement systems, an ace (1) is variously a foot, a pound and a grain, and that these are invariably decimally counted (centar = 100 lb, millier = 1000 lb, mile = 100 paces), but divided approximately duodecimally (eg uncia = 1/12).
The sexagesimal numbers form the sumerian division system, these being to avoid division. For example, the most significant column is on the right, and subsequent places are divisions of the first. Zeros occur where they add meaning (eg leading, medially), but not finally, so 3 and 0 3 are different (3 and 1/20 respectively), but 3 0 is the same as 3 (ie as we write 3 vs 3.0). The count of numbers in the common system is the motely collection of decimal, sexagesimal etc (eg 192 = 100 60 30 2) See eg O Neugebaur.
That the system is a system for divisions is seen by the contents of the reckoners that come to us: tables of multiples of x by 1..20, 40, and tables of recriprocals (in ascending order logrithmically over sixty). The method of calculation was to determine the recriprocal and then look up these in the reckoners. (x = 44:26.40 exists, because this is 1/81.] We further note the existance of papers of the style of 'the problem of seven brothers' exist, giving 1/7 lieing between 0:8 34 16 and : 8 34 18, supporting the notion that it is indeed a system for fractions.
Sixty spread, along with the astronomy it used, both eastwards to India etc and westwards to Europe etc.
We see this fantasy with the duodecimal system. Historically, 12 is a division number, and that dozens and grosses were "super-divisions", ie measures, that on division, will reveal a unit peice. We have a grocer as one who deals in grosses, and sells off dozens and units.
The use of 10-like numbers (8, 12, 14, 16), is more to do with the recently devised method of using tables (the first tables, along with the first modern 0, appeare in late greece, and spread by the muslims to india and europe.
Wendy.krieger ( talk) 06:35, 2 June 2008 (UTC)
I think we should start using the unambiguous word aal instead of decimal, because every base is decimal in its own base. Actually every time we say "base 10" we should say "base A" instead.
In this way we would always represent the base with the first digit that is not used for that base eg.:
base 2 ( = 10 in base 2) -> digits 0,1
base 3 ( = 10 in base 3) -> digits 0,1,2
base 9 ( = 10 in base 9) -> digits 0,1,2,3,4,5,6,7,8
base A ( = 10 in base A) -> digits 0,1,2,3,4,5,6,7,8,9
base B ( = 10 in base B) -> digits 0,1,2,3,4,5,6,7,8,9,A
I've been thinking about this for years, so I hope you all will agree with me on this.
-- Ortonormale 00:47, 2005 May 11 (UTC)
It may be good to remember that the root "deci" means ten and "a" is a letter that is not associated with the base ten number system (why add another thing to confuse people?). Besides, saying "aal" would be more ambiguous than saying "Decimal". It sounds the same as "all"
-Michael
Yes, you would be right. I mean that since the discovery of base conversion, numerals have acquired new meanings while losing the direct link to their etymology. We could say that a new abstract level has been introduced between the original etymological meaning and the new virtual meaning. For example: 11 in base 2 represents the same quantity represented by 3 in base 8. Luckily or unluckily (according to your point of view) we have not a different set of names for each numeral in each base, therefore we have two possibilities:
In this latter case, we could simply say "eleven" to read the numeral 11 in whichever base. The same concept would apply to "ten", "decimal" and "digit".
Obviously, we would have ambiguities when not specifying the actual base, but this already happens when writing.
Nothing really fun so far.
The funny part comes when we want to read numbers like
Again: obviously (as you have noticed) we would have an obstacle to complexity increase trying to use bases that are greater than Z, but this already happens when writing. It is a common problem for non positional numbering systems, but a simple solution consists in grouping. So for example we could use the base 2xG (or simply 2G) in which each digit is represented by a group of 2 digits in base G, like
-- Ortonormale 00:22, 2005 May 19 (UTC)
Wendy.krieger ( talk) 07:03, 5 June 2008 (UTC)
Is there any other theory at all for explaining the decimal system?
From a mathematical point of view, I see no argument that could be made for ten - two (or powers of two) is special, of course, since it's the smallest possible base (powers of two are just a neat way of cramming several binary digits into one handy symbol), three would give you balanced ternary, and I believe you can formalise the fact that 12 has a large number of factors.
Of course, it's possible that there might be a psychological aspect that makes 10 a natural choice, or that it was just an accident of history, but in the absence of support for either of those theories, maybe we should state this a bit more strongly?
RandomP 18:51, 13 May 2006 (UTC)
The article confuses base 10 with positional systems. Someone commented on this above, but was never answered. If there is no discussion here, I'll go ahead and rewrite the article.
Chinese numerals are decimal, even though they're not positional. Likewise, Roman numerals are also decimal, though with a minor auxiliary base in 5. Hebrew gematria are decimal. There are very few written systems which are not decimal—Mayan and Babylonian are the only ones which comes to mind—though of course in spoken languages there are all kinds of bases and base combinations.
Besides decimal numeration, there are decimal fractions. All this requires is extending base 10 to fractional notation, though in practice in the modern world it nearly always implies a positional system. (Roman combined decimal numeration with duodecimal fractions, neither of which were positional.) India did not invent decimal numeration, which is the most common in the world, and AFAIK did not invent decimal fractions either; it invented the positional system and the zero that went along with it. (Mayans had a zero but not a fully positional system, due perhaps to religious considerations.) kwami ( talk) 02:44, 26 February 2009 (UTC)
Our number words go this way. Butterworth (The mathematical brain) notes that this is the most advanced form, since one is less likely to read two thousand and six as 20006 (ie 2000 6).
The lead says:
and someone added
and I thought: Don't be ridiculous... but, thinking a bit more about it, I realized that the most widely used base IN NUMERICAL CALCULATIONS is binary, in the sense that most of the additions, multipliplications, etc. that are performed on any given day are done by computers, not by humans. So while we don't really need a source, we may need a qualification; something like:
... but I don't really like that either. Any good ideas?-- Noe ( talk) 06:48, 21 October 2009 (UTC)
The article claims "decimal fractions were first used ... by Arab mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century". That is incorrect. He was not the 1st person to use it.
According to the Cambridge University in England, decimal fractions were 1st developed and used by the Chinese in the 1st century BC, and then spread to the Middle East and then to Europe.
Source : Science and Civilization in China (Vol. 3) (Published by the Cambridge University Press)
Wikiwikidaddy ( talk) 07:45, 30 October 2009 (UTC)
We have a "list of recorded decimal writers" in this article:
What is the point of this? It is not explained at all. At first, I assumed it was notable developments in the use of the Hindu-Arabic numeral system, but it also includes modern writers who discuss binary and related issues for computing. I think this section should be better motivated, focused and pared down. I've commented out most of the modern authors because I don't think that they belong here. Cheers, — sligocki ( talk) 21:20, 30 October 2009 (UTC)
Simon Stevin's contribution to decimals is generally recognized to be the seminal one, see for example van der Waerden, or the St Andrews pair of articles which clearly relate to Stevin as a watershed. Is it reasonable to have all sorts of multicultural characters mentioned here, and leave out Stevin? Tkuvho ( talk) 15:11, 21 February 2010 (UTC)
Is there actually a specific reason that almost the entire world uses the decimal system, i.e. is there a logically imperative reason for its popularity or is this simply arbitrary? Is there a scientfically valid difference in using another base system? —Preceding unsigned comment added by 217.85.239.236 ( talk • contribs) 19:31, 22 February 2010
The article claims "The modern number system originated in India". That is incorrect.
According to the Cambridge University, the decimal system (together with the digit zero) originated in China. The most conservative estimate for the use of the decimal system dates it to no later than the 14th century BC (although it is known to have been in use long before that).
Source (1) : Science and Civilization in China (Published by the Cambridge University Press)
Source (2) : Genius of China (by Robert Temple) (This book has won numerous major literary awards including ones from the American Library Association and the New York Academy of Sciences, and was translated by UNESCO into 43 different languages ).
Wikiwikidaddy ( talk) 08:42, 30 October 2009 (UTC)
I have some serious issues with the 'Genius of China' by Robert Temple - this is an author who believes that extra-terrestrials had contact with early humans! I would like to see a more in depth discussion of these supposed inscriptions from the 14/13th century BC!
by al-Uqlidisi, with a Latin tranlation of Musa al-Khwrizmi of 825, with works by Kushyar ibn Labban, and founnd that in these early islam mathematic works, the method of division using Hindu-Arabic numerals is indentical to the Chinese rod numeral method described in The Mathematical Classic of Sun Zi, to the finest detail, even the shifting of the numbers of multiplier from left to right by one position, was copied in toto in these early ISlam works. Even the expression of the remainder after division as fraction is identical to Sun Zi.
This is more mind boggling, given that the fact the rod numeral decimal system is a operational system by moving rods on counting board(actually on floor or table top), while the these islam works written more than 400 years after and based on WRITTEN calcuation, shared the exact procedures to the last minutes, some of these operation such as after divsion by one digit, must move the whole set of divisor numbers from left to right one position, which is whole un necessary and and cumbersome in a calculation system based on written symbols, one cannot just simply move the numbers around, like move counting rods on floor, but must involve re writting. Too much conincidence to explain away with independent development. Further, Dr Lam also pointed out the fact the before the advent of 0 in India, Indians used a blank space to represent a zero, which is extremely odd and un natural in a written system; while in rod calculus, a blank space in counting board (read counting table top) is the intrinsic of rod system, for example 3 minus 3 means take away 3 rods from 3 rods, naturally no more rods left on the board and left a blank. The blank in rod numerals in natural, the blank in written symbol is not intrinsic in Hindu Arab system.
Dr Lam believes, that the only logical explanation of these perplexing facts is that the Indian-Arab decimal had its origin in Chinese rod numeral system, which was in used in China much earlier than the earliest Indian record of decimal system. The Indian version was introduced to Islamic world by Musa al-Khwzizmi, the translated into Latin and transmitted to the west.
Propronents of Indian origin must answer the following facts, why an empty space in their early decimal system ? Why translated Indian system as appeared in several Islam works show such striking similarity up to the last minute with Sun Zi'w work ?
It is not difficult to explain the transmission of Chinese rod numeral system (the only methd of calculation used by the Chinese, until the advent of abacus) from China to India. From 266-to 399, there were on record, Zhu Fahu, Kang Falang, Yu falan, Zhu Niafo, Hei Chang, Hui Bian, Zi Faling, Fa Jin, anf Fa Xian travelled to India.
I believe Cambridge University and Rober Temple is right, the decimal system was originated in China, not India -- 70.50.200.249 ( talk) 23:51, 8 April 2010 (UTC).
Joseph Needham, Robert Temple never claimed that the written 0 was invented in China, probably invented in eastern region of India close the southern China culture, or in Cambodia. Chinese carried out complex mathematical calculation with counting rods, they don't need a special 0 symbol, not until 13th century, 0 symbol appeared. It must be emphasiz here, the appearance of written 0 does not implied conceptual invention, as Needham pointed out, the Brahmi numerals which the Hindu- Arab system supposed to derived from, was no improvement from the Greek and Hebrew numeral system.-- 70.50.200.249 ( talk) 00:02, 9 April 2010 (UTC).
There is good answer as to why the Chinese counting rods of the Spring and Autumn period stop at 9, and no more then nine symbols.
Because, the ancient Chinese had "Worship of Nine" culture, stemmed from the Book of Chang. Ancient Chinese classified even numbers such as 1,3,5,7,9 as Yang, and 2,4,6,8 as Ying, 9 being the highest of the Yang number, was considered the supreme number, thus an emperor was called "Nine five supremacy", correspond to the the first Hexagram of I Ching, the "Heaven, Yang, and Male" Hexagram, which, each bar was called a Nine, the fifth bar called a Nine-Five, corresponding to "Flying dragon on the Heaven"-- the emperor. Do you think a court mathematician who held the highest math post in a kingom dared to get ahead of "nine" and higher than the emperor ? Thus the counting rod must stop at nine and no more.
The worship of Nine casted a deep mark on history of Chinese mathematic:
Recently a priority claim for chinese mathematics was added to this page, which seemed to be properly sourced in a publication in a respectable journal (as well as a respectful mathscinet review). The changes were reverted together with some argumentative material. This should probably be discussed here. My own feeling is that both indian contribution and the chinese contribution should be discussed, preferably avoiding dramatic priority claims, but this also shouuld be discussed. Tkuvho ( talk) 12:05, 8 April 2010 (UTC)
1) the title of this article is Decimal, not "positional decimal" 2) Positional decimal is a subset of decimal, in China, non positional decimal appeared first, than evolved into positional. The counting rod was positional from the start. 3) To full understanding how non positional decimal evolved into positional decimal, one must examine the step by step history, it is no use just pointing to a piece of artifact and declared it to be a smoking gun evidence. -- Gisling ( talk) 02:22, 12 April 2010 (UTC).
parallel lines of decimal, written Chinese decimal was not decimal, counting rod is. A good analogy is our daily written numeral is not binary, but the computer we us is. Counting rod was the computer of ancient China, neglect this is a big mistake. Put it in other words, the
Chinese used positional decimal computing device a millenium before any other civiliztion --- Gisling ( talk) 02:22, 12 April 2010 (UTC)
Gisling wrote: "Your classificaion of Wu, Shen, Li as "offical Chinese line" will be a laughing stock for international scholars on history of Chinese mathematics." I did not classify either of them as "official chinese line". When speaking of the "official chinese line", I was referring to reliance on the great chinese encyclopedia, whose objectivity I think is questionable. Work by Wu, Shen, and Li published in reliable western periodicals would be just as welcome as work of Lam Lay Yong. A critical attitude toward the chinese encyclopedia does not bring politics into the discussion, as you suggest. On the contrary, such a critical attitude is an effort to keep politics out of the discussion. We all know who made a laughing stock of themselves in pursuing chinese priority for the proof of the Poincare conjecture. What is not sufficiently realized is that, were it not for the efforts of single individuals such as Sylvia Nasar, the Poincare conjecture page would currently present a 450 explanation of how the chinese proved it. I appreciate your willingness to rely on western sources in documenting decimals and positional decimals. Given that distinguished scholars such as Joseph Dauben worked in the history of chinese mathematics, this should not prove an impossible task, and I appreciate your putting in the time. Tkuvho ( talk) 07:46, 12 April 2010 (UTC)
The current series of edits by Gisling started by quoting a paper by Lam Lay Yong, in a reputable western journal "Archive for History of Exact Sciences". Since then, Gisling's additions have been dominated by the official chinese line. Thus, the typical "Footnote 6" currently states: "This view was adopted by the editorial board headed by Wu wen Tsun of Chinese Academy of Science for The Grand Series of History of Chinese Mathematics" (the editor appears under Wu Wenjun). Now the official chinese line may not be consistent with Western scholarship, any more than the Great Soviet Encyclopedia on the issue of priority of invention of non-Euclidean geometry. I would suggest moving all material not sourced in Western sources, to the talkpage for discission. Tkuvho ( talk) 11:45, 11 April 2010 (UTC)
Wu Wenjun, Shen Kangshen, Li Di are all well respected historians in Chinese mathematics, ASAIK, none them are communists, where comes this label "Chinese lines ", just is is unreasonable to label books by Cambridge U as "Capitalisism line, imperialist line" .Shen Kangshen published book with Cambridge University Press, the historian of math is a small world, Jean Claude Martzloff, K Chemla, U. Libbrecht, Lam Lay Yong met in international conferences in China and abroad every year,every one knows other one's work, and Martzloff, Librecht, all has Chinese name, in short, they are like a family. Your classificaion of Wu, Shen, Li as "offical Chinese line" will be a laughing stock for international scholars on history of Chinese mathematics.
I absolutely oppose Western Central Point of View, "western scholarship" is pure prejudice.
Once politics enters wikipedia, it will be doomed -- Gisling ( talk) 01:59, 12 April 2010 (UTC).
In considering the fact that most reader of the en.wikipedia do not read Chinese, I shall try my best to replace a part of the Chinese references with English reference, just for the convenience of readers of en.wiki, not a matter of principle-- Gisling ( talk) 04:06, 12 April 2010 (UTC).
I have move most materials from Chinese language sources to talk page, leaving only one citation on archeological evidences. Now in this paragraph, the citations are mostly from English literatures by Joseph Needham, Robert Temple, Lam Lay Yong and Yoshio Mikami-- Gisling ( talk) 10:42, 12 April 2010 (UTC).
Suan shu shu. A book on numbers and computations. Translated from the Chinese and with commentary by Joseph W. Dauben. Arch. Hist. Exact Sci. 62 (2008), no. 2, 91--178.
In this article "The modern numeral system format, known as the Hindu-Arabic numeral system, originated in Indian mathematics[15] by the 9th century."
but in Hindu–Arabic numeral system
"The development of the positional decimal system takes its origins in Indian mathematics during the Gupta period. Around 500 CE the astronomer Aryabhata uses the word kha ("emptiness") to mark "zero" in tabular arrangements of digits. "
"The earliest surviving evidence of decimal place value numerals in India and southeast Asia is from the middle of the first millennium CE.[52] A copper plate from Gujarat, India mentions the date 595 CE, written in a decimal place value notation, although there is some doubt as to the authenticity of the plate.[52] Decimal numerals recording the years 683 CE have also been found in stone inscriptions in Indonesia and Cambodia, where Indian cultural influence was substantial.[52]"
any one who knows more about Indian mathematics, please fix this inconsistency. Please provide more concrete evidence, such as how the ancient Indians carried out calculation ? On paper ? with abacus etc etc, dates ?-- Gisling ( talk) 13:18, 12 April 2010 (UTC).
This book gives detailed number systems, with plenty of examples of digits from various epochs.
The previous decimal system in places like china, is that of number exponent pairs, eg 9 C 2 X 5 for 925 (ie 9 hundred 2 ten 5). Since the chinese use characters as words, this could as equally be the written form.
The forms given for india, show large variations in the digits 1-9, but 0 is consistantly shown in two forms: as an open circle, and as a point like a modern bullet-point. This suggests that 0 was borrowed into Indian culture. The chinese form is an open circle, but this is entirely uncharacteristic of the caligraphy of the time, suggests that China borrows it from the Indians.
For the Arabs, that the entire alphabet was reworked from traditional Semetic order to a form more accomidating of the greek alphabet, largely to allow the greek numbers to be used without modification. The order of borrowing is to use greek letters as numbers, then arabic numbers, then hindoo numbers.
The suggested migration is then from the Muslims to the Indians to the Chinese.
The greeks already had iota representing both 10, and in a different system, 0. This system existed around C4 (ie late 300's). This is what i consider to be the source of the modern decimal system.
One notes with Butterworth (The mathematical brain), that the use of number + weight (eg 9c2x5) is less prone to give errors, and a more advanced system than long digit strings (eg 925). One particular error avoided is writing '1008' for 108, or 1c8, in the sense of 1 00 (hundred) and 8 ie 1008. -- Wendy.krieger ( talk) 07:42, 13 April 2010 (UTC)
I've just removed the following reference from this page:
If you look at the date, it was clearly written as a term paper when that author was an undergraduate.
Just to clarify that. I meant Chinese shí (=10), of course, in my edit summary. Gun Powder Ma ( talk) 22:01, 21 April 2010 (UTC)
Gun Powder Ma ( talk · contribs) has been reinserting material which I consider inappropriate into the article. Although he/she was the first to Boldly insert the material, I'm willing to be the first to discuss it. My specific concerns on the latest reinsertion:
A former French school teacher, in order to answer pupil's question, determined to become Indiana Jones of math, wrote a popular book on numbers.-- Gisling ( talk) 08:07, 1 May 2010 (UTC).
“Historians of mathematics in particular have voiced strong reservations about Ifrah’s pronouncements on the history of number systems... In 1995 a group of five experts in France agreed it was necessary to confront the popularity Ifrah’s work was being accorded and to point out explicitly his numerous misreadings, misinterpretations, and pure fabrications....Lévy explains that he and his colleagues felt an obligation to “rectify [Ifrah’s] deceptive, confused,even muddle-headed views.” They felt compelled to do so he says because of Ifrah’s relentless habit of presenting conclusions that are “often debatable,generally weak, and at times wholly imaginary,”as if they were “historically valid theses”
Dauben review of Ifrah' book]-- Gisling ( talk) 10:43, 1 May 2010 (UTC).
statements of supported by references than it should be considered reliable, otherwise, should be deemed his "orginal research" and used with caution. -- Gisling ( talk) 13:12, 1 May 2010 (UTC).
A lot of statements in Ifrah's book were stated without reference. This makes citing his book as reference problematic. For example the statement about|pañchabhyah khalu shûnyebhyah param dve sapta châmbaram ekam trîni cha rûpam cha" has no reference. A search with google leads to Ifrah only, looks like his own opinion, but then, is he an ancient Indian language expert ? How reliable is his statement ?, Given the fact that he stated that eka,pitamaha,adi,tanu……all meant "one" ,dvi,ashvin,Yama, yamala, netra,bahu,guophau, paksha all meant "two"...|nava,anka,graha,chhidra meant nine, shunya,binda,kha,ambraha...meant zero . All these makes people confuse.
-- Gisling ( talk) 01:01, 5 May 2010 (UTC).
Imagine someone with two digits on each hand developing their own numerical system. This system goes 1, 2, 3, 10, 11, so on and so forth... Now imagine one of us were to meet this person in a neutral location. We observe that there is a cluster of rocks on the ground. We count all of the rocks using the fingers (excluding our thumb) on one of our hands. This special someone counts the rocks using their numerical system. They conclude that there are 10 rocks in this cluster. You of course make note of this fact and exclaim that this person must be using base 4, and express your preferred usage of base 10. They are confused, because they are using base 10, and base 4 doesn't make sense to them. All articles on Wikipedia regarding numerical systems must therefore make note of the fact that the naming system for any base is itself based upon base 10. 98.218.122.127 ( talk) 11:19, 23 May 2010 (UTC)
The following reference "Azar, Beth (1999). "English words may hinder math skills development". American Psychology Association Monitor 30 (4). http://www.apa.org/monitor/apr99/english.html." links to an empty page. I did not edit the article but I thought you should be aware. Also, why isn't there more mention in the lead for this article about a connection (or lack of connection) between the assumption that our pre-homosapien/homosapien species having ten fingers was THE decider for base 10 being what we use everywhere today, maybe even coded in our genes (if there was a gene that made the understanding of base 10 easier, and also if an understanding of base 10 has been natural selection factor for long enough)? Unsigned intentionally. —Preceding unsigned comment added by 211.29.174.138 ( talk) 17:29, 31 August 2010 (UTC) (Autosigned by SineBot)
The introduction indicates that mathematics education uses the word "decimal" to refer specifically to a decimal fraction as described later. This indicates that teachers and students do not use the word "decimal" for irrational numbers or numbers with infinitely repeating decimal expansions. This is ludicrous. Most students and teachers use the word "decimal" to discuss numbers that are not integers, refusing to acknowledge the integers as decimals. If no objections, I will edit the article to read, “In some contexts, especially mathematics education, the term decimal can refer specifically non-integer numbers. In such a case, the number 1.234234234... is called a decimal while the number 1234 is not. ” I'm not too happy with the example, but it is certainly better than the rubbish that was there before. Clifsportland ( talk) 18:59, 26 August 2010 (UTC)
I've made two changes. First, there was a statement that "It is the most widely used numeral system, perhaps because a human usually has four
fingers and a thumb on each hand, giving a total of ten digits on both hands." The proper preposition is "over", not "on". "On" creates an ambiguity as to whether it means that each hand has a total of 10 fingers, or together have 10 fingers.
Also, there was a statement that + means plus and - means minus. When it comes to sign, that is WRONG. The signs are positive and negative, not plus and minus.
Decimal is the number system humans use because of the fact that we have ten fingers.
I heard that some cultures prefered to use the hexadecimal system because they didn't count their fingers on their hands. But instead, they counted with one hand using one thumb to touch on the finger tips and the bends at their finger joints. (There are 16 points on each human hand, hence a hexidecimal system.) However, the decimal system became so wide spread internationally that it dominates now.
I heard about this over twenty years ago from my high school teacher. I don't know his source of this information. I am wondering if any wikipedians out there can confirm this.
If the counting finger-joints technique were more prevailing than counting fingers, human society could have adopted the hexadecimal system which is much better compatible with binary computers nowadays.
The ancient Mayan civilization used base 20 in their numbering system. Their numeric symbols denote values from 0 to 19. (source: http://www.eecis.udel.edu/~mills/maya.htm)
Avoid fallacies in arguments. Just because the people that use decimal do so because they have 10 fingers doesn't mean that all humans use decimal. Nor does it invalidate any of these base 16 or base 20 systems. The article should point out that not all people use decimal (and I will edit it). -- drj
I don't think there are any societies that used base 16 though. The highschool teachers story seems suspect. Base 20 is of course fingers and toes. But where does base 12 come from? --AxelBoldt
12 presumably comes from months of the year. Many calendars have 12 months in a year (not just because it is nearly the number of lunar months in a year). Imagine you are an early geek into factors and astronomy. Observe: 360 days in a year, aha! that factorises easily with nice factors like 12, 60, 24, etc. The base 16 claim seems very dubious to me. Fingers and toes didn't occur to me though it is plausible. -- drj.
I think the 12, 24, 60 business came from the Babylonians/Persians? Somewhere that direction and long before Greece. --rmhermen I said "geek" not "greek"! Bablylonians/Mesopotamia is the generally agreed source I believe. -- drj
The babylonian number system was base 60 according to Math historian, David M. Burton. He suprisigingly doesn't have a wikipedia page. Clifsportland ( talk) 18:59, 26 August 2010 (UTC)
Are roman numerals a number system? What is the base?
So perhaps the article on number systems should mention it?
In the US weighing system, one pound = 16 ounces. In Chinese weighing system, one catty = 16 taels. Though they are not number systems, but at least it give some hints why the number 16 is involved in measurements universally. In any systems that use division, any power of 2 is a good candidate for convenience sake. For example, a gallon = 4 quarts = 8 pints = 128 fluid ounces = 1024 fluid drams etc.
Looks like human are attracted to the power of 2 and astronmonical periods and our fingers and toes.
A old British pound = 20 shillings
one old shilling = 12 pences
20 and 12 can still be explained, but 1 mile = 1760 yards??? how did they come up with that number?
Have you heard the story about how the butt size of the Roman horses decided the rail guage in the current US railroad system?
In decimal counting, the Fibonacci numbers repeat the sequence of the last digit over a period of 60. Every other numeral system with base less than 14, repeats in less than half of this (often 24).
Base Period of last digit of Fibonnacci Numbers 2 3 3 8 4 6 5 20 6 24 (last two digits too) 7 16 8 12 9 24 10 60 (unusually big) 11 10 12 24 (last two digits too) 13 28 14 48
I realize I am jumping to this without most of your comments. The statement is slightly misleading. I won't change it until I think of a way of wording the correction. It just happens that everybody uses arabic numbers when they write english so it is easier to convert all numbers to that system which happens to based on base 10. For example you could use base 60 for time, but the symbols are not universally recognized and you can easily flip from base ten to base 60 when talking about seconds and minutes. I am certain there are languages that use another base or consider it significant. Look at binary. Still base 10 is huge compared to it. Tempust ( talk) 05:28, 24 February 2010 (UTC)
This article does not make it clear whether it is about the decimal aspect of the current world system, or the positional aspect. It says that our system is the one of two decimal positional systems. But then it compares non decimal systems to the system only discussing their base. What is truly needed is a grid of articlesh that looks like this, having an introductary article for decimal systems, binary systems, dodecimal, binary, vigesimal and sexigesimal systems, as well as an introduction for each of the ways of denoting the powers, positional, different symbols.. &c. However, as a start, the following might make sense:
an article on systems that use a different symbol to show how many, but use positions for powers -can be based on this article after a title change, and moving some stuff around -will also contain mention of common binary notation, and its dervitives (hex &c) -will also discuss all the different notations for the decimal system of this type, arab, western, gujarati, &c -base sixty fractions
an article about systems that have a different symbol for each amount in each order such as greek, hebrew, older arabic one -(abjad systems???)
an article about systems that have a different symbol for each power of the base, but write it multiple times in order to show amount -decimal ones: Roman, Egyptian, that other greek one that looks like hang man -sexigesimal ones: Sumerian, babylonian
an article about systems that use positions to show order and use accumalation of the symbols to show amound -sexigesimal: later babylonian -vigesimal: maya (the above two both use alternating symbol sets for the two factors of their base, so are not really pure)
Once this framework is done, there are probably lots of main articles that can be pointed to. —Preceding unsigned comment added by Alexwebjitsu ( talk • contribs) 03:43, 18 February 2008 (UTC)
Decimals (decimal place) - see wikitonary
Decimals also refer to decimal fractions, either separately or in contrast to vulgar fractions. In this context, a decimal is a tenth part, and decimals become a series of nested tenths. There was a notation in use like 'tenth-metre', meaning the tenth decimal of the metre, currently an Angstrom. The contrast here is between decimals and vulgar fractions, and decimal divisions and other divisions of measures, like the inch. It is possible to follow a decimal expansion with a vulgar fraction, this is done with the recent divisions of the troy ounce, which has three places of decimals, followed by a trinary place.
The use of ordinals to designate repeated fractions is seen in sexigesimal (second and third minutes, Newton goes as far as vi and vii), decimal (see, eg tenth-metre), duodecimal. Just as counting up is remainders by division by 10, so is fractions made by multiples of 10 and 'carry'. A method to convert this to another base is to carry out exactly this equation, eg the duodecimal of 0.14 becomes (by multiplying the fractions by 12) 1.68, 8.16, 1.92, 11.04, ... the integer parts become the duodecimal fractions: 0.1 8 1 11 .... -- Wendy.krieger ( talk) 08:14, 25 December 2010 (UTC)
I tidied up some fiddly mechanical bits in the first half of the article, but I had to leave the "History" section alone. This section has a great many issues; I think it needs to be extensively rewritten, but I lack the background knowledge (Chinese history, counting rods, abaci) to do so myself. Any thoughts? -- Majestic-chimp ( talk) 23:40, 31 December 2010 (UTC)
A good measure of the talk seems to be given over to discussing the nature of zero in modern usage, and the origin of the modern digital number system. This has nothing to do with decimal.
Zero, in its modern use, was used by the mayans in base 20. The Sumerian fraction system, used zero in leading and medial positions, eg 0 0 1 = 1 second, and 1 0 6 for 1h 6s, but not trailing positions (1 0 and 1 are identical to one). However, one can use a decimal system without using a zero, just as one can use such without a decimal point.
The modern western digits are indeed of indian origin, the etymology of zero (from 'sunna = empty'), suggests this too. The arabs were the ones that the Europeans borrowed it from, and the Chinese seemed to have borrowed the European scheme, making their traditional runes similar to names for these numbers, eg 'five ty six' but '56'.
Of course, 'base 10' is not the only historically relative base: one has many examples of 'base 100', that is, alternation of the base number over two places (ie 6-10 or 4-10 or 8-10 or 2-10 or 4-5 etc), by having the units row and the tens-row at different values. Even the examples of the chinese stick-numbers are 2-5, reflect the abacus they inherited from the romans.
And in this sense, "decimal" is not a particular creation that is carried from place to place, but something that arises freely in different places. Suggesting otherwise is to suggest the mayans and the celts (with histories of base 20), derive from a common pan-atlantic source, such as atlantis.
-- Wendy.krieger ( talk) 07:46, 25 May 2010 (UTC)
The 2nd last sentence in the 1st paragraph of section "History of the Hindu-Arabic numeral system" is misleading given that the section directly above already puts in serious doubt such claim.
If no-one objects, I will change the wording to remove the ambiguity. The change proposed is as follows:
Original : "On this theory, the ideas were then transmitted..."
Clarified sentence : "According to those who are willing to accept Georges Ifrah's claim despite the seemingly contradictory evidence suggested in the section above, the ideas are believed to have been later transmitted ..."
This change should reduce the disjointed feel of the article. Marcopolo112233 ( talk) 05:49, 10 January 2011 (UTC)
There have been some recent changes, back and forth, regarding the wording of the section on Notation. The question seems to be whether the choice of comma or period is dependent upon language or geography/politics. Before we continue to change the article, we should discuss this point and come as close to a consensus as possible. Additionally, any changes should be supported by a reference. My understanding was that the use of a comma does not depend upon language, but rather geography. I thought that the UK used a comma when doing their “maths”. The US definitely uses a period. Clifsportland ( talk) 20:48, 10 January 2011 (UTC)
The reference to the floor function after mentioning the integral portion of a decimal fraction may be very misleading. For instance truncate(-1.3)=-1, which is NOT equal to floor(-1.3)=-2. This is a common error. Even if that was not the intention of the article, it may still obscure rather than elucidate. — Preceding unsigned comment added by Nielsed ( talk • contribs) 17:48, 12 March 2011 (UTC)
Regarding this section, the sentence directly before the common fraction list reads "The decimal fractions are those with a denominator whose only prime factors are 2 and/or 5" (bold added). That is followed by a list of common fractions whose denominator is prime factored by only 2 & 5, until the list item that reads "1/3 =", which fails that particular pattern, as does what follows it. Is this (see Table 4-1) what is meant? Is the list meant to be misleading? Gzuufy ( talk) 19:19, 8 May 2011 (UTC)
Recently there are multiple attempts at disruption without going thru discussion. Sucth disruption is contrary to wiki's policy, should be banned -- Gisling ( talk) 00:18, 23 June 2011 (UTC).
The 1st sentence of the 1st paragraph of section "Possible Chinese origin of Hindu–Arabic numeral system" starts with the statement "It has been suggested that ...".
The rule of Wikipaedia is that if you cannot provide a source for a claim, you should not state the claim. Given that is the case, either the entire 1st sentence should be removed or if it is accepted, then the qualifier statement "It has been suggested" should not be necessary.
If no-one objects, I will remove that qualifier statement from the sentence. Marcopolo112233 ( talk) 06:10, 10 January 2011 (UTC)
"I thought it was a question of the source being reliable" is false and without any merit. The author Lam Lay Yong was an associate editor of Historia Mathematica and a member of Académie Internationale d'Histoire des Sciences. She also won the higest award in History of Mathematics, how dare you said "unreliable"---00:36, 23 June 2011 (UTC)
I am the opion that positional decimal system IS a subset of decimal system, it is also the dorminat decimal system in the world to day. It is far more imporatant than general decimal, hence need to be address separately. It is strange that en.wiki does not have article on this imporant topic.--- Gisling ( talk) 09:13, 23 June 2011 (UTC).
The comment(s) below were originally left at Talk:Decimal/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
History could be in prose. Salix alba ( talk) 19:14, 29 September 2006 (UTC) Needs longer lead and more references. Geometry guy 20:51, 9 June 2007 (UTC) |
Last edited at 20:51, 9 June 2007 (UTC). Substituted at 20:22, 2 May 2016 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 |
The article claims that we use decimal numbering because humans have 10 fingers. I find this claim highly suspect: 10 fingers is sufficent to count in base 11 (just as one finger is sufficent to count in base 2). Does someone have a good citation for this? -- Gmaxwell 20:33, 22 May 2005 (UTC)
Zero is an artificial mathematical symbol, unnatural for human perception. "Decimal" does not *necesarily* imply that 10 is spelled using two symbols. When you start counting fingers, 10 ranks the same as each of the 1 to 9 numerals. So, why ten and not eleven? Try to quickly show the number 30 by flashing your fingers. It's as natural as... 123. Now, try with 33. Still think that base eleven suits your fingers? Luciand 15:50, 29 December 2005 (UTC)
I am not really happy with the current TOC:
Contents * 1 Decimal notation o 1.1 Alternative notations o 1.2 Decimal fractions o 1.3 Other rational numbers o 1.4 Real numbers * 2 History o 2.1 Decimal writers * 3 See also * 4 External links
The article is about decimal notation, so it does not make sense (to me) to have a section titled "decimal notation". And even if it is there, I don't see why one should have a subsection called "Alternative notation". That should be its own section, preferably at the bottom, as it is a related topic to decimal notation, but not the focus of the article. Comments? Oleg Alexandrov ( talk) 00:54, 22 February 2006 (UTC)
I failed the article for two reasons:
After that is done, feel free to renominate it at any time. Titoxd( ?!? - cool stuff) 18:40, 27 April 2007 (UTC)
One should note that Multiplication and Division take part in different parts of the brain (see Butterworth "The Mathematical Brain". and by separate processes. Multiplication is closer to animate numbers (such as other animals recognise), division more distant.
While a single method of counting is reckoned (a count of batches), there are many different division systems. The simple representation of numbers can be shown on a stone-board, where N stones in one column becomes 1 stone in the right. The most common form of number is the alternating system, where one replaces M stones for a single stone in the row above, and D stones in the top row for a single stone in the bottom row, one to the right. M is usually a number of count (eg 5, 10), where D is usually a division number (2, 4, 6, 8, 12). The chinese abacus is D=2 over M=5.
A precusros for an alternating system is a system of stand-alone fractions in D. This is known of the sumerians, and of the romans, but not elsewhere. However, the roman uncia is probably not the source of the germanic 100 of vi score.
One sees that many different systems become apparant eg 20 = 4*5 or 2*10, 40=4*10, 60=6*10, 120=12*10 are all historically known. The inherent 'decimal' system is seen, except that some have '5' at that point. To some extent, these arise by "making things bigger". The prehistory of 60 is 3*20. [O. Neugebauer - the exact sciences in ancient times]
Fractions are more complex. One has the Greek system (also mayan), where one makes ratio, eg 1944 parts where 2000 make the English foot, or the Roman weight-fractions (an uncia of weight, length and time, and number = 1/2, whence ounce and inch). One sees from their measurement systems, an ace (1) is variously a foot, a pound and a grain, and that these are invariably decimally counted (centar = 100 lb, millier = 1000 lb, mile = 100 paces), but divided approximately duodecimally (eg uncia = 1/12).
The sexagesimal numbers form the sumerian division system, these being to avoid division. For example, the most significant column is on the right, and subsequent places are divisions of the first. Zeros occur where they add meaning (eg leading, medially), but not finally, so 3 and 0 3 are different (3 and 1/20 respectively), but 3 0 is the same as 3 (ie as we write 3 vs 3.0). The count of numbers in the common system is the motely collection of decimal, sexagesimal etc (eg 192 = 100 60 30 2) See eg O Neugebaur.
That the system is a system for divisions is seen by the contents of the reckoners that come to us: tables of multiples of x by 1..20, 40, and tables of recriprocals (in ascending order logrithmically over sixty). The method of calculation was to determine the recriprocal and then look up these in the reckoners. (x = 44:26.40 exists, because this is 1/81.] We further note the existance of papers of the style of 'the problem of seven brothers' exist, giving 1/7 lieing between 0:8 34 16 and : 8 34 18, supporting the notion that it is indeed a system for fractions.
Sixty spread, along with the astronomy it used, both eastwards to India etc and westwards to Europe etc.
We see this fantasy with the duodecimal system. Historically, 12 is a division number, and that dozens and grosses were "super-divisions", ie measures, that on division, will reveal a unit peice. We have a grocer as one who deals in grosses, and sells off dozens and units.
The use of 10-like numbers (8, 12, 14, 16), is more to do with the recently devised method of using tables (the first tables, along with the first modern 0, appeare in late greece, and spread by the muslims to india and europe.
Wendy.krieger ( talk) 06:35, 2 June 2008 (UTC)
I think we should start using the unambiguous word aal instead of decimal, because every base is decimal in its own base. Actually every time we say "base 10" we should say "base A" instead.
In this way we would always represent the base with the first digit that is not used for that base eg.:
base 2 ( = 10 in base 2) -> digits 0,1
base 3 ( = 10 in base 3) -> digits 0,1,2
base 9 ( = 10 in base 9) -> digits 0,1,2,3,4,5,6,7,8
base A ( = 10 in base A) -> digits 0,1,2,3,4,5,6,7,8,9
base B ( = 10 in base B) -> digits 0,1,2,3,4,5,6,7,8,9,A
I've been thinking about this for years, so I hope you all will agree with me on this.
-- Ortonormale 00:47, 2005 May 11 (UTC)
It may be good to remember that the root "deci" means ten and "a" is a letter that is not associated with the base ten number system (why add another thing to confuse people?). Besides, saying "aal" would be more ambiguous than saying "Decimal". It sounds the same as "all"
-Michael
Yes, you would be right. I mean that since the discovery of base conversion, numerals have acquired new meanings while losing the direct link to their etymology. We could say that a new abstract level has been introduced between the original etymological meaning and the new virtual meaning. For example: 11 in base 2 represents the same quantity represented by 3 in base 8. Luckily or unluckily (according to your point of view) we have not a different set of names for each numeral in each base, therefore we have two possibilities:
In this latter case, we could simply say "eleven" to read the numeral 11 in whichever base. The same concept would apply to "ten", "decimal" and "digit".
Obviously, we would have ambiguities when not specifying the actual base, but this already happens when writing.
Nothing really fun so far.
The funny part comes when we want to read numbers like
Again: obviously (as you have noticed) we would have an obstacle to complexity increase trying to use bases that are greater than Z, but this already happens when writing. It is a common problem for non positional numbering systems, but a simple solution consists in grouping. So for example we could use the base 2xG (or simply 2G) in which each digit is represented by a group of 2 digits in base G, like
-- Ortonormale 00:22, 2005 May 19 (UTC)
Wendy.krieger ( talk) 07:03, 5 June 2008 (UTC)
Is there any other theory at all for explaining the decimal system?
From a mathematical point of view, I see no argument that could be made for ten - two (or powers of two) is special, of course, since it's the smallest possible base (powers of two are just a neat way of cramming several binary digits into one handy symbol), three would give you balanced ternary, and I believe you can formalise the fact that 12 has a large number of factors.
Of course, it's possible that there might be a psychological aspect that makes 10 a natural choice, or that it was just an accident of history, but in the absence of support for either of those theories, maybe we should state this a bit more strongly?
RandomP 18:51, 13 May 2006 (UTC)
The article confuses base 10 with positional systems. Someone commented on this above, but was never answered. If there is no discussion here, I'll go ahead and rewrite the article.
Chinese numerals are decimal, even though they're not positional. Likewise, Roman numerals are also decimal, though with a minor auxiliary base in 5. Hebrew gematria are decimal. There are very few written systems which are not decimal—Mayan and Babylonian are the only ones which comes to mind—though of course in spoken languages there are all kinds of bases and base combinations.
Besides decimal numeration, there are decimal fractions. All this requires is extending base 10 to fractional notation, though in practice in the modern world it nearly always implies a positional system. (Roman combined decimal numeration with duodecimal fractions, neither of which were positional.) India did not invent decimal numeration, which is the most common in the world, and AFAIK did not invent decimal fractions either; it invented the positional system and the zero that went along with it. (Mayans had a zero but not a fully positional system, due perhaps to religious considerations.) kwami ( talk) 02:44, 26 February 2009 (UTC)
Our number words go this way. Butterworth (The mathematical brain) notes that this is the most advanced form, since one is less likely to read two thousand and six as 20006 (ie 2000 6).
The lead says:
and someone added
and I thought: Don't be ridiculous... but, thinking a bit more about it, I realized that the most widely used base IN NUMERICAL CALCULATIONS is binary, in the sense that most of the additions, multipliplications, etc. that are performed on any given day are done by computers, not by humans. So while we don't really need a source, we may need a qualification; something like:
... but I don't really like that either. Any good ideas?-- Noe ( talk) 06:48, 21 October 2009 (UTC)
The article claims "decimal fractions were first used ... by Arab mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century". That is incorrect. He was not the 1st person to use it.
According to the Cambridge University in England, decimal fractions were 1st developed and used by the Chinese in the 1st century BC, and then spread to the Middle East and then to Europe.
Source : Science and Civilization in China (Vol. 3) (Published by the Cambridge University Press)
Wikiwikidaddy ( talk) 07:45, 30 October 2009 (UTC)
We have a "list of recorded decimal writers" in this article:
What is the point of this? It is not explained at all. At first, I assumed it was notable developments in the use of the Hindu-Arabic numeral system, but it also includes modern writers who discuss binary and related issues for computing. I think this section should be better motivated, focused and pared down. I've commented out most of the modern authors because I don't think that they belong here. Cheers, — sligocki ( talk) 21:20, 30 October 2009 (UTC)
Simon Stevin's contribution to decimals is generally recognized to be the seminal one, see for example van der Waerden, or the St Andrews pair of articles which clearly relate to Stevin as a watershed. Is it reasonable to have all sorts of multicultural characters mentioned here, and leave out Stevin? Tkuvho ( talk) 15:11, 21 February 2010 (UTC)
Is there actually a specific reason that almost the entire world uses the decimal system, i.e. is there a logically imperative reason for its popularity or is this simply arbitrary? Is there a scientfically valid difference in using another base system? —Preceding unsigned comment added by 217.85.239.236 ( talk • contribs) 19:31, 22 February 2010
The article claims "The modern number system originated in India". That is incorrect.
According to the Cambridge University, the decimal system (together with the digit zero) originated in China. The most conservative estimate for the use of the decimal system dates it to no later than the 14th century BC (although it is known to have been in use long before that).
Source (1) : Science and Civilization in China (Published by the Cambridge University Press)
Source (2) : Genius of China (by Robert Temple) (This book has won numerous major literary awards including ones from the American Library Association and the New York Academy of Sciences, and was translated by UNESCO into 43 different languages ).
Wikiwikidaddy ( talk) 08:42, 30 October 2009 (UTC)
I have some serious issues with the 'Genius of China' by Robert Temple - this is an author who believes that extra-terrestrials had contact with early humans! I would like to see a more in depth discussion of these supposed inscriptions from the 14/13th century BC!
by al-Uqlidisi, with a Latin tranlation of Musa al-Khwrizmi of 825, with works by Kushyar ibn Labban, and founnd that in these early islam mathematic works, the method of division using Hindu-Arabic numerals is indentical to the Chinese rod numeral method described in The Mathematical Classic of Sun Zi, to the finest detail, even the shifting of the numbers of multiplier from left to right by one position, was copied in toto in these early ISlam works. Even the expression of the remainder after division as fraction is identical to Sun Zi.
This is more mind boggling, given that the fact the rod numeral decimal system is a operational system by moving rods on counting board(actually on floor or table top), while the these islam works written more than 400 years after and based on WRITTEN calcuation, shared the exact procedures to the last minutes, some of these operation such as after divsion by one digit, must move the whole set of divisor numbers from left to right one position, which is whole un necessary and and cumbersome in a calculation system based on written symbols, one cannot just simply move the numbers around, like move counting rods on floor, but must involve re writting. Too much conincidence to explain away with independent development. Further, Dr Lam also pointed out the fact the before the advent of 0 in India, Indians used a blank space to represent a zero, which is extremely odd and un natural in a written system; while in rod calculus, a blank space in counting board (read counting table top) is the intrinsic of rod system, for example 3 minus 3 means take away 3 rods from 3 rods, naturally no more rods left on the board and left a blank. The blank in rod numerals in natural, the blank in written symbol is not intrinsic in Hindu Arab system.
Dr Lam believes, that the only logical explanation of these perplexing facts is that the Indian-Arab decimal had its origin in Chinese rod numeral system, which was in used in China much earlier than the earliest Indian record of decimal system. The Indian version was introduced to Islamic world by Musa al-Khwzizmi, the translated into Latin and transmitted to the west.
Propronents of Indian origin must answer the following facts, why an empty space in their early decimal system ? Why translated Indian system as appeared in several Islam works show such striking similarity up to the last minute with Sun Zi'w work ?
It is not difficult to explain the transmission of Chinese rod numeral system (the only methd of calculation used by the Chinese, until the advent of abacus) from China to India. From 266-to 399, there were on record, Zhu Fahu, Kang Falang, Yu falan, Zhu Niafo, Hei Chang, Hui Bian, Zi Faling, Fa Jin, anf Fa Xian travelled to India.
I believe Cambridge University and Rober Temple is right, the decimal system was originated in China, not India -- 70.50.200.249 ( talk) 23:51, 8 April 2010 (UTC).
Joseph Needham, Robert Temple never claimed that the written 0 was invented in China, probably invented in eastern region of India close the southern China culture, or in Cambodia. Chinese carried out complex mathematical calculation with counting rods, they don't need a special 0 symbol, not until 13th century, 0 symbol appeared. It must be emphasiz here, the appearance of written 0 does not implied conceptual invention, as Needham pointed out, the Brahmi numerals which the Hindu- Arab system supposed to derived from, was no improvement from the Greek and Hebrew numeral system.-- 70.50.200.249 ( talk) 00:02, 9 April 2010 (UTC).
There is good answer as to why the Chinese counting rods of the Spring and Autumn period stop at 9, and no more then nine symbols.
Because, the ancient Chinese had "Worship of Nine" culture, stemmed from the Book of Chang. Ancient Chinese classified even numbers such as 1,3,5,7,9 as Yang, and 2,4,6,8 as Ying, 9 being the highest of the Yang number, was considered the supreme number, thus an emperor was called "Nine five supremacy", correspond to the the first Hexagram of I Ching, the "Heaven, Yang, and Male" Hexagram, which, each bar was called a Nine, the fifth bar called a Nine-Five, corresponding to "Flying dragon on the Heaven"-- the emperor. Do you think a court mathematician who held the highest math post in a kingom dared to get ahead of "nine" and higher than the emperor ? Thus the counting rod must stop at nine and no more.
The worship of Nine casted a deep mark on history of Chinese mathematic:
Recently a priority claim for chinese mathematics was added to this page, which seemed to be properly sourced in a publication in a respectable journal (as well as a respectful mathscinet review). The changes were reverted together with some argumentative material. This should probably be discussed here. My own feeling is that both indian contribution and the chinese contribution should be discussed, preferably avoiding dramatic priority claims, but this also shouuld be discussed. Tkuvho ( talk) 12:05, 8 April 2010 (UTC)
1) the title of this article is Decimal, not "positional decimal" 2) Positional decimal is a subset of decimal, in China, non positional decimal appeared first, than evolved into positional. The counting rod was positional from the start. 3) To full understanding how non positional decimal evolved into positional decimal, one must examine the step by step history, it is no use just pointing to a piece of artifact and declared it to be a smoking gun evidence. -- Gisling ( talk) 02:22, 12 April 2010 (UTC).
parallel lines of decimal, written Chinese decimal was not decimal, counting rod is. A good analogy is our daily written numeral is not binary, but the computer we us is. Counting rod was the computer of ancient China, neglect this is a big mistake. Put it in other words, the
Chinese used positional decimal computing device a millenium before any other civiliztion --- Gisling ( talk) 02:22, 12 April 2010 (UTC)
Gisling wrote: "Your classificaion of Wu, Shen, Li as "offical Chinese line" will be a laughing stock for international scholars on history of Chinese mathematics." I did not classify either of them as "official chinese line". When speaking of the "official chinese line", I was referring to reliance on the great chinese encyclopedia, whose objectivity I think is questionable. Work by Wu, Shen, and Li published in reliable western periodicals would be just as welcome as work of Lam Lay Yong. A critical attitude toward the chinese encyclopedia does not bring politics into the discussion, as you suggest. On the contrary, such a critical attitude is an effort to keep politics out of the discussion. We all know who made a laughing stock of themselves in pursuing chinese priority for the proof of the Poincare conjecture. What is not sufficiently realized is that, were it not for the efforts of single individuals such as Sylvia Nasar, the Poincare conjecture page would currently present a 450 explanation of how the chinese proved it. I appreciate your willingness to rely on western sources in documenting decimals and positional decimals. Given that distinguished scholars such as Joseph Dauben worked in the history of chinese mathematics, this should not prove an impossible task, and I appreciate your putting in the time. Tkuvho ( talk) 07:46, 12 April 2010 (UTC)
The current series of edits by Gisling started by quoting a paper by Lam Lay Yong, in a reputable western journal "Archive for History of Exact Sciences". Since then, Gisling's additions have been dominated by the official chinese line. Thus, the typical "Footnote 6" currently states: "This view was adopted by the editorial board headed by Wu wen Tsun of Chinese Academy of Science for The Grand Series of History of Chinese Mathematics" (the editor appears under Wu Wenjun). Now the official chinese line may not be consistent with Western scholarship, any more than the Great Soviet Encyclopedia on the issue of priority of invention of non-Euclidean geometry. I would suggest moving all material not sourced in Western sources, to the talkpage for discission. Tkuvho ( talk) 11:45, 11 April 2010 (UTC)
Wu Wenjun, Shen Kangshen, Li Di are all well respected historians in Chinese mathematics, ASAIK, none them are communists, where comes this label "Chinese lines ", just is is unreasonable to label books by Cambridge U as "Capitalisism line, imperialist line" .Shen Kangshen published book with Cambridge University Press, the historian of math is a small world, Jean Claude Martzloff, K Chemla, U. Libbrecht, Lam Lay Yong met in international conferences in China and abroad every year,every one knows other one's work, and Martzloff, Librecht, all has Chinese name, in short, they are like a family. Your classificaion of Wu, Shen, Li as "offical Chinese line" will be a laughing stock for international scholars on history of Chinese mathematics.
I absolutely oppose Western Central Point of View, "western scholarship" is pure prejudice.
Once politics enters wikipedia, it will be doomed -- Gisling ( talk) 01:59, 12 April 2010 (UTC).
In considering the fact that most reader of the en.wikipedia do not read Chinese, I shall try my best to replace a part of the Chinese references with English reference, just for the convenience of readers of en.wiki, not a matter of principle-- Gisling ( talk) 04:06, 12 April 2010 (UTC).
I have move most materials from Chinese language sources to talk page, leaving only one citation on archeological evidences. Now in this paragraph, the citations are mostly from English literatures by Joseph Needham, Robert Temple, Lam Lay Yong and Yoshio Mikami-- Gisling ( talk) 10:42, 12 April 2010 (UTC).
Suan shu shu. A book on numbers and computations. Translated from the Chinese and with commentary by Joseph W. Dauben. Arch. Hist. Exact Sci. 62 (2008), no. 2, 91--178.
In this article "The modern numeral system format, known as the Hindu-Arabic numeral system, originated in Indian mathematics[15] by the 9th century."
but in Hindu–Arabic numeral system
"The development of the positional decimal system takes its origins in Indian mathematics during the Gupta period. Around 500 CE the astronomer Aryabhata uses the word kha ("emptiness") to mark "zero" in tabular arrangements of digits. "
"The earliest surviving evidence of decimal place value numerals in India and southeast Asia is from the middle of the first millennium CE.[52] A copper plate from Gujarat, India mentions the date 595 CE, written in a decimal place value notation, although there is some doubt as to the authenticity of the plate.[52] Decimal numerals recording the years 683 CE have also been found in stone inscriptions in Indonesia and Cambodia, where Indian cultural influence was substantial.[52]"
any one who knows more about Indian mathematics, please fix this inconsistency. Please provide more concrete evidence, such as how the ancient Indians carried out calculation ? On paper ? with abacus etc etc, dates ?-- Gisling ( talk) 13:18, 12 April 2010 (UTC).
This book gives detailed number systems, with plenty of examples of digits from various epochs.
The previous decimal system in places like china, is that of number exponent pairs, eg 9 C 2 X 5 for 925 (ie 9 hundred 2 ten 5). Since the chinese use characters as words, this could as equally be the written form.
The forms given for india, show large variations in the digits 1-9, but 0 is consistantly shown in two forms: as an open circle, and as a point like a modern bullet-point. This suggests that 0 was borrowed into Indian culture. The chinese form is an open circle, but this is entirely uncharacteristic of the caligraphy of the time, suggests that China borrows it from the Indians.
For the Arabs, that the entire alphabet was reworked from traditional Semetic order to a form more accomidating of the greek alphabet, largely to allow the greek numbers to be used without modification. The order of borrowing is to use greek letters as numbers, then arabic numbers, then hindoo numbers.
The suggested migration is then from the Muslims to the Indians to the Chinese.
The greeks already had iota representing both 10, and in a different system, 0. This system existed around C4 (ie late 300's). This is what i consider to be the source of the modern decimal system.
One notes with Butterworth (The mathematical brain), that the use of number + weight (eg 9c2x5) is less prone to give errors, and a more advanced system than long digit strings (eg 925). One particular error avoided is writing '1008' for 108, or 1c8, in the sense of 1 00 (hundred) and 8 ie 1008. -- Wendy.krieger ( talk) 07:42, 13 April 2010 (UTC)
I've just removed the following reference from this page:
If you look at the date, it was clearly written as a term paper when that author was an undergraduate.
Just to clarify that. I meant Chinese shí (=10), of course, in my edit summary. Gun Powder Ma ( talk) 22:01, 21 April 2010 (UTC)
Gun Powder Ma ( talk · contribs) has been reinserting material which I consider inappropriate into the article. Although he/she was the first to Boldly insert the material, I'm willing to be the first to discuss it. My specific concerns on the latest reinsertion:
A former French school teacher, in order to answer pupil's question, determined to become Indiana Jones of math, wrote a popular book on numbers.-- Gisling ( talk) 08:07, 1 May 2010 (UTC).
“Historians of mathematics in particular have voiced strong reservations about Ifrah’s pronouncements on the history of number systems... In 1995 a group of five experts in France agreed it was necessary to confront the popularity Ifrah’s work was being accorded and to point out explicitly his numerous misreadings, misinterpretations, and pure fabrications....Lévy explains that he and his colleagues felt an obligation to “rectify [Ifrah’s] deceptive, confused,even muddle-headed views.” They felt compelled to do so he says because of Ifrah’s relentless habit of presenting conclusions that are “often debatable,generally weak, and at times wholly imaginary,”as if they were “historically valid theses”
Dauben review of Ifrah' book]-- Gisling ( talk) 10:43, 1 May 2010 (UTC).
statements of supported by references than it should be considered reliable, otherwise, should be deemed his "orginal research" and used with caution. -- Gisling ( talk) 13:12, 1 May 2010 (UTC).
A lot of statements in Ifrah's book were stated without reference. This makes citing his book as reference problematic. For example the statement about|pañchabhyah khalu shûnyebhyah param dve sapta châmbaram ekam trîni cha rûpam cha" has no reference. A search with google leads to Ifrah only, looks like his own opinion, but then, is he an ancient Indian language expert ? How reliable is his statement ?, Given the fact that he stated that eka,pitamaha,adi,tanu……all meant "one" ,dvi,ashvin,Yama, yamala, netra,bahu,guophau, paksha all meant "two"...|nava,anka,graha,chhidra meant nine, shunya,binda,kha,ambraha...meant zero . All these makes people confuse.
-- Gisling ( talk) 01:01, 5 May 2010 (UTC).
Imagine someone with two digits on each hand developing their own numerical system. This system goes 1, 2, 3, 10, 11, so on and so forth... Now imagine one of us were to meet this person in a neutral location. We observe that there is a cluster of rocks on the ground. We count all of the rocks using the fingers (excluding our thumb) on one of our hands. This special someone counts the rocks using their numerical system. They conclude that there are 10 rocks in this cluster. You of course make note of this fact and exclaim that this person must be using base 4, and express your preferred usage of base 10. They are confused, because they are using base 10, and base 4 doesn't make sense to them. All articles on Wikipedia regarding numerical systems must therefore make note of the fact that the naming system for any base is itself based upon base 10. 98.218.122.127 ( talk) 11:19, 23 May 2010 (UTC)
The following reference "Azar, Beth (1999). "English words may hinder math skills development". American Psychology Association Monitor 30 (4). http://www.apa.org/monitor/apr99/english.html." links to an empty page. I did not edit the article but I thought you should be aware. Also, why isn't there more mention in the lead for this article about a connection (or lack of connection) between the assumption that our pre-homosapien/homosapien species having ten fingers was THE decider for base 10 being what we use everywhere today, maybe even coded in our genes (if there was a gene that made the understanding of base 10 easier, and also if an understanding of base 10 has been natural selection factor for long enough)? Unsigned intentionally. —Preceding unsigned comment added by 211.29.174.138 ( talk) 17:29, 31 August 2010 (UTC) (Autosigned by SineBot)
The introduction indicates that mathematics education uses the word "decimal" to refer specifically to a decimal fraction as described later. This indicates that teachers and students do not use the word "decimal" for irrational numbers or numbers with infinitely repeating decimal expansions. This is ludicrous. Most students and teachers use the word "decimal" to discuss numbers that are not integers, refusing to acknowledge the integers as decimals. If no objections, I will edit the article to read, “In some contexts, especially mathematics education, the term decimal can refer specifically non-integer numbers. In such a case, the number 1.234234234... is called a decimal while the number 1234 is not. ” I'm not too happy with the example, but it is certainly better than the rubbish that was there before. Clifsportland ( talk) 18:59, 26 August 2010 (UTC)
I've made two changes. First, there was a statement that "It is the most widely used numeral system, perhaps because a human usually has four
fingers and a thumb on each hand, giving a total of ten digits on both hands." The proper preposition is "over", not "on". "On" creates an ambiguity as to whether it means that each hand has a total of 10 fingers, or together have 10 fingers.
Also, there was a statement that + means plus and - means minus. When it comes to sign, that is WRONG. The signs are positive and negative, not plus and minus.
Decimal is the number system humans use because of the fact that we have ten fingers.
I heard that some cultures prefered to use the hexadecimal system because they didn't count their fingers on their hands. But instead, they counted with one hand using one thumb to touch on the finger tips and the bends at their finger joints. (There are 16 points on each human hand, hence a hexidecimal system.) However, the decimal system became so wide spread internationally that it dominates now.
I heard about this over twenty years ago from my high school teacher. I don't know his source of this information. I am wondering if any wikipedians out there can confirm this.
If the counting finger-joints technique were more prevailing than counting fingers, human society could have adopted the hexadecimal system which is much better compatible with binary computers nowadays.
The ancient Mayan civilization used base 20 in their numbering system. Their numeric symbols denote values from 0 to 19. (source: http://www.eecis.udel.edu/~mills/maya.htm)
Avoid fallacies in arguments. Just because the people that use decimal do so because they have 10 fingers doesn't mean that all humans use decimal. Nor does it invalidate any of these base 16 or base 20 systems. The article should point out that not all people use decimal (and I will edit it). -- drj
I don't think there are any societies that used base 16 though. The highschool teachers story seems suspect. Base 20 is of course fingers and toes. But where does base 12 come from? --AxelBoldt
12 presumably comes from months of the year. Many calendars have 12 months in a year (not just because it is nearly the number of lunar months in a year). Imagine you are an early geek into factors and astronomy. Observe: 360 days in a year, aha! that factorises easily with nice factors like 12, 60, 24, etc. The base 16 claim seems very dubious to me. Fingers and toes didn't occur to me though it is plausible. -- drj.
I think the 12, 24, 60 business came from the Babylonians/Persians? Somewhere that direction and long before Greece. --rmhermen I said "geek" not "greek"! Bablylonians/Mesopotamia is the generally agreed source I believe. -- drj
The babylonian number system was base 60 according to Math historian, David M. Burton. He suprisigingly doesn't have a wikipedia page. Clifsportland ( talk) 18:59, 26 August 2010 (UTC)
Are roman numerals a number system? What is the base?
So perhaps the article on number systems should mention it?
In the US weighing system, one pound = 16 ounces. In Chinese weighing system, one catty = 16 taels. Though they are not number systems, but at least it give some hints why the number 16 is involved in measurements universally. In any systems that use division, any power of 2 is a good candidate for convenience sake. For example, a gallon = 4 quarts = 8 pints = 128 fluid ounces = 1024 fluid drams etc.
Looks like human are attracted to the power of 2 and astronmonical periods and our fingers and toes.
A old British pound = 20 shillings
one old shilling = 12 pences
20 and 12 can still be explained, but 1 mile = 1760 yards??? how did they come up with that number?
Have you heard the story about how the butt size of the Roman horses decided the rail guage in the current US railroad system?
In decimal counting, the Fibonacci numbers repeat the sequence of the last digit over a period of 60. Every other numeral system with base less than 14, repeats in less than half of this (often 24).
Base Period of last digit of Fibonnacci Numbers 2 3 3 8 4 6 5 20 6 24 (last two digits too) 7 16 8 12 9 24 10 60 (unusually big) 11 10 12 24 (last two digits too) 13 28 14 48
I realize I am jumping to this without most of your comments. The statement is slightly misleading. I won't change it until I think of a way of wording the correction. It just happens that everybody uses arabic numbers when they write english so it is easier to convert all numbers to that system which happens to based on base 10. For example you could use base 60 for time, but the symbols are not universally recognized and you can easily flip from base ten to base 60 when talking about seconds and minutes. I am certain there are languages that use another base or consider it significant. Look at binary. Still base 10 is huge compared to it. Tempust ( talk) 05:28, 24 February 2010 (UTC)
This article does not make it clear whether it is about the decimal aspect of the current world system, or the positional aspect. It says that our system is the one of two decimal positional systems. But then it compares non decimal systems to the system only discussing their base. What is truly needed is a grid of articlesh that looks like this, having an introductary article for decimal systems, binary systems, dodecimal, binary, vigesimal and sexigesimal systems, as well as an introduction for each of the ways of denoting the powers, positional, different symbols.. &c. However, as a start, the following might make sense:
an article on systems that use a different symbol to show how many, but use positions for powers -can be based on this article after a title change, and moving some stuff around -will also contain mention of common binary notation, and its dervitives (hex &c) -will also discuss all the different notations for the decimal system of this type, arab, western, gujarati, &c -base sixty fractions
an article about systems that have a different symbol for each amount in each order such as greek, hebrew, older arabic one -(abjad systems???)
an article about systems that have a different symbol for each power of the base, but write it multiple times in order to show amount -decimal ones: Roman, Egyptian, that other greek one that looks like hang man -sexigesimal ones: Sumerian, babylonian
an article about systems that use positions to show order and use accumalation of the symbols to show amound -sexigesimal: later babylonian -vigesimal: maya (the above two both use alternating symbol sets for the two factors of their base, so are not really pure)
Once this framework is done, there are probably lots of main articles that can be pointed to. —Preceding unsigned comment added by Alexwebjitsu ( talk • contribs) 03:43, 18 February 2008 (UTC)
Decimals (decimal place) - see wikitonary
Decimals also refer to decimal fractions, either separately or in contrast to vulgar fractions. In this context, a decimal is a tenth part, and decimals become a series of nested tenths. There was a notation in use like 'tenth-metre', meaning the tenth decimal of the metre, currently an Angstrom. The contrast here is between decimals and vulgar fractions, and decimal divisions and other divisions of measures, like the inch. It is possible to follow a decimal expansion with a vulgar fraction, this is done with the recent divisions of the troy ounce, which has three places of decimals, followed by a trinary place.
The use of ordinals to designate repeated fractions is seen in sexigesimal (second and third minutes, Newton goes as far as vi and vii), decimal (see, eg tenth-metre), duodecimal. Just as counting up is remainders by division by 10, so is fractions made by multiples of 10 and 'carry'. A method to convert this to another base is to carry out exactly this equation, eg the duodecimal of 0.14 becomes (by multiplying the fractions by 12) 1.68, 8.16, 1.92, 11.04, ... the integer parts become the duodecimal fractions: 0.1 8 1 11 .... -- Wendy.krieger ( talk) 08:14, 25 December 2010 (UTC)
I tidied up some fiddly mechanical bits in the first half of the article, but I had to leave the "History" section alone. This section has a great many issues; I think it needs to be extensively rewritten, but I lack the background knowledge (Chinese history, counting rods, abaci) to do so myself. Any thoughts? -- Majestic-chimp ( talk) 23:40, 31 December 2010 (UTC)
A good measure of the talk seems to be given over to discussing the nature of zero in modern usage, and the origin of the modern digital number system. This has nothing to do with decimal.
Zero, in its modern use, was used by the mayans in base 20. The Sumerian fraction system, used zero in leading and medial positions, eg 0 0 1 = 1 second, and 1 0 6 for 1h 6s, but not trailing positions (1 0 and 1 are identical to one). However, one can use a decimal system without using a zero, just as one can use such without a decimal point.
The modern western digits are indeed of indian origin, the etymology of zero (from 'sunna = empty'), suggests this too. The arabs were the ones that the Europeans borrowed it from, and the Chinese seemed to have borrowed the European scheme, making their traditional runes similar to names for these numbers, eg 'five ty six' but '56'.
Of course, 'base 10' is not the only historically relative base: one has many examples of 'base 100', that is, alternation of the base number over two places (ie 6-10 or 4-10 or 8-10 or 2-10 or 4-5 etc), by having the units row and the tens-row at different values. Even the examples of the chinese stick-numbers are 2-5, reflect the abacus they inherited from the romans.
And in this sense, "decimal" is not a particular creation that is carried from place to place, but something that arises freely in different places. Suggesting otherwise is to suggest the mayans and the celts (with histories of base 20), derive from a common pan-atlantic source, such as atlantis.
-- Wendy.krieger ( talk) 07:46, 25 May 2010 (UTC)
The 2nd last sentence in the 1st paragraph of section "History of the Hindu-Arabic numeral system" is misleading given that the section directly above already puts in serious doubt such claim.
If no-one objects, I will change the wording to remove the ambiguity. The change proposed is as follows:
Original : "On this theory, the ideas were then transmitted..."
Clarified sentence : "According to those who are willing to accept Georges Ifrah's claim despite the seemingly contradictory evidence suggested in the section above, the ideas are believed to have been later transmitted ..."
This change should reduce the disjointed feel of the article. Marcopolo112233 ( talk) 05:49, 10 January 2011 (UTC)
There have been some recent changes, back and forth, regarding the wording of the section on Notation. The question seems to be whether the choice of comma or period is dependent upon language or geography/politics. Before we continue to change the article, we should discuss this point and come as close to a consensus as possible. Additionally, any changes should be supported by a reference. My understanding was that the use of a comma does not depend upon language, but rather geography. I thought that the UK used a comma when doing their “maths”. The US definitely uses a period. Clifsportland ( talk) 20:48, 10 January 2011 (UTC)
The reference to the floor function after mentioning the integral portion of a decimal fraction may be very misleading. For instance truncate(-1.3)=-1, which is NOT equal to floor(-1.3)=-2. This is a common error. Even if that was not the intention of the article, it may still obscure rather than elucidate. — Preceding unsigned comment added by Nielsed ( talk • contribs) 17:48, 12 March 2011 (UTC)
Regarding this section, the sentence directly before the common fraction list reads "The decimal fractions are those with a denominator whose only prime factors are 2 and/or 5" (bold added). That is followed by a list of common fractions whose denominator is prime factored by only 2 & 5, until the list item that reads "1/3 =", which fails that particular pattern, as does what follows it. Is this (see Table 4-1) what is meant? Is the list meant to be misleading? Gzuufy ( talk) 19:19, 8 May 2011 (UTC)
Recently there are multiple attempts at disruption without going thru discussion. Sucth disruption is contrary to wiki's policy, should be banned -- Gisling ( talk) 00:18, 23 June 2011 (UTC).
The 1st sentence of the 1st paragraph of section "Possible Chinese origin of Hindu–Arabic numeral system" starts with the statement "It has been suggested that ...".
The rule of Wikipaedia is that if you cannot provide a source for a claim, you should not state the claim. Given that is the case, either the entire 1st sentence should be removed or if it is accepted, then the qualifier statement "It has been suggested" should not be necessary.
If no-one objects, I will remove that qualifier statement from the sentence. Marcopolo112233 ( talk) 06:10, 10 January 2011 (UTC)
"I thought it was a question of the source being reliable" is false and without any merit. The author Lam Lay Yong was an associate editor of Historia Mathematica and a member of Académie Internationale d'Histoire des Sciences. She also won the higest award in History of Mathematics, how dare you said "unreliable"---00:36, 23 June 2011 (UTC)
I am the opion that positional decimal system IS a subset of decimal system, it is also the dorminat decimal system in the world to day. It is far more imporatant than general decimal, hence need to be address separately. It is strange that en.wiki does not have article on this imporant topic.--- Gisling ( talk) 09:13, 23 June 2011 (UTC).
The comment(s) below were originally left at Talk:Decimal/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
History could be in prose. Salix alba ( talk) 19:14, 29 September 2006 (UTC) Needs longer lead and more references. Geometry guy 20:51, 9 June 2007 (UTC) |
Last edited at 20:51, 9 June 2007 (UTC). Substituted at 20:22, 2 May 2016 (UTC)