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I have addressed certain issues by creating the article Non-standard positional numeral systems, and making related changes to Unary numeral system, Golden ratio base, Quater-imaginary base, Positional notation, Base (mathematics), and Category:Positional numeral systems. I suggest further discussion of these issues takes place here.-- Niels Ø 14:44, 26 February 2006 (UTC)
I have now made related changes to Negabinary, Negaternary, Mixed radix and Bijective numeration as well. I'm not quite happy with the development at the category page category:Positional numeral systems - can someone help me with the cat sorting tags used for the non-standard systems? They should appear separate from the standard ones, perhaps in this order:
-- Niels Ø 21:04, 26 February 2006 (UTC)
The first paragraph is erroneous and the article needs some Wikification. As the article positional notation indicates, a positional notation system does not contain a base number of glyphs. For example, the sexagesimal system does not contain 60 glyphs—the number varies from two glyphs in Babylonia to fifteen in the Greek form (there are ten in the modern form). But this article is not about standard systems, so I'm not sure whether to correct it or delete it. Wikipedia requires the article title to appear in bold as close to the beginning of the article as possible. You only have This article. This means that the first paragraph should introduce non-standard systems, it should not discuss standard systems first, maybe later. — Joe Kress 05:57, 27 February 2006 (UTC)
Two possibilities, "representations" or "positions", neither of which sound good. An alternative would be to classify the sexagesimal system itself as a non-standard system because it does not use sixty glyphs. Unfortunately, that opens up a Pandora's box because the vigesimal system used by MesoAmerican peoples does not use twenty symbols, rather it uses three: a shell for zero, a dot for one, and a bar for five. I note that the vigesimal article has the same error as this article, assuming that it has twenty glyphs, or at least it only mentions modern respresentations. The title of this article itself is unfortunate. I suspect that whoever invented the term "non-standard positional numeral systems" was only thinking of the decimal, hexagesimal, and other computer systems. It would be quite odd to include both sexagesimal and vigesimal as non-standard when both were invented long before the decimal system. That makes the decimal system itself non-standard because it is so recent. Maybe exclude "classic" numeral systems? Or maybe call these "invented positional numeral systems"? — Joe Kress 19:33, 24 March 2006 (UTC)
It also appears that there's a problem with the claim that with just numerals, a radix, and the minus sign, all reals can be represented. It doesn't appear to me that any real that's not also a rational can be represented with just those three things, in order to represent a non-rational real, you'd need more symbols. And not even all rationals can be represented, those with repeating digits need a symbol to indicate that they're repeating. — Preceding unsigned comment added by 157.166.167.129 ( talk) 12:54, 28 June 2018 (UTC)
I'm quite happy with the improvements made by others to "my" article. There is an issue bothering me, relevant to many of the articles on numeral systems: Some have a focus on the abstract mathematical idea of various numeral systems, and others focus on the cultural history of numeral systems. Many mix these two subject areas, and a clearer distinction between them would improve many of the articles. I don't really see how to do it, though. Quoting Joe Kress above, "the sexagesimal system does not contain 60 glyphs—the number varies from two glyphs in Babylonia to fifteen in the Greek form (there are ten in the modern form)." Now, that's cultural history; in the mathematical ideal sexagesimal system, there definitely are sixty somethings, that now are called numerals instead of glyphs in the article. The word glyph that I originally used was a bad choice, as it puts focus on the physical manifestation, and hence on the cultural history, and not on the mathematical idea I intended.-- Niels Ø 09:18, 25 March 2006 (UTC)
As the originator of this article, I must confess the title was a neologism. However,
Still I wonder, have I sinned here?-- Niels Ø (noe) 13:14, 13 June 2007 (UTC)
There's an interwiki link to ja:広義の記数法 - I've no idea what that article is saying, but it clearly has material we don't have.-- Niels Ø (noe) ( talk) 17:02, 6 December 2007 (UTC)
The Gray code does not currently appear in this article, or in the associated category. Should it do so?-- Noe ( talk) 19:54, 8 August 2008 (UTC)
I've just removed a general citations-needed-tag from the article - I don't think it is relevant.
The article is little more than a brief summary of and pointer to uncontroversial information found in other wikipedia articles; if they lack sources, they should be flagged. (To my knowledge, the only thing that some editors feel is controversial is the inclusion of Unary as a Positional system - but I think that is dealt with in a satisfactory way in the article.)
And if anything in particular in this article lacks sources, that should be flagged.
As can be gathered from the posts above, the title of this article is a neologism, or (as I prefer to see it) a description of something that it was convenient to collect in one place as a separate wikipedia article. Perhaps that idea is challenged by the editor asking for sources for the concept "Non-standard positional numeral systems". Such sources do not exist! (Actually they do now - but only in the multitudes of wiki mirrors and in a few scientific articles that also have picked it up from us.)
Think of this article as similar to the many articles called "List of (blah blah)"!-- Nø ( talk) 13:30, 28 June 2010 (UTC)
Are there positional number systems where the least significant digits are on the left? Like decimal number written in reverse. — Preceding unsigned comment added by 195.113.21.109 ( talk) 10:55, 24 October 2012 (UTC)
If "x may be a y", it is implied the x may also not be a y. To say that "x may be denoted a y" adds nothing. Bhny ( talk) 05:31, 28 February 2013 (UTC)
Alternative suggestion:
What do you think?-- Nø ( talk) 10:19, 13 April 2013 (UTC)
In Frederik Pohl's 1984 novel Starbust, one of the characters has to transmit a vast amount of information across space, and uses a process she calls " Gödelization": After encoding the information into an integer, she somehow reduces the integer to a short summation of integer powers (e.g. 11^4+31^3+43^17). This is somewhat different from Gödel numbering and I wonder if it's really something Gödel descrbed. But it seems to be a candidate to put in this article.
There are 4 Wikipedia articles that use the term " Gödelization" in passing : Counter machine, Register machine, Turing's proof, and Algorithm characterizations
Casu Marzu ( talk) 18:53, 31 October 2013 (UTC)
There are no article or information about numeration systems for real (or more general sets) which do not require the use of a radix point symbol. That's important because the radix point is an underutilized symbol, since it can appear only once, so it is wasteful from a coding efficiency perspective. — Preceding unsigned comment added by 181.20.129.191 ( talk) 02:51, 28 February 2015 (UTC)
The category with the same name as this article includes the articles
that are not currently linked in the article. I haven't checked each to see if it makes sense to include them - but it would be woth looking into.-- Nø ( talk) 11:56, 3 November 2016 (UTC)
A subsection on "Asymmetric numeral systems" has been added by an IP user to the section "Bases that are not positive integers". But as far as I can tell, asymmetric numeral systems do not have a single well-defined base, so I think it belongs as a separate section following "Mixed bases" (or perhaps as a subsection of "Mixed bases"). But I do not understand asymmetric numeral systems well enough to be sure.-- Nø ( talk) 09:23, 31 January 2020 (UTC)
I am someone who isn't completely stupid about math, and this article is too technical for most people. I added the template at the top to help with the cleanup.
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
I have addressed certain issues by creating the article Non-standard positional numeral systems, and making related changes to Unary numeral system, Golden ratio base, Quater-imaginary base, Positional notation, Base (mathematics), and Category:Positional numeral systems. I suggest further discussion of these issues takes place here.-- Niels Ø 14:44, 26 February 2006 (UTC)
I have now made related changes to Negabinary, Negaternary, Mixed radix and Bijective numeration as well. I'm not quite happy with the development at the category page category:Positional numeral systems - can someone help me with the cat sorting tags used for the non-standard systems? They should appear separate from the standard ones, perhaps in this order:
-- Niels Ø 21:04, 26 February 2006 (UTC)
The first paragraph is erroneous and the article needs some Wikification. As the article positional notation indicates, a positional notation system does not contain a base number of glyphs. For example, the sexagesimal system does not contain 60 glyphs—the number varies from two glyphs in Babylonia to fifteen in the Greek form (there are ten in the modern form). But this article is not about standard systems, so I'm not sure whether to correct it or delete it. Wikipedia requires the article title to appear in bold as close to the beginning of the article as possible. You only have This article. This means that the first paragraph should introduce non-standard systems, it should not discuss standard systems first, maybe later. — Joe Kress 05:57, 27 February 2006 (UTC)
Two possibilities, "representations" or "positions", neither of which sound good. An alternative would be to classify the sexagesimal system itself as a non-standard system because it does not use sixty glyphs. Unfortunately, that opens up a Pandora's box because the vigesimal system used by MesoAmerican peoples does not use twenty symbols, rather it uses three: a shell for zero, a dot for one, and a bar for five. I note that the vigesimal article has the same error as this article, assuming that it has twenty glyphs, or at least it only mentions modern respresentations. The title of this article itself is unfortunate. I suspect that whoever invented the term "non-standard positional numeral systems" was only thinking of the decimal, hexagesimal, and other computer systems. It would be quite odd to include both sexagesimal and vigesimal as non-standard when both were invented long before the decimal system. That makes the decimal system itself non-standard because it is so recent. Maybe exclude "classic" numeral systems? Or maybe call these "invented positional numeral systems"? — Joe Kress 19:33, 24 March 2006 (UTC)
It also appears that there's a problem with the claim that with just numerals, a radix, and the minus sign, all reals can be represented. It doesn't appear to me that any real that's not also a rational can be represented with just those three things, in order to represent a non-rational real, you'd need more symbols. And not even all rationals can be represented, those with repeating digits need a symbol to indicate that they're repeating. — Preceding unsigned comment added by 157.166.167.129 ( talk) 12:54, 28 June 2018 (UTC)
I'm quite happy with the improvements made by others to "my" article. There is an issue bothering me, relevant to many of the articles on numeral systems: Some have a focus on the abstract mathematical idea of various numeral systems, and others focus on the cultural history of numeral systems. Many mix these two subject areas, and a clearer distinction between them would improve many of the articles. I don't really see how to do it, though. Quoting Joe Kress above, "the sexagesimal system does not contain 60 glyphs—the number varies from two glyphs in Babylonia to fifteen in the Greek form (there are ten in the modern form)." Now, that's cultural history; in the mathematical ideal sexagesimal system, there definitely are sixty somethings, that now are called numerals instead of glyphs in the article. The word glyph that I originally used was a bad choice, as it puts focus on the physical manifestation, and hence on the cultural history, and not on the mathematical idea I intended.-- Niels Ø 09:18, 25 March 2006 (UTC)
As the originator of this article, I must confess the title was a neologism. However,
Still I wonder, have I sinned here?-- Niels Ø (noe) 13:14, 13 June 2007 (UTC)
There's an interwiki link to ja:広義の記数法 - I've no idea what that article is saying, but it clearly has material we don't have.-- Niels Ø (noe) ( talk) 17:02, 6 December 2007 (UTC)
The Gray code does not currently appear in this article, or in the associated category. Should it do so?-- Noe ( talk) 19:54, 8 August 2008 (UTC)
I've just removed a general citations-needed-tag from the article - I don't think it is relevant.
The article is little more than a brief summary of and pointer to uncontroversial information found in other wikipedia articles; if they lack sources, they should be flagged. (To my knowledge, the only thing that some editors feel is controversial is the inclusion of Unary as a Positional system - but I think that is dealt with in a satisfactory way in the article.)
And if anything in particular in this article lacks sources, that should be flagged.
As can be gathered from the posts above, the title of this article is a neologism, or (as I prefer to see it) a description of something that it was convenient to collect in one place as a separate wikipedia article. Perhaps that idea is challenged by the editor asking for sources for the concept "Non-standard positional numeral systems". Such sources do not exist! (Actually they do now - but only in the multitudes of wiki mirrors and in a few scientific articles that also have picked it up from us.)
Think of this article as similar to the many articles called "List of (blah blah)"!-- Nø ( talk) 13:30, 28 June 2010 (UTC)
Are there positional number systems where the least significant digits are on the left? Like decimal number written in reverse. — Preceding unsigned comment added by 195.113.21.109 ( talk) 10:55, 24 October 2012 (UTC)
If "x may be a y", it is implied the x may also not be a y. To say that "x may be denoted a y" adds nothing. Bhny ( talk) 05:31, 28 February 2013 (UTC)
Alternative suggestion:
What do you think?-- Nø ( talk) 10:19, 13 April 2013 (UTC)
In Frederik Pohl's 1984 novel Starbust, one of the characters has to transmit a vast amount of information across space, and uses a process she calls " Gödelization": After encoding the information into an integer, she somehow reduces the integer to a short summation of integer powers (e.g. 11^4+31^3+43^17). This is somewhat different from Gödel numbering and I wonder if it's really something Gödel descrbed. But it seems to be a candidate to put in this article.
There are 4 Wikipedia articles that use the term " Gödelization" in passing : Counter machine, Register machine, Turing's proof, and Algorithm characterizations
Casu Marzu ( talk) 18:53, 31 October 2013 (UTC)
There are no article or information about numeration systems for real (or more general sets) which do not require the use of a radix point symbol. That's important because the radix point is an underutilized symbol, since it can appear only once, so it is wasteful from a coding efficiency perspective. — Preceding unsigned comment added by 181.20.129.191 ( talk) 02:51, 28 February 2015 (UTC)
The category with the same name as this article includes the articles
that are not currently linked in the article. I haven't checked each to see if it makes sense to include them - but it would be woth looking into.-- Nø ( talk) 11:56, 3 November 2016 (UTC)
A subsection on "Asymmetric numeral systems" has been added by an IP user to the section "Bases that are not positive integers". But as far as I can tell, asymmetric numeral systems do not have a single well-defined base, so I think it belongs as a separate section following "Mixed bases" (or perhaps as a subsection of "Mixed bases"). But I do not understand asymmetric numeral systems well enough to be sure.-- Nø ( talk) 09:23, 31 January 2020 (UTC)
I am someone who isn't completely stupid about math, and this article is too technical for most people. I added the template at the top to help with the cleanup.