I'm a little unsure about the last paragraph. Do modern theologans and philosophers (it's not really a question of mathematics) have any interest in relating infinity to God? -- Robert Merkel
I think infinity is typically taken to be one of the properties of God. My problem with the last paragraph is that Goedel did not use infinity at all, he defined God as "absolute perfection" and came up with some axioms which establish the existance of an entity which is absolutely perfect. I don't see how that relates to infinity at all. --AxelBoldt
I like the history section, but it looks like it belongs in a different article. I don't think the Arabs used "1001" to mean infinity. Nor did the French with "million", nor Buddha with "10^421", nor the Romans with decies centena milia. The only sentence that might be relevant is the one about infinity being called "zero denominator". Other than that sentence, how about moving the rest to number names? -- LC
I agree. Also, the claim that "infinity has greatly increasd in size over the years" is pretty hilarious. AxelBoldt
Isn't it generally assumed by astonomers and physicists that our universe, forget about any other ones, is not infinite? - Tubby
ok - thats confused me - its hard to imagine a finite universe - this would menan that there is something beyod the universe - to expand into, meaning that that universe would be infinate - or finut wich would then mean that it would carry on going on like that - being infinate????? or am i just being super confused lol -- Infinitive definition 14:20, 4 April 2007 (UTC)
In my opinion the definition at the beginning (the one before the TOC) is severely wrong.
Even if in common use the term infinity is also the one describe there, this is not the precise tecnical (especially in Math) definition.
The definition given is that of unlimited or unbounded not of infinty. Infinity means with no end, a set is infinity if when you count the number of its member you can not arrive at the point you have cont all the member. This definition is consistence with the rest of the article. (Phereps I have to rewrite it in a better way).
An equivalent (but more difficult to understand) definition is that a set is infinite if there exist an its proper parts that is as big as the wole set (where as big as is to be understood in a sense proper to this branch of math)
Also the traslation of the etimologhy is wrong: Infinitum in latin is not without limit but it is without end or not eneded. As a prove of that consider that from the word finitum and fines derived the Italian Fine and French Fin that mean end in English
Neverless the word infinity and infinite are common used in the meanig stated there and also to describe a very big set but finite. Maybe it will be worthly to add a section on this and on the difference on these term.
A tecnical mathematical note to use the terms limited, unlimited (or the equivalent bounded and unbounded) you have to fix the way you do the measure of distance (you have to be in a Metric space). You have not to have this to speak of infinity/infinte AnyFile 18:16, 8 Sep 2004 (UTC)
I believe the points raised on the talk page are now covered. Of course using "infinity" in describing a finite is wrong, but it is a popular mistake that needs to be included, clearly labeled as such. Kyz 10:49, 11 Sep 2004 (UTC)
Since I think the people reading this will know - it was my impression that the symbol for Infinity was the Möbius Band however maybe it's accurate to say that the Möbius Band is a specific case of the lemniscate?
Thanks,
R.
This article seems to be a mushy mix of philosophy, intellectual history, and mathematics, and has a lot of outright errors. Can someone explain if this should be made more mathematical, by clarifying what the purpose of it is?
Historically, "a mushy mix of philosophy, [religion,] and mathematics" is pretty much what people thinking about infinity used to do.
Still, this article is still in need of a lot of attention. I'd suggest starting by ripping out all the parts referring to current mathematics (after Cantor's Absolute Infinite, I think).
In current mathematics, infinity pops up in exactly two places:
So many things are called finite, infinite, or infinity in mathematics that a complete list of the various usages would probably be completely useless (as well as virtually impossible). Just off the top of my head:
I'd be willing to turn these into a separate article if anyone thinks it'd help. I don't, but they're certainly just confusing in an article about infinity. As an analogy, it's a bit like talking about rational numbers in the rationality article. They happen to use the same term, but that's it, as far as their relationship goes. Today, of course, mathematical objects and properties are commonly named after their inventors, which might be the only reason Noetherian rings aren't called finite.
So, to sum things up, let's throw out all the mathematics, redirect people who're just looking for an article about the mathematical term to a separate article (I think that'd be most of them), then get back to writing an article about the philosophical issues.
Prumpf 16:38, 16 Oct 2004 (UTC)
I'm putting this here because I don't see anywhere else to put it. I was in bed sleeping one time when I came out of the sleep state to what I call the vision state or a condition of higher consciousness. In this state I realised I was looking into infinity and not just something similar to looking at a non descript gray sky for example. Definitely unlike any normal vision experinece but just as real or more real. I said to my self "Holy shit I was looking at infinity!"
Hi newbies, if you didn't realise, Wikipedia says that removing swathes of material, especially without permission or discussion beforehand, is wrong. Infinity is supposed to be a general article, so don't delete explanations even if they're covered in independent, separate articles. The coverage before was excellent. If there are mistakes, say so here [or there] and fix them rather than being stupid. lysdexia 03:25, 21 Oct 2004 (UTC)
In the context:
I don't think so. Let's consider Electrical resistance. There are conductors with zero resistance ( Superconductors). Now consider Electrical conductance. They are related by
So the conductance of an object with zero resistance (superconductors!) is infinity. -- Kenny TM~ 11:59, Nov 23, 2004 (UTC)
As a number wouldn't infinity = 9 repeat
I notice the character for infinity (∞) is never actually included in this article, other than in graphics. I was wondering why this was... Perhaps it was simply not known? Well, anyway... does anyone else think the the graphics should be replaced by the character? Oscar Evans December 14th 2004.
I do not like very much the susection Infinity in real analysis. The difference between infinity as a real number (opps ... extended-real) and as a limit is not clear. In my opinion it should be point out that when infinity is a limit you could not treat it as a number. This to avoid that someone could thing that he/she could do ∞ - ∞ = 0 AnyFile 21:30, 30 Jan 2005 (UTC)
1/1=1, 1/0=Infinity, (0/0=1 and Infinity) Please verify? Why are the past, the present and the future is the same time as January 2005, some cluster of stars(many galaxies) we can see by light speed only and after that human mind memory recall in only 0.0001 second, it means infinity light speed can touch by human mind in 0.0001 second too.
I don't know what the rest of the stuff you're saying means, but I'm pretty confident 1/0 is not infinity, since the inverse of infinity is the infinitesimal, while the inverse of 1/0 is simply zero. Citizen Premier 15:54, 10 Jun 2005 (UTC)
You can not divide anything by zero
Try this book called "0". In the apendix it show how if you could divide by zero (which you really can't)that you could prove any thing (it proves that Winston Chirch Hill is a carrot).
Also the reason you can't divide by zero is that X*0 = 0, and 1*0 = 0, and 2*0 = 0, and 3*0 = 0, so X/0 is every number. You might have gotten confused on the Y*X^-1 = Y/X, and here is were you might have made you mistake 0^X =0. That applies to every number execpt 0 (Y*X^-1 = Y/X). Another thing you might have done is that 1/.01= 100, and 1/.001 = 1000 so you might have done as the denominator aproches 0 then the answer will approch infinity. But the lim is 0 so it will never get to 0.
Would you consider interesting to put a note why infinity numbers are called (starting form Cantor) transfinite numbers? AnyFile 10:45, 2 May 2005 (UTC)
I think both of these points (if I'm right about them) could be useful additions to the article. -- Trovatore 01:47, 25 July 2005 (UTC)
Because infinity is not exactly equal to any finite number, and acts differently than any (other) number, many people find it easier to understand explainations that state right up front that "infinity is not a number".
"While zero is a concept and a number, infinity is not a number. Infinity is the name for a concept. Infinity cannot be considered as a number since since it does not follow numbers' properties. "Infinity" is not a number. ... When mathematicians say "x approaches infinity", or write "x→∞", they mean "x grows arbitrarily large. And when they say that the limit of something is 0, they mean that it can go as close to 0 as you want it to, but it may or may not be actually equal to 0."
OK if I use that definition on Infinity and Infinity plus 1 ? If no one comes up with a better suggestion the next time I come by, I'll just stick that definition in the article and watch the reaction.
-- DavidCary 01:58, 12 May 2005 (UTC)
I hate it when people try to claim there is such a thing as "negative infinity". That's the most absurd thing I've ever been taught in school. Like the comment above, infinity is not a number and therefore cannot be negative. You can go approach infinity in a negative direction, but you can't go to "negative infinity". Phew... got that off my chest. -- Lord Voldemort (Dark Mark) 21:26, 22 August 2005 (UTC)
Moved over here for easier discussion... First, please do not try and belittle me. I quite understand both "negative" and "infinity". You don't need to try and be condescending. Secondly, no, you cannot have a "negative mile". A mile is a measure of distance. And you could have negative money since it is a real object. But on second thought, perhaps you cannot have "negative money". You may owe people money, but you cannot posses "negative money". I don't recall ever seeing that term in an economic book or journal. But I digress... I don't care what you label infinity, if prixibeen means the same thing as infinity, you would not be able to have "negative prixibeen". Basically all I am saying is that you may be able to go prixibeen in the negative direction, but how can you label something as "negative" if it is not a number? Can you have "negative democracy", "negative art", "negative file cabinets"? (and I am talking about mathematical "negative", not the generic adjective) I just think it is absurd to call something negative when it cannot be negative. -- Lord Voldemort (Dark Mark) 18:36, 23 August 2005 (UTC)
I asked for help, and you try and belittle me. Oh gee golly, thanks a bunch! I just feel like this whole thing is a crock, and wanted to know if someone could explain it. Hopefully you are not a math teacher, because if you are I would be amazed if your students could learn anything from you. I was asking a serious question. Some people are honestly trying to help. I thank them for their work, although I fear it may be in vain. I may never get the whole "negative infinity" thing, and thanks to responses like yours, I might not want to ask you guys for help again. Thank you to all who tried to help. I guess I was made to live in the real world, and not the world of theoretical mathematics. -- Lord Voldemort (Dark Mark) 18:48, 23 August 2005 (UTC)
Voldemort, I had a very similar argument when being interviewed for an undergraduate university place. I was asked the value of x / sin x at 0. I replied that the limit as you approach 0 is 1, but I insisted that actually at 0 it is undefined, since there is a divide by 0. I have no idea what bearing this has on the existence or not of a minus infinity. -- stochata 16:17, 26 August 2005 (UTC)
A long-ish comment by Nowhither:
Infinity in space, time has alway been an issue in philosophy (
Aristotle,
Zenon, etc), physics, theology, and of course mathematics (starting with
Bolzano,
Cantor).
I can go on to infinity with this remark. However, I would like to point out the view of Wittgenstein. In mathematics, they operate with symbols according to some pre-set rules. There is nothing infinite in this operation, in the symbols, in the grammar, or in the rules. It is just a game, where they try to eliminate contradictions. A claim that there is no infinity has nothing to to with the symbol .
— Igny 18:31, 30 August 2005 (UTC)
I've done some minor cleanup on this section (original author didn't mention extended reals, for example). But wording and organization are still strange, and frankly I question the need for the section at all, given the prominent links to extended real number line elsewhere in the article. What do others think? -- Trovatore 15:17, 15 September 2005 (UTC)
I've removed the link to the "Infinity Society", http://www.infinitysociety.org/index.html . The site is definitely worth a look, though. I like this passage:
He doesn't tell us what the last benefits are. Anyway he does seem a decent sort of person, at least from what you can tell from what he says; I'm just not convinced his site is a correct link for an encyclopedia article on infinity. -- Trovatore 02:32, 23 November 2005 (UTC)
Assuming that when we write we mean the remainder (there are other meaning of the symbol mod) then is undefined.
The statement " in undefined" is not true.
First we never define if is negative so we should only look at .
I claim we can consistantly define
Mungbean 12:05, 25 November 2005 (UTC)
etc Mungbean 12:02, 30 November 2005 (UTC)
I have reverted this claim:
The notion of "number" in mathematics is not sufficiently well-defined to say whether infinity is or is not a number. In the extended real numbers there are explicit values ∞ and −∞. See also cardinal number and ordinal number, which include infinite examples of each (though none of them is called simply "infinity"). -- Trovatore 19:14, 29 November 2005 (UTC)
The statement that 'infinity is not a number' is a direct quote from: Mathematics: from the Birth of Numbers, by Jan Gullberg, 1997, ISBN 0-393-04002-X, pub. by W.W. Norton & Co., Inc..
It also is supported by Comment 10, above. Duncan.france 19:56, 29 November 2005 (UTC)
The statements (which I have modified):
are problematic. What is this business about upper bounds increasing limitlessly?:
The new wording isn't ideal, but at least it isn't as wrong.... -- Macrakis 01:55, 1 December 2005 (UTC)
The ancient Indian conceptions of infinity are very interesting. Apparently they are documented in R.C. Gupta, "The first unenumerable number in Jaina mathematics", Ganita Bharati 14 (1-4) (1992), 11-24. Could someone please look up this article and report back on what it says? Apparently Jaina mathematics included more than one magnitude of infinity, which is fascinating. It seems like a leap, though, to compare that to Cantor's work on transfinite numbers. -- Macrakis 17:21, 5 December 2005 (UTC)
There is no need to have a separate disambig from Nissan Infiniti; that's one of the articles covered at Infinity (disambiguation), which is linked to from the "For other uses ..." line at the top of the page. -- Trovatore 18:34, 11 February 2006 (UTC)
In reference to
where a couple of editors have wanted to say the area is "not bounded". That doesn't make sense; it's a single quantity. Now, you could say, if you wanted to, that the set of all integrals , where 0<a<b<∞, is not bounded. That would be one way for the integral to have an infinite value (though not the only way, as the integral could already be infinite for some particular a and b). If it were specified that f is continuous, then it would be the only way. -- Trovatore 16:39, 17 February 2006 (UTC)
The difficulty comes from the occurrence of infinity in the left hand expression. The integral is not a priori a number, but a limit. The proper way to express it would be: for every y there is a value x>0 such that . Or stated otherwise: the set of for all x>0, is not bounded above.− Woodstone 19:04, 17 February 2006 (UTC)
You seem to assume that the function f is continuous, how else can you have an area bounded by its graph. In integration of a function like this, only a lebesgue measure is defined on the integration domain (here indicated by t). There is no need for a 2-dimensional measure. The definition of the integral as a limit does not need the function to be continuous and is therefore more general (and correct). − Woodstone 21:34, 17 February 2006 (UTC)
The limit formulation does not require Riemann integration, it can just as well be Lebesgue integration. Still no 2-D measure is needed. (But yes, the set as defined above would be well defined for "reasonable" functions, assuming a 2-D measure.) Still, defining infinite in terms of infinite does not seem right. − Woodstone 13:24, 18 February 2006 (UTC)
There are an infinite number of numbers between 0 and 1. There are an infinite number of numbers between 0 and 2. Is the second infinity twice as large as the first? Or are they equal? The Disco King
e.g. 0.9 recurring. There are infinite 9s. Does this number necessarily equal 1?
This article needs a better lead - it weasels its way around, without saying what infinity actually is - which it should say in the first paragraph, if not the first sentence. zafiroblue05 | Talk 04:57, 2 April 2006 (UTC)
I need clarification after reading the previous discussions (perhaps I missed the definitive answer on this)...
Is the statement: ...true or false?
-- PCE 20:25, 5 May 2006 (UTC)
The article says the following is an undefined "operation":
I interpret it to mean the number "1" raised to an infinitely large (or small) power. But my understanding is that multiplying one by itself always equals one, no matter how many times multiplied. So I would think it equals "1". What have I missed? Dagoldman 08:33, 17 May 2006 (UTC)
Yes, the same "intuitive reasoning" can also be applied to "zero times infinity". It seems to be carrying out a known simple operation (adding zero and zero) an infinite number of times. So it seems that the outcome is always "0". So what's the proof that "zero times infinity" is not zero? Or what's the logical flaw in this "intuitive reasoning"? I might buy your second explanation as a proof that "one raised to the power infinity" is not one. As a first step, I would have to be convinced that is a valid equation. But is this operation valid if the exponent is infinity? I would not assume that it's valid, since "infinity" is not a real number. Does anyone have a reference or proof that you can move "infinity" out of the exponent in this manner? By the way, I'm treating "1" as EXACTLY 1, not a limit. Ditto for "0". Of course, if these quantities were limits, then "zero times infinity" and "one raised to the power infinity" would be undefined. But if you want to treat these quantities as limits, I think they need to be differently expressed, which is certainly easily done. Dagoldman 06:42, 18 May 2006 (UTC)
Has anyone defined zero or infinity mathematically? 88.109.19.139 19:32, 28 June 2006 (UTC)
`
I have no idea what i am talking about, but i heard "accountable and unaccountable infinity" mentioned. it was something like accountable is where you have say 1, 3, 5, 7, 9... and you pair those numbers up with 1, 2, 3, 4, 5... etc. and so every number can be assigned another number and so on. Unaccountable was where if you invent a whole lot of random numbers, say:
238973847692384
238477456902843076587323
7823465874638597263498574
982643586348576398456
9384658346587648
382746821947378468921
etc.
and this list is infinite. and then you go diagonally from the top right, so you'd get 232666... and this number can never appear in the first list.
a friend tried to explain this to me and i didn't get it so i went on google and then wikipedia to see if there was anything about it. does anyone know what i am talking about? --58.107.95.163
Ok there is an infinte way to make a chair, but the is also an inifine ite way not to make a chair, there is more ways not to make a chair than there is ways to make a chair, so one infinity is greater than another, how can this be, (maybe reading the atrical more closely would help) There is an Infite number of things that arn't a chair 12:26, 26 July 2006 (UTC) sorry if i have done makeing this question bad, i am new to wiki langualge There is an Infite number of things that arn't a chair 12:26, 26 July 2006 (UTC)
In a footnote to his short story 'The Library of Babel' Jorge Luis Borges describes:
A volume of ordinary format, printed in nine or ten point type, containing an infinite number of infinitely thin leaves. (In the early seventeenth century, Cavalieri said that all solid bodies are the superimposition of an infinite number of planes.) The handling of this silky vade mecum would not be convenient: each apparent page would unfold into other analogous ones; the inconceivable middle page would have no reverse.
FIRST QUESTION: The pages are infinitely thin and therefore, if I am not mistaken, have a mass that can be computed at 0; however, they are infinite in number. What is the total mass of the book? In other words, if you multiply something of infinite smallness an infinite number of times, what is the resulting mass? Would an infinite number of gravitational singularities be infinite in size, or the same size as a single singularity?
SECOND QUESTION: Can anyone tell me why the middle page of this book has no reverse? I believe there is an answer, involving the mobius strip.
Thanks.
(I ask these questions because their solution might eventually feed into the article. Borges writes obsessively of infinity. It'd be nice to see an Infinity in Literature section to this article.)
Isn't this article about infinity in general? And what do you mean about a hard Sci-Fi writer being expected to get it "right". I can't be sure, but I suspect half of what you are saying is crap. "Correctness" should not be the single criterion for the inclusion of material in an article. The treatment of infinity in literature -- a part of the cultural impact of the idea of infinity -- has an unquestionable right to be included in this article; as much right as theological ideas in an article on cosmogony.
Everything that I have currently read on Cosmology and the Universe seems to suggest a finite universe not an infinite one. Anyone care to provide facts to backup a case for a infinite one? Since the Bang Bang, I don't believe we deal with the universe in terms of infinity any more. ( Simonapro 14:10, 28 August 2006 (UTC))
Is an infinite universe as an alternative for big bang cosmology. ( 88.101.172.224 20:24, 28 August 2006 (UTC))
∞/2 = ∞
i'v been charged by the group who came up with this to spread there idea on infinity. they claim that inifinity is the numbers 0-9. they numbers that appear everywhere.
thats it.
Perhaps something can be mentioned about the infinite scope of mathematical entities such as Pi and some types of Fractals? HighInBC 02:04, 13 September 2006 (UTC)
By infinite scope, I meant that that it has an infinite number of non-repeating decimals, and thus involve infinity. But I don't know much about Pi, other than what you just told me. But I do know that the Mandelbrot set has infinite detial. HighInBC 02:28, 13 September 2006 (UTC)
I dunno HighInBC 03:38, 14 September 2006 (UTC)
Is this external link appropriate?
It most definitely is since it is the only religious text I've seen that identifies Infinity.
I would like to suggest splitting off the mathematical concept of infinity to its own article and leaving a summary here, with {{ main}}. There's a lot more to be said:
and so forth. Some of these are already represented, but not in much depth. Further, there are few citations for what little content is there. I have three concerns that this solution would address:
What do you think? CRGreathouse ( t | c) 23:17, 6 October 2006 (UTC)
I'd love to read about the fact that there are at least two kinds of infinites:
It can be mathematically proven that the numerosity (?) of the above two is different, that is, the second constitutes a "bigger infinite" than the first. Adam78 11:15, 25 October 2006 (UTC)
Thank you! It's an interesting bit of info so I hope it won't be lost in the article. Adam78 20:49, 25 October 2006 (UTC)
Just to add my two cents worth: The two mathematical infinities could also be designated:
Pardon, but what is the reference for the section, "Infinities as part of the extended real number line?" specifically the equations listed -- JohnLattier 07:32, 15 November 2006 (UTC)
Isn't Unrelative infinity a repeating number of nines in both directions of the decimal point because 888888...88.99999.. would not be the maxamum number because you can create a larger number which is 999999..99999.99999.....
Also if infinity plus one is equal to infinity then if you subtract infinity on both side of the equation we can see that 1=0 in which we could prove anything. However infinity plus one is equal to x but if you think about it their is no real number for x thus it is a form of an imaginary number. oo+1=oo, then oo-oo+1=oo-oo, 1=0 which cannot happen however oo+1=(a form of an imaginary number), then oo-oo+1=(a form of an imaginary number)-oo, then 1=1 which works.
but then again what do I know?
This information cannot go in the lead section, which should only be used in summarizing the article. If it is worthy of being here, it will need its own section, though it doesn't seem to relate to any other heading in the contents so I'm not really sure what to do with it. Richard001 23:44, 2 January 2007 (UTC)
In my opinion the paragraph on photography needs further explanation or should be removed. In particular the statement that a lens can focus on an object which is "past infinity" is very counterintuitive and serves only to confuse matters especially as it is located at the beginning of the article without a rigorous mathematical/geometric optics explanation of how this can be. I have read the photography articles and cannot fathom, even from a theoretical standpoint, what this statement is supposed to mean not to mention from a practical real world photography standpoint. From what I gather a camera focuses on a theoretical object at infinity when the lens is adjusted to the focal length. At this setting it focuses parallel light rays emanating from a theoretical point at infinity (in the real world this point would presumably be at the edge of an infinite universe). I can only surmise that an optical system focusing on a subject which is "past infinity" is designed to focus light emanating from a point which is anti-parallel and in fact is converging (as opposed to diverging) as it approaches the lens. If this has been demonstrated experimentally it should be explained in the article otherwise it is an abstraction in the realm of pure mathematics which does not belong in the article. From a mathematical standpoint my best guess as to what focusing "past infinity" means would be something like saying a divergent sequence converges past infinity. While this abstract concept might be worthy of consideration from a pure math standpoint it is not useful in terms of applied mathematics and therefore because there is no correlation with the scientific method has no real world significance. I have no clue as to how the wavelength of the light under consideration has any bearing on the matter. All light (including IR) in the known universe has wavelength of a finite size. There is no light in the real world with infinitesimal or infinite wavelength. By the same token the first paragraph mentions that the concept of infinity occurs in everyday life, however the article does not cite any examples of this. There are no observable infinities in the known universe (with perhaps the one possible exception of staring at the night sky). There are only observable potential infinities. One might suggest that for example a drawing of a Serpinski Triangle is a physical example of an infinity...however obviously in the real world it is always incomplete as it can never be drawn with infinite resolution (or at least nobody has done it yet;). While the concept of infinity may occasionally come up in everyday life I think it is very important to stress the fact that infinity is a concept which unlike other mathematical concepts such as angles and quantities has no example in the real world. If there is no objection I will be deleting the aforementioned paragraph and statement. Also just an observation...there seem to be a lot of discussions on 0/infinity and 0*infinity etc. I think it should be sufficient to say that they are NOT DEFINED, and that when something is NOT DEFINED in mathematics that is generally because it is NOT USEFUL in terms of applied mathematics/theoretical physics and is therefore relegated to the realm of philosophy and/or pure mathematics. Excimer3.141597 08:25, 12 February 2007 (UTC)
You are making things too complicated. The "focus" markings for a lens are calibrated for the middle of the visible spectrum. "Focussing beyond infinity" simply means setting the lens beyond the visible-light infinity mark, and therefore possibly at infinity for longer wavelengths. Also, lenses have a non-zero depth of field. Focussing "beyond" infinity throws closer objects further out of focus, which may be desirable. Anyway, this discussion belongs in a photography article. -- Macrakis 14:36, 12 February 2007 (UTC)
Yes, I suspected thats what it meant but I was giving the author of the paragraph the benefit of doubt. In the first sentence he states that "infinity is used as the furthest point that a lens can resolve focusing of the subject. This is not exactly true though, as some lens are designed to focus past infinity". By furthest point it would seem he meant furthest subject distance and not furthest rotation of the camera's focus ring which is trivial. Anyway it has little or nothing to do with the concept of infinity and I have deleted it. Excimer3.141597 15:44, 12 February 2007 (UTC)
one divided in infinity does not equal zero, it aproaches zero, zero is like an asymtote. the real equation is 1/infinity = 1x10 to the power of negative infinity ps i couldnt find out the button for infinity so i used the word, sorry. im in grade 11 and i figured that out. how could 1/infinity equal zero if that means that zero times infinity equals one????
regarding the use of infinity as a number (which I am happy to accept it is not), There are some purposes in mathematics, most commonly in the case of x tends to infinity when it is helpful to use infinity as a number. The best example of this is probably the graph this graph is asymptotic to y=pi for large positive and negative values of x but this can only be really be appreciated if it can be accepted that:
a)
b) therefore
c) and most importantly for the value of 0 that is equal to
I would like to edit this article to explain this but I am new to the site and it would be helpful if a more experienced editor would second (or condemn) this change.
A mathematician 21:48, 6 February 2007 (UTC)
I don't think the [ image] on top of the article is very well chosen. It shows the infinity symbol in eight different fonts that look essentially the same. What does this illustrate? Isn't one symbol enough? Or waht about a picture illustrating the concept of infinity, such as a foto of someone holding the same foto of someone holding the same… — Ocolon 09:29, 14 March 2007 (UTC)
In absence of objections, I'm going to add a section on the 'role' of infinity in ethics. I was first made aware of this by the philosophy of Emmanuel Levinas, whose magnum opus, "
Totality and Infinity" discusses the concept. Levinas believes infinity is an ethical concept which denotes that which cannot be encompassed, which cannot be reduced, etc... For Levinas infinity plays a role in responsibility -the infinite responsibility for the other person, and the 'ungraspability' or 'reducibility' of whatever is other or external. For anyone looking for an introduction to Levinas' philosophy, start with an early lecture of his, "Time and the Other", or check out the philosopher and mathematician
Hilary Putnam's essay in the Cambridge Companion to Levinas, "Levinas and Judaism".
Teetotaler
I can think of a couple of objections:
1. This is a relatively minor (esoteric?) usage of the term infinity. I would posit that much of humanity knows of infinity in the sense that it is a "number" that is "very large". All fundamentally non-mathematical usages (Ethics, Theology, etc.) properly belong in a different page.
2. Levinas may have pulled a weasel manouver by co-opting a fairly important mathematical concept to promote his pet philosophy. By putting this entry here, you are essentially legitimizing his intellectual incompetence at not coining a new term for his ideas.
I would suggest just make a new page and pull this out of this one.
Redblue
16:19, 19 May 2007 (UTC)
Do you think that the symbol for infinity, could be a representation of a 1 turn (10 pairs) of DNA? Does make sense on a metaphysical perspective. Thanks Dreedee 13:08, 7 April 2007 (UTC)
I always thought it was a symbol created by ancient Egyptians. It would make sense in a society that emphasized the daily death and rebirth of the sun. Check this out
http://antwrp.gsfc.nasa.gov/apod/ap020709.html
HighPriest
16:47, 14 June 2007 (UTC)
I think it might make sense to link in cultural references to infinity. In particular, I've seen the "Lazy Eight" reference to infinity reflected in Aviation [1], Cinema Lazy_Eight#History, Livestock branding, and even in Science Fiction. In Science Fiction, Larry Niven used the "Lazy Eight" as the name of a series of ships in his Known Space series of stories. Lent 13:17, 7 April 2007 (UTC)
The page states:
The mathematical symbol for infinity, " ∞", looks like a sideways "8" and is commonly thought to be derived from the Möbius strip.
Can someone confirm this?
NevilleDNZ
03:11, 2 May 2007 (UTC)
Would this help? if you follow the link you will get a copy of an article I wrote which gives a quite simple contruction of a set which extends the integers to contain positive and negative infinites, in the sense that it contains the integers and numbers which are greater in absolute value than any positive integer.
In this extension you can only add and subtract. It may not be very useful but is gives a flavour of how, given a context, infinitely large can be given a rigorous meaning. Odonovanr 16:38, 10 May 2007 (UTC)
We need to expand this article to make it infinitely long. Does anyone have a lot of stuff to add to it to help us reach that goal? 4.235.108.45 18:42, 20 May 2007 (UTC)
I realise that this is not primarily a Maths article however I think we should be a bit more careful about the use of these terms here. Cardinality is a rigourously defined term (given ZFC). Size is a more nebulous notion. Equating them is therefore a bit tricky.
For example "Cardinal numbers define the size of sets" is wrong. In particular, Cardinal numbers do not define anything. Cardinal numbers are often identified with the size of sets (but this is a delicate philosophical question). I will make some adjustments, but would like to hear some comments first.
Thehalfone
09:11, 23 May 2007 (UTC)
I'm a little unsure about the last paragraph. Do modern theologans and philosophers (it's not really a question of mathematics) have any interest in relating infinity to God? -- Robert Merkel
I think infinity is typically taken to be one of the properties of God. My problem with the last paragraph is that Goedel did not use infinity at all, he defined God as "absolute perfection" and came up with some axioms which establish the existance of an entity which is absolutely perfect. I don't see how that relates to infinity at all. --AxelBoldt
I like the history section, but it looks like it belongs in a different article. I don't think the Arabs used "1001" to mean infinity. Nor did the French with "million", nor Buddha with "10^421", nor the Romans with decies centena milia. The only sentence that might be relevant is the one about infinity being called "zero denominator". Other than that sentence, how about moving the rest to number names? -- LC
I agree. Also, the claim that "infinity has greatly increasd in size over the years" is pretty hilarious. AxelBoldt
Isn't it generally assumed by astonomers and physicists that our universe, forget about any other ones, is not infinite? - Tubby
ok - thats confused me - its hard to imagine a finite universe - this would menan that there is something beyod the universe - to expand into, meaning that that universe would be infinate - or finut wich would then mean that it would carry on going on like that - being infinate????? or am i just being super confused lol -- Infinitive definition 14:20, 4 April 2007 (UTC)
In my opinion the definition at the beginning (the one before the TOC) is severely wrong.
Even if in common use the term infinity is also the one describe there, this is not the precise tecnical (especially in Math) definition.
The definition given is that of unlimited or unbounded not of infinty. Infinity means with no end, a set is infinity if when you count the number of its member you can not arrive at the point you have cont all the member. This definition is consistence with the rest of the article. (Phereps I have to rewrite it in a better way).
An equivalent (but more difficult to understand) definition is that a set is infinite if there exist an its proper parts that is as big as the wole set (where as big as is to be understood in a sense proper to this branch of math)
Also the traslation of the etimologhy is wrong: Infinitum in latin is not without limit but it is without end or not eneded. As a prove of that consider that from the word finitum and fines derived the Italian Fine and French Fin that mean end in English
Neverless the word infinity and infinite are common used in the meanig stated there and also to describe a very big set but finite. Maybe it will be worthly to add a section on this and on the difference on these term.
A tecnical mathematical note to use the terms limited, unlimited (or the equivalent bounded and unbounded) you have to fix the way you do the measure of distance (you have to be in a Metric space). You have not to have this to speak of infinity/infinte AnyFile 18:16, 8 Sep 2004 (UTC)
I believe the points raised on the talk page are now covered. Of course using "infinity" in describing a finite is wrong, but it is a popular mistake that needs to be included, clearly labeled as such. Kyz 10:49, 11 Sep 2004 (UTC)
Since I think the people reading this will know - it was my impression that the symbol for Infinity was the Möbius Band however maybe it's accurate to say that the Möbius Band is a specific case of the lemniscate?
Thanks,
R.
This article seems to be a mushy mix of philosophy, intellectual history, and mathematics, and has a lot of outright errors. Can someone explain if this should be made more mathematical, by clarifying what the purpose of it is?
Historically, "a mushy mix of philosophy, [religion,] and mathematics" is pretty much what people thinking about infinity used to do.
Still, this article is still in need of a lot of attention. I'd suggest starting by ripping out all the parts referring to current mathematics (after Cantor's Absolute Infinite, I think).
In current mathematics, infinity pops up in exactly two places:
So many things are called finite, infinite, or infinity in mathematics that a complete list of the various usages would probably be completely useless (as well as virtually impossible). Just off the top of my head:
I'd be willing to turn these into a separate article if anyone thinks it'd help. I don't, but they're certainly just confusing in an article about infinity. As an analogy, it's a bit like talking about rational numbers in the rationality article. They happen to use the same term, but that's it, as far as their relationship goes. Today, of course, mathematical objects and properties are commonly named after their inventors, which might be the only reason Noetherian rings aren't called finite.
So, to sum things up, let's throw out all the mathematics, redirect people who're just looking for an article about the mathematical term to a separate article (I think that'd be most of them), then get back to writing an article about the philosophical issues.
Prumpf 16:38, 16 Oct 2004 (UTC)
I'm putting this here because I don't see anywhere else to put it. I was in bed sleeping one time when I came out of the sleep state to what I call the vision state or a condition of higher consciousness. In this state I realised I was looking into infinity and not just something similar to looking at a non descript gray sky for example. Definitely unlike any normal vision experinece but just as real or more real. I said to my self "Holy shit I was looking at infinity!"
Hi newbies, if you didn't realise, Wikipedia says that removing swathes of material, especially without permission or discussion beforehand, is wrong. Infinity is supposed to be a general article, so don't delete explanations even if they're covered in independent, separate articles. The coverage before was excellent. If there are mistakes, say so here [or there] and fix them rather than being stupid. lysdexia 03:25, 21 Oct 2004 (UTC)
In the context:
I don't think so. Let's consider Electrical resistance. There are conductors with zero resistance ( Superconductors). Now consider Electrical conductance. They are related by
So the conductance of an object with zero resistance (superconductors!) is infinity. -- Kenny TM~ 11:59, Nov 23, 2004 (UTC)
As a number wouldn't infinity = 9 repeat
I notice the character for infinity (∞) is never actually included in this article, other than in graphics. I was wondering why this was... Perhaps it was simply not known? Well, anyway... does anyone else think the the graphics should be replaced by the character? Oscar Evans December 14th 2004.
I do not like very much the susection Infinity in real analysis. The difference between infinity as a real number (opps ... extended-real) and as a limit is not clear. In my opinion it should be point out that when infinity is a limit you could not treat it as a number. This to avoid that someone could thing that he/she could do ∞ - ∞ = 0 AnyFile 21:30, 30 Jan 2005 (UTC)
1/1=1, 1/0=Infinity, (0/0=1 and Infinity) Please verify? Why are the past, the present and the future is the same time as January 2005, some cluster of stars(many galaxies) we can see by light speed only and after that human mind memory recall in only 0.0001 second, it means infinity light speed can touch by human mind in 0.0001 second too.
I don't know what the rest of the stuff you're saying means, but I'm pretty confident 1/0 is not infinity, since the inverse of infinity is the infinitesimal, while the inverse of 1/0 is simply zero. Citizen Premier 15:54, 10 Jun 2005 (UTC)
You can not divide anything by zero
Try this book called "0". In the apendix it show how if you could divide by zero (which you really can't)that you could prove any thing (it proves that Winston Chirch Hill is a carrot).
Also the reason you can't divide by zero is that X*0 = 0, and 1*0 = 0, and 2*0 = 0, and 3*0 = 0, so X/0 is every number. You might have gotten confused on the Y*X^-1 = Y/X, and here is were you might have made you mistake 0^X =0. That applies to every number execpt 0 (Y*X^-1 = Y/X). Another thing you might have done is that 1/.01= 100, and 1/.001 = 1000 so you might have done as the denominator aproches 0 then the answer will approch infinity. But the lim is 0 so it will never get to 0.
Would you consider interesting to put a note why infinity numbers are called (starting form Cantor) transfinite numbers? AnyFile 10:45, 2 May 2005 (UTC)
I think both of these points (if I'm right about them) could be useful additions to the article. -- Trovatore 01:47, 25 July 2005 (UTC)
Because infinity is not exactly equal to any finite number, and acts differently than any (other) number, many people find it easier to understand explainations that state right up front that "infinity is not a number".
"While zero is a concept and a number, infinity is not a number. Infinity is the name for a concept. Infinity cannot be considered as a number since since it does not follow numbers' properties. "Infinity" is not a number. ... When mathematicians say "x approaches infinity", or write "x→∞", they mean "x grows arbitrarily large. And when they say that the limit of something is 0, they mean that it can go as close to 0 as you want it to, but it may or may not be actually equal to 0."
OK if I use that definition on Infinity and Infinity plus 1 ? If no one comes up with a better suggestion the next time I come by, I'll just stick that definition in the article and watch the reaction.
-- DavidCary 01:58, 12 May 2005 (UTC)
I hate it when people try to claim there is such a thing as "negative infinity". That's the most absurd thing I've ever been taught in school. Like the comment above, infinity is not a number and therefore cannot be negative. You can go approach infinity in a negative direction, but you can't go to "negative infinity". Phew... got that off my chest. -- Lord Voldemort (Dark Mark) 21:26, 22 August 2005 (UTC)
Moved over here for easier discussion... First, please do not try and belittle me. I quite understand both "negative" and "infinity". You don't need to try and be condescending. Secondly, no, you cannot have a "negative mile". A mile is a measure of distance. And you could have negative money since it is a real object. But on second thought, perhaps you cannot have "negative money". You may owe people money, but you cannot posses "negative money". I don't recall ever seeing that term in an economic book or journal. But I digress... I don't care what you label infinity, if prixibeen means the same thing as infinity, you would not be able to have "negative prixibeen". Basically all I am saying is that you may be able to go prixibeen in the negative direction, but how can you label something as "negative" if it is not a number? Can you have "negative democracy", "negative art", "negative file cabinets"? (and I am talking about mathematical "negative", not the generic adjective) I just think it is absurd to call something negative when it cannot be negative. -- Lord Voldemort (Dark Mark) 18:36, 23 August 2005 (UTC)
I asked for help, and you try and belittle me. Oh gee golly, thanks a bunch! I just feel like this whole thing is a crock, and wanted to know if someone could explain it. Hopefully you are not a math teacher, because if you are I would be amazed if your students could learn anything from you. I was asking a serious question. Some people are honestly trying to help. I thank them for their work, although I fear it may be in vain. I may never get the whole "negative infinity" thing, and thanks to responses like yours, I might not want to ask you guys for help again. Thank you to all who tried to help. I guess I was made to live in the real world, and not the world of theoretical mathematics. -- Lord Voldemort (Dark Mark) 18:48, 23 August 2005 (UTC)
Voldemort, I had a very similar argument when being interviewed for an undergraduate university place. I was asked the value of x / sin x at 0. I replied that the limit as you approach 0 is 1, but I insisted that actually at 0 it is undefined, since there is a divide by 0. I have no idea what bearing this has on the existence or not of a minus infinity. -- stochata 16:17, 26 August 2005 (UTC)
A long-ish comment by Nowhither:
Infinity in space, time has alway been an issue in philosophy (
Aristotle,
Zenon, etc), physics, theology, and of course mathematics (starting with
Bolzano,
Cantor).
I can go on to infinity with this remark. However, I would like to point out the view of Wittgenstein. In mathematics, they operate with symbols according to some pre-set rules. There is nothing infinite in this operation, in the symbols, in the grammar, or in the rules. It is just a game, where they try to eliminate contradictions. A claim that there is no infinity has nothing to to with the symbol .
— Igny 18:31, 30 August 2005 (UTC)
I've done some minor cleanup on this section (original author didn't mention extended reals, for example). But wording and organization are still strange, and frankly I question the need for the section at all, given the prominent links to extended real number line elsewhere in the article. What do others think? -- Trovatore 15:17, 15 September 2005 (UTC)
I've removed the link to the "Infinity Society", http://www.infinitysociety.org/index.html . The site is definitely worth a look, though. I like this passage:
He doesn't tell us what the last benefits are. Anyway he does seem a decent sort of person, at least from what you can tell from what he says; I'm just not convinced his site is a correct link for an encyclopedia article on infinity. -- Trovatore 02:32, 23 November 2005 (UTC)
Assuming that when we write we mean the remainder (there are other meaning of the symbol mod) then is undefined.
The statement " in undefined" is not true.
First we never define if is negative so we should only look at .
I claim we can consistantly define
Mungbean 12:05, 25 November 2005 (UTC)
etc Mungbean 12:02, 30 November 2005 (UTC)
I have reverted this claim:
The notion of "number" in mathematics is not sufficiently well-defined to say whether infinity is or is not a number. In the extended real numbers there are explicit values ∞ and −∞. See also cardinal number and ordinal number, which include infinite examples of each (though none of them is called simply "infinity"). -- Trovatore 19:14, 29 November 2005 (UTC)
The statement that 'infinity is not a number' is a direct quote from: Mathematics: from the Birth of Numbers, by Jan Gullberg, 1997, ISBN 0-393-04002-X, pub. by W.W. Norton & Co., Inc..
It also is supported by Comment 10, above. Duncan.france 19:56, 29 November 2005 (UTC)
The statements (which I have modified):
are problematic. What is this business about upper bounds increasing limitlessly?:
The new wording isn't ideal, but at least it isn't as wrong.... -- Macrakis 01:55, 1 December 2005 (UTC)
The ancient Indian conceptions of infinity are very interesting. Apparently they are documented in R.C. Gupta, "The first unenumerable number in Jaina mathematics", Ganita Bharati 14 (1-4) (1992), 11-24. Could someone please look up this article and report back on what it says? Apparently Jaina mathematics included more than one magnitude of infinity, which is fascinating. It seems like a leap, though, to compare that to Cantor's work on transfinite numbers. -- Macrakis 17:21, 5 December 2005 (UTC)
There is no need to have a separate disambig from Nissan Infiniti; that's one of the articles covered at Infinity (disambiguation), which is linked to from the "For other uses ..." line at the top of the page. -- Trovatore 18:34, 11 February 2006 (UTC)
In reference to
where a couple of editors have wanted to say the area is "not bounded". That doesn't make sense; it's a single quantity. Now, you could say, if you wanted to, that the set of all integrals , where 0<a<b<∞, is not bounded. That would be one way for the integral to have an infinite value (though not the only way, as the integral could already be infinite for some particular a and b). If it were specified that f is continuous, then it would be the only way. -- Trovatore 16:39, 17 February 2006 (UTC)
The difficulty comes from the occurrence of infinity in the left hand expression. The integral is not a priori a number, but a limit. The proper way to express it would be: for every y there is a value x>0 such that . Or stated otherwise: the set of for all x>0, is not bounded above.− Woodstone 19:04, 17 February 2006 (UTC)
You seem to assume that the function f is continuous, how else can you have an area bounded by its graph. In integration of a function like this, only a lebesgue measure is defined on the integration domain (here indicated by t). There is no need for a 2-dimensional measure. The definition of the integral as a limit does not need the function to be continuous and is therefore more general (and correct). − Woodstone 21:34, 17 February 2006 (UTC)
The limit formulation does not require Riemann integration, it can just as well be Lebesgue integration. Still no 2-D measure is needed. (But yes, the set as defined above would be well defined for "reasonable" functions, assuming a 2-D measure.) Still, defining infinite in terms of infinite does not seem right. − Woodstone 13:24, 18 February 2006 (UTC)
There are an infinite number of numbers between 0 and 1. There are an infinite number of numbers between 0 and 2. Is the second infinity twice as large as the first? Or are they equal? The Disco King
e.g. 0.9 recurring. There are infinite 9s. Does this number necessarily equal 1?
This article needs a better lead - it weasels its way around, without saying what infinity actually is - which it should say in the first paragraph, if not the first sentence. zafiroblue05 | Talk 04:57, 2 April 2006 (UTC)
I need clarification after reading the previous discussions (perhaps I missed the definitive answer on this)...
Is the statement: ...true or false?
-- PCE 20:25, 5 May 2006 (UTC)
The article says the following is an undefined "operation":
I interpret it to mean the number "1" raised to an infinitely large (or small) power. But my understanding is that multiplying one by itself always equals one, no matter how many times multiplied. So I would think it equals "1". What have I missed? Dagoldman 08:33, 17 May 2006 (UTC)
Yes, the same "intuitive reasoning" can also be applied to "zero times infinity". It seems to be carrying out a known simple operation (adding zero and zero) an infinite number of times. So it seems that the outcome is always "0". So what's the proof that "zero times infinity" is not zero? Or what's the logical flaw in this "intuitive reasoning"? I might buy your second explanation as a proof that "one raised to the power infinity" is not one. As a first step, I would have to be convinced that is a valid equation. But is this operation valid if the exponent is infinity? I would not assume that it's valid, since "infinity" is not a real number. Does anyone have a reference or proof that you can move "infinity" out of the exponent in this manner? By the way, I'm treating "1" as EXACTLY 1, not a limit. Ditto for "0". Of course, if these quantities were limits, then "zero times infinity" and "one raised to the power infinity" would be undefined. But if you want to treat these quantities as limits, I think they need to be differently expressed, which is certainly easily done. Dagoldman 06:42, 18 May 2006 (UTC)
Has anyone defined zero or infinity mathematically? 88.109.19.139 19:32, 28 June 2006 (UTC)
`
I have no idea what i am talking about, but i heard "accountable and unaccountable infinity" mentioned. it was something like accountable is where you have say 1, 3, 5, 7, 9... and you pair those numbers up with 1, 2, 3, 4, 5... etc. and so every number can be assigned another number and so on. Unaccountable was where if you invent a whole lot of random numbers, say:
238973847692384
238477456902843076587323
7823465874638597263498574
982643586348576398456
9384658346587648
382746821947378468921
etc.
and this list is infinite. and then you go diagonally from the top right, so you'd get 232666... and this number can never appear in the first list.
a friend tried to explain this to me and i didn't get it so i went on google and then wikipedia to see if there was anything about it. does anyone know what i am talking about? --58.107.95.163
Ok there is an infinte way to make a chair, but the is also an inifine ite way not to make a chair, there is more ways not to make a chair than there is ways to make a chair, so one infinity is greater than another, how can this be, (maybe reading the atrical more closely would help) There is an Infite number of things that arn't a chair 12:26, 26 July 2006 (UTC) sorry if i have done makeing this question bad, i am new to wiki langualge There is an Infite number of things that arn't a chair 12:26, 26 July 2006 (UTC)
In a footnote to his short story 'The Library of Babel' Jorge Luis Borges describes:
A volume of ordinary format, printed in nine or ten point type, containing an infinite number of infinitely thin leaves. (In the early seventeenth century, Cavalieri said that all solid bodies are the superimposition of an infinite number of planes.) The handling of this silky vade mecum would not be convenient: each apparent page would unfold into other analogous ones; the inconceivable middle page would have no reverse.
FIRST QUESTION: The pages are infinitely thin and therefore, if I am not mistaken, have a mass that can be computed at 0; however, they are infinite in number. What is the total mass of the book? In other words, if you multiply something of infinite smallness an infinite number of times, what is the resulting mass? Would an infinite number of gravitational singularities be infinite in size, or the same size as a single singularity?
SECOND QUESTION: Can anyone tell me why the middle page of this book has no reverse? I believe there is an answer, involving the mobius strip.
Thanks.
(I ask these questions because their solution might eventually feed into the article. Borges writes obsessively of infinity. It'd be nice to see an Infinity in Literature section to this article.)
Isn't this article about infinity in general? And what do you mean about a hard Sci-Fi writer being expected to get it "right". I can't be sure, but I suspect half of what you are saying is crap. "Correctness" should not be the single criterion for the inclusion of material in an article. The treatment of infinity in literature -- a part of the cultural impact of the idea of infinity -- has an unquestionable right to be included in this article; as much right as theological ideas in an article on cosmogony.
Everything that I have currently read on Cosmology and the Universe seems to suggest a finite universe not an infinite one. Anyone care to provide facts to backup a case for a infinite one? Since the Bang Bang, I don't believe we deal with the universe in terms of infinity any more. ( Simonapro 14:10, 28 August 2006 (UTC))
Is an infinite universe as an alternative for big bang cosmology. ( 88.101.172.224 20:24, 28 August 2006 (UTC))
∞/2 = ∞
i'v been charged by the group who came up with this to spread there idea on infinity. they claim that inifinity is the numbers 0-9. they numbers that appear everywhere.
thats it.
Perhaps something can be mentioned about the infinite scope of mathematical entities such as Pi and some types of Fractals? HighInBC 02:04, 13 September 2006 (UTC)
By infinite scope, I meant that that it has an infinite number of non-repeating decimals, and thus involve infinity. But I don't know much about Pi, other than what you just told me. But I do know that the Mandelbrot set has infinite detial. HighInBC 02:28, 13 September 2006 (UTC)
I dunno HighInBC 03:38, 14 September 2006 (UTC)
Is this external link appropriate?
It most definitely is since it is the only religious text I've seen that identifies Infinity.
I would like to suggest splitting off the mathematical concept of infinity to its own article and leaving a summary here, with {{ main}}. There's a lot more to be said:
and so forth. Some of these are already represented, but not in much depth. Further, there are few citations for what little content is there. I have three concerns that this solution would address:
What do you think? CRGreathouse ( t | c) 23:17, 6 October 2006 (UTC)
I'd love to read about the fact that there are at least two kinds of infinites:
It can be mathematically proven that the numerosity (?) of the above two is different, that is, the second constitutes a "bigger infinite" than the first. Adam78 11:15, 25 October 2006 (UTC)
Thank you! It's an interesting bit of info so I hope it won't be lost in the article. Adam78 20:49, 25 October 2006 (UTC)
Just to add my two cents worth: The two mathematical infinities could also be designated:
Pardon, but what is the reference for the section, "Infinities as part of the extended real number line?" specifically the equations listed -- JohnLattier 07:32, 15 November 2006 (UTC)
Isn't Unrelative infinity a repeating number of nines in both directions of the decimal point because 888888...88.99999.. would not be the maxamum number because you can create a larger number which is 999999..99999.99999.....
Also if infinity plus one is equal to infinity then if you subtract infinity on both side of the equation we can see that 1=0 in which we could prove anything. However infinity plus one is equal to x but if you think about it their is no real number for x thus it is a form of an imaginary number. oo+1=oo, then oo-oo+1=oo-oo, 1=0 which cannot happen however oo+1=(a form of an imaginary number), then oo-oo+1=(a form of an imaginary number)-oo, then 1=1 which works.
but then again what do I know?
This information cannot go in the lead section, which should only be used in summarizing the article. If it is worthy of being here, it will need its own section, though it doesn't seem to relate to any other heading in the contents so I'm not really sure what to do with it. Richard001 23:44, 2 January 2007 (UTC)
In my opinion the paragraph on photography needs further explanation or should be removed. In particular the statement that a lens can focus on an object which is "past infinity" is very counterintuitive and serves only to confuse matters especially as it is located at the beginning of the article without a rigorous mathematical/geometric optics explanation of how this can be. I have read the photography articles and cannot fathom, even from a theoretical standpoint, what this statement is supposed to mean not to mention from a practical real world photography standpoint. From what I gather a camera focuses on a theoretical object at infinity when the lens is adjusted to the focal length. At this setting it focuses parallel light rays emanating from a theoretical point at infinity (in the real world this point would presumably be at the edge of an infinite universe). I can only surmise that an optical system focusing on a subject which is "past infinity" is designed to focus light emanating from a point which is anti-parallel and in fact is converging (as opposed to diverging) as it approaches the lens. If this has been demonstrated experimentally it should be explained in the article otherwise it is an abstraction in the realm of pure mathematics which does not belong in the article. From a mathematical standpoint my best guess as to what focusing "past infinity" means would be something like saying a divergent sequence converges past infinity. While this abstract concept might be worthy of consideration from a pure math standpoint it is not useful in terms of applied mathematics and therefore because there is no correlation with the scientific method has no real world significance. I have no clue as to how the wavelength of the light under consideration has any bearing on the matter. All light (including IR) in the known universe has wavelength of a finite size. There is no light in the real world with infinitesimal or infinite wavelength. By the same token the first paragraph mentions that the concept of infinity occurs in everyday life, however the article does not cite any examples of this. There are no observable infinities in the known universe (with perhaps the one possible exception of staring at the night sky). There are only observable potential infinities. One might suggest that for example a drawing of a Serpinski Triangle is a physical example of an infinity...however obviously in the real world it is always incomplete as it can never be drawn with infinite resolution (or at least nobody has done it yet;). While the concept of infinity may occasionally come up in everyday life I think it is very important to stress the fact that infinity is a concept which unlike other mathematical concepts such as angles and quantities has no example in the real world. If there is no objection I will be deleting the aforementioned paragraph and statement. Also just an observation...there seem to be a lot of discussions on 0/infinity and 0*infinity etc. I think it should be sufficient to say that they are NOT DEFINED, and that when something is NOT DEFINED in mathematics that is generally because it is NOT USEFUL in terms of applied mathematics/theoretical physics and is therefore relegated to the realm of philosophy and/or pure mathematics. Excimer3.141597 08:25, 12 February 2007 (UTC)
You are making things too complicated. The "focus" markings for a lens are calibrated for the middle of the visible spectrum. "Focussing beyond infinity" simply means setting the lens beyond the visible-light infinity mark, and therefore possibly at infinity for longer wavelengths. Also, lenses have a non-zero depth of field. Focussing "beyond" infinity throws closer objects further out of focus, which may be desirable. Anyway, this discussion belongs in a photography article. -- Macrakis 14:36, 12 February 2007 (UTC)
Yes, I suspected thats what it meant but I was giving the author of the paragraph the benefit of doubt. In the first sentence he states that "infinity is used as the furthest point that a lens can resolve focusing of the subject. This is not exactly true though, as some lens are designed to focus past infinity". By furthest point it would seem he meant furthest subject distance and not furthest rotation of the camera's focus ring which is trivial. Anyway it has little or nothing to do with the concept of infinity and I have deleted it. Excimer3.141597 15:44, 12 February 2007 (UTC)
one divided in infinity does not equal zero, it aproaches zero, zero is like an asymtote. the real equation is 1/infinity = 1x10 to the power of negative infinity ps i couldnt find out the button for infinity so i used the word, sorry. im in grade 11 and i figured that out. how could 1/infinity equal zero if that means that zero times infinity equals one????
regarding the use of infinity as a number (which I am happy to accept it is not), There are some purposes in mathematics, most commonly in the case of x tends to infinity when it is helpful to use infinity as a number. The best example of this is probably the graph this graph is asymptotic to y=pi for large positive and negative values of x but this can only be really be appreciated if it can be accepted that:
a)
b) therefore
c) and most importantly for the value of 0 that is equal to
I would like to edit this article to explain this but I am new to the site and it would be helpful if a more experienced editor would second (or condemn) this change.
A mathematician 21:48, 6 February 2007 (UTC)
I don't think the [ image] on top of the article is very well chosen. It shows the infinity symbol in eight different fonts that look essentially the same. What does this illustrate? Isn't one symbol enough? Or waht about a picture illustrating the concept of infinity, such as a foto of someone holding the same foto of someone holding the same… — Ocolon 09:29, 14 March 2007 (UTC)
In absence of objections, I'm going to add a section on the 'role' of infinity in ethics. I was first made aware of this by the philosophy of Emmanuel Levinas, whose magnum opus, "
Totality and Infinity" discusses the concept. Levinas believes infinity is an ethical concept which denotes that which cannot be encompassed, which cannot be reduced, etc... For Levinas infinity plays a role in responsibility -the infinite responsibility for the other person, and the 'ungraspability' or 'reducibility' of whatever is other or external. For anyone looking for an introduction to Levinas' philosophy, start with an early lecture of his, "Time and the Other", or check out the philosopher and mathematician
Hilary Putnam's essay in the Cambridge Companion to Levinas, "Levinas and Judaism".
Teetotaler
I can think of a couple of objections:
1. This is a relatively minor (esoteric?) usage of the term infinity. I would posit that much of humanity knows of infinity in the sense that it is a "number" that is "very large". All fundamentally non-mathematical usages (Ethics, Theology, etc.) properly belong in a different page.
2. Levinas may have pulled a weasel manouver by co-opting a fairly important mathematical concept to promote his pet philosophy. By putting this entry here, you are essentially legitimizing his intellectual incompetence at not coining a new term for his ideas.
I would suggest just make a new page and pull this out of this one.
Redblue
16:19, 19 May 2007 (UTC)
Do you think that the symbol for infinity, could be a representation of a 1 turn (10 pairs) of DNA? Does make sense on a metaphysical perspective. Thanks Dreedee 13:08, 7 April 2007 (UTC)
I always thought it was a symbol created by ancient Egyptians. It would make sense in a society that emphasized the daily death and rebirth of the sun. Check this out
http://antwrp.gsfc.nasa.gov/apod/ap020709.html
HighPriest
16:47, 14 June 2007 (UTC)
I think it might make sense to link in cultural references to infinity. In particular, I've seen the "Lazy Eight" reference to infinity reflected in Aviation [1], Cinema Lazy_Eight#History, Livestock branding, and even in Science Fiction. In Science Fiction, Larry Niven used the "Lazy Eight" as the name of a series of ships in his Known Space series of stories. Lent 13:17, 7 April 2007 (UTC)
The page states:
The mathematical symbol for infinity, " ∞", looks like a sideways "8" and is commonly thought to be derived from the Möbius strip.
Can someone confirm this?
NevilleDNZ
03:11, 2 May 2007 (UTC)
Would this help? if you follow the link you will get a copy of an article I wrote which gives a quite simple contruction of a set which extends the integers to contain positive and negative infinites, in the sense that it contains the integers and numbers which are greater in absolute value than any positive integer.
In this extension you can only add and subtract. It may not be very useful but is gives a flavour of how, given a context, infinitely large can be given a rigorous meaning. Odonovanr 16:38, 10 May 2007 (UTC)
We need to expand this article to make it infinitely long. Does anyone have a lot of stuff to add to it to help us reach that goal? 4.235.108.45 18:42, 20 May 2007 (UTC)
I realise that this is not primarily a Maths article however I think we should be a bit more careful about the use of these terms here. Cardinality is a rigourously defined term (given ZFC). Size is a more nebulous notion. Equating them is therefore a bit tricky.
For example "Cardinal numbers define the size of sets" is wrong. In particular, Cardinal numbers do not define anything. Cardinal numbers are often identified with the size of sets (but this is a delicate philosophical question). I will make some adjustments, but would like to hear some comments first.
Thehalfone
09:11, 23 May 2007 (UTC)