Talk:Infinity/Archive 1

message: Isn't it generally assumed by astonomers and physicists that our universe, forget about any other ones, is not infinite? -Tubby
:Yep - finite. However at the same time it is unbounded (meaning that there is no inherent max size). --mav
:Universe by definition is finite, containing within itself the root for one, uni; infinity is by definition some process which can continue indefinitely, for example, imagine a faster than light ship using a drive which (because of the peculiarities of faster than light travel accelerates as a function of the square of the product of speed and distance traveled). A journey on such a ship in a finite universe would nevertheless never reach the "edge" and "fall off". Fredbauder 10:33 Oct 15, 2002 (UTC)
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)
replies: text: Yes, you are confused. mav is referring to a curved space manifold that is curved, so that is has no "edge" or boundary, but is also unbounded, so that it has no measurable maximum "width". Current cosmological models posit that the visible universe has a relative diameter of about 90 billion light-years, but say nothing about what lies "outside" or "beyond" what is visible. This diameter is the same as seen from any point in the universe; if you traveled in one direction you would never reach the "edge", because our universe is a 3D volume curved within 4D space-time. You get confused if you think of it as a normal 3D object within a 3D Euclidean space, because it's not as simple as that. — Loadmaster 18:51, 7 May 2007 (UTC)
thread_title:  Infinitude of the universe 

message: 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)
thread_title:  Definition 

message: 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)
thread_title:  Is the dispute over? 

message: 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.
:As far as I can tell, this isn't true at all.  The Möbius strip doesn't look very much like the symbol for infinity, and the apocryphal explanation that it symbolises infinity because you can go on forever on it is equally true of the circle.  They've got nothing to do with each other, and I've always thought that the infinity symbol was chosen because it was a fairly regular symbol that wasn't taken up already, freeing the precious ω for redefinition (much as ∈ used to be written ε).  No idea whether that's true either.
:Prumpf 16:02, 16 Oct 2004 (UTC)
replies: text: Apocryphal or not, these explanations are widely circulated (by math professors even !!!) and should at least be mentioned in the article so that viewers can realize that they may not be true rather than continue in ignorant bliss.  I'll go ahead and add a bit of text about it... --Umofomia 12:29, 14 Mar 2005 (UTC)
replies: text: My recollection is that the infinity symbol first appeared in Roman times (B.C.E.) and it represented 1,000,000 sesterce. I'm sorry I can't cite the source it was some dusty old mathematics history book. I have a photo of the artifact stashed somewhere files in storage.  I'll see if I can dig it out sometime in the coming months.--YORD-the-unknown 23:46, 7 July 2006 (UTC)
thread_title:  Symbol for Infinity 

message: 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?
user: Gene Ward Smith
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:
*in the axiom of infinity (and its various cognates in other axiom systems for set theory):  for the formalist, this is just another axiom like all the others, but for those who (still) take a more platonistic view, it might have deeper meaning.
*as a name or symbol to be used however you choose.  This isn't much of an exaggeration.  Depending on what I'm doing, I might very well end up in a situation where &infinity; is the same thing as the real number 1 (or any other real number), or the set of natural numbers, or what-have-you.  When this is made explicit, I'd probably avoid the symbol, since it might be a bit confusing, but it wouldn't be wrong.  Note that for strict formalists, the axiom of infinity fits in here as well.  We just define some sets to be finite, and if one of them is not, well, that's an infinite set.
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:
*maximal element of an ordered set
*extra point(s) in one-point/any other compactification
*non-affine points in projective space (a special case of the preceding for the real numbers, different in general)
*limit notation, even when no compactification is involved
*objects in any category that can't be cancelled in direct sums
*elements of monoids that can't be cancelled
*positive hyperreal numbers whose standard part can't be defined
*cardinals and ordinals, of course
*various other things like finite CW-complexes.  Depending on your definition, this might not be finite as a set.
*for von Neumann algebras, the various -finite terms used to have conflicting definitions (though that's all cleared up now, I hope).  Still, they can be hyperfinite, finite, infinite, purely infinite, and of course none of this will hold true for the sets.  Furthermore, the trivial von Neumann algebra is usually considered finite and purely infinite.
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.
:I don't think we should "throw out all the mathematics", the mathematics is inherently intertwined with the philosophical and physical issues. Paul August 17:47, Oct 21, 2004 (UTC)
Prumpf 16:38, 16 Oct 2004 (UTC)
thread_title:  What is this article about? 

message: In the context:
:... It is therefore assumed by physicists that no measurable quantity could have an infinite value, ... This point of view does not mean that infinity cannot be used in physics. For convenience sake, calculations, equations, theories and approximations, often use infinite series, unbounded functions, etc., and may involve infinite quantities. Physicists however require that the end result be physically meaningful. ...
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
: S = \frac{1}{R}
So the conductance of an object with zero resistance (superconductors!) is infinity. --Kenny TM~ 11:59, Nov 23, 2004 (UTC)
:Are you sure the resistence is zero? If you cool down a superconductor you see that the resistence go down (very sharply or more slowly, this depends on the type of superconductor). It go down a lot, you can see a lot of current passing. Comparing to to room temperature resistence this resistence is incredible smaller and in current speacking world we can say that this is an infinite difference. Often physicist say a quantity to be infinite to meaning very very much more than anything else in the surroundig. But can you really (in strict math and phys sense) say tha resistence is zero and conductance infinite? For a physicist to say tha means that you have measure. How could you have measure it! We have not an instrument to measure really zero resistence. When you have a real electric circuit (I am meanig a board with electrical contact, wires, resistence, like the board of a computer) and you schematic it, we usally say that wire have zero resistence and 2 not connected point have infinite resistence between them. This is not completly true. I am not saying tha is not true. It is true in the sense we usually meaning it (and that is the sense physicist use when speacking of infinite). It is true that between 2 not connected have between them a very high impedence compared to any other resistence you have put in the board, but if you measure it (with the appropiate instrument) you will find that the reistence is finite, very high but finite. You may found out value of houndreds of gigaohm or more (but sometime less, sometimes only 1 GΩ). Usually all the tester you use display OVL but this not mean infinite, means more than the tester can measure. I have worked with circuit where we deliberately put resistor of 10-100 GΩ and if I did  not considere this I would  have some problem in finding where some current were going. In the same faschion a wire is not a zero resistence conductor, and if you are dealing with supercoductor you have to take this well in consideration. 
:You have found out a real thing. If infinite does not exist in physics so does not exist zero. (I teacher of mine Giuliano Preparata said infinite and zero does not exist). (Of course exist in the case of natural number if you have an apple and it it you have zero apple)AnyFile 15:26, 24 Nov 2004 (UTC)
thread_title:  Physical infinity -- impossible or not? 

message: 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".
* http://home.ubalt.edu/ntsbarsh/zero/ZERO.HTM#roriginf
* http://www.kuro5hin.org/story/2003/6/3/95744/71866
"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)
replies: text: No, I don't think that's a good idea.  The word "number" is pretty vague; it's not clear what content is expressed by the claim that something is (or is not) a number. It's true that contemporary set theorists usually drop the word "number" from the locutions "cardinal (number)" or "ordinal (number)", but it's not clear whether this is from queasiness about calling such things "numbers"; could just be for economy. BTW your quote above seems to be restricted to the notion of "potential infinity", which is only one of the concepts developed in the article. --Trovatore 20:53, 24 July 2005 (UTC)
replies: text: Agree with Trovatore. Infinity is not one concept, but many. Point on Riemann sphere, cardinal, ordinal, extended real, etc. --MarSch 10:45, 30 August 2005 (UTC)
thread_title:  &infin; infinity is not a number 

message: 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:
:Jean-Pierre Ady Fenyô, is an internationally-recognized philosopher currently residing in Budapest whose main work is on the penultimate positive social benefits of contemplating the infinite.
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)
replies: text: I've put a note on Wikipedia talk:WikiProject Philosophy to see if anyone's heard of this Fenyo character, and in the mean time I've removed the reference to him on Infinity. --Trovatore 03:38, 23 November 2005 (UTC)
replies: text: I've put Jean-Pierre Ady Fenyo on AfD. If anyone knows anything about this, please contribute, especially if you can back up the claim that he's notable and the article should be kept. --Trovatore 20:49, 23 November 2005 (UTC)
replies: text: I found somthing about him here: http://www.reference.com/browse/wiki/Jean-Pierre_Ady_Fenyo. The site claims to be "Powered by Wikipedia", but I'm not sure what they mean by that.--67.188.80.67 23:39, 7 February 2006 (UTC)
replies: text: It means that they're a mirror site of WP, and on articles like this they're what you might call a "mirror into the past", because WP's article was deleted more than two months ago. See Wikipedia:Articles for deletion/Jean-Pierre Ady Fenyo. --Trovatore 01:39, 8 February 2006 (UTC)
thread_title: Infinity society

message: I have reverted this claim:
:In mathematics, infinity is not a number but a concept of increase beyond bounds.
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)
thread_title: explanation of revert

message: 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)
replies: text: No doubt there are sources that will say that. It's a commonplace among high school math teachers who are trying to keep their students from treating infinity according to the usual algebraic rules they're used to, and getting into trouble that way. But it's not a meaningful claim in the categories most contemporary mathematicians use, and it's not helpful in the context of the article. --Trovatore 20:02, 29 November 2005 (UTC)
replies: text: The most recent version looks fine, even if "a concept of increase beyond bounds" falls oddly on my ear--I want to read "increase" as a verb, so it brings back memories of scrolls of confuse monsters. But that's OK. --Trovatore 22:48, 29 November 2005 (UTC)
thread_title:  Comment on 'Explanation of revert' 

message: The statements (which I have modified):
*\int_{0}^{\infty} \, f(t) dt \  = \infty means that the area under f(t) increases without bound as its upper bound increases limitlessly
*\int_{0}^{\infty} \, f(t) dt \  = 1 means that the area under f(t) approaches 1, though its upper bound increases limitlessly.
are problematic.  What is this business about upper bounds increasing limitlessly?:
* For f(t)=(t<1: 1/t^2; t>=1: 0), the integral is already infinite for [0,1].
* For f(t)=(t<1:1 ; t>=1: 0), the integral is 1 for [0,1] and remains 1.
The new wording isn't ideal, but at least it isn't as wrong.... --Macrakis 01:55, 1 December 2005 (UTC)
thread_title: Infinite integrals

message: 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)
thread_title: Jaina conceptions of infinity

message: 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)
thread_title: Nissan Infiniti

message: 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
:There is a one-to-one mapping between those two sets given by f(x) = 2x. If there is a one-to-one mapping between two sets, we say they have the same number of elements. —Keenan Pepper 04:55, 22 February 2006 (UTC)
replies: text: But, there are infinitely many integers and also infinitely many reals, but there is no 1-1 mapping between them; so there are really more reals than integers. There are many different "infinite" cardinalities of sets. −Woodstone 14:24, 22 February 2006 (UTC)
thread_title: So are some infinities bigger than others or not?

message: e.g. 0.9 recurring.  There are infinite 9s.  Does this number necessarily equal 1?
:Yes.  You can see this by subtracting 1.000... - 0.999....  What is the first non-zero digit of the result?  The answer is that there is no non-zero digit in the result.  You can formalize this using limits, etc. I'm assuming of course that we're talking about the ordinary real number system (not non-standard analysis with infinitesimals etc.). --Macrakis 21:48, 19 March 2006 (UTC)
replies: text: That 0.99999... is equal to 1, came out from the way we choose in order to give a decimal rappresentation of real number (and of course from the definition of real number). AnyFile 10:43, 23 April 2006 (UTC)
thread_title:  Recurring numbers 

message: The article says the following is an undefined "operation": 1^{\pm\infty}
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)
replies: text: Well, zero times any finite number is zero, but that doesn't mean zero times infinity is zero. Analogously, one raised to any finite power is one, but that doesn't mean one raised to the power infinity is one. If you have an expression involving limits and you get 1^\infty by simple substitution, then it doesn't necessarily equal one, and you have to take the log and use l'Hôpital's rule. In fact, that's a good way to see why it's undefined. It's logarithm is log(1^\infty) = log(1)\cdot\infty = 0\cdot\infty, another undefined expression. —Keenan Pepper 01:01, 18 May 2006 (UTC)

text: I've never seen exponentiation defined on \pm\infty (where of course \pm\infty here means the additional elements of the extended real numbers).  It's misleading to say that 1^{\pm\infty} is undefined, when in fact a^{\pm\infty} is not defined in any standard sense for all a \in R.  I think I'll remove this part from the "undefined operations" if there are no objections. Kier07 06:15, 11 January 2007 (UTC)
replies: text: No, on the extended reals, the natural reading of a^{\infty} is \infty for a > 1, 0 for |a| < 1, and conversely for a^{-\infty}.  Obviously, equivalent limit statements hold in the standard reals.  However, 1^{\pm\infty} can take any limit, although the set-theoretical arithmetic value of 1^{\omega} for any infinite \omega is clearly 1. –EdC 13:23, 11 January 2007 (UTC)

text: Yes; they're mathematical concepts. Zero is the cardinality of the empty set, and a set is infinite if there exists a bijection from the whole set to a proper subset of itself. —Keenan Pepper 21:54, 28 June 2006 (UTC)
thread_title:  undefined operation? 

message: 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
:The terms are countable and uncountable. See also Cantor's diagonal argument. --Zundark 11:59, 18 July 2006 (UTC)
thread_title:  Accountable and Unaccountable 

message: 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.)
:Hmm, wasn't Borges an early magic realist? I think comparing his writings to the notions of mathematicians might kind of miss the point. If he were a hard SF writer we'd expect him to get it right.
:Anyway, the answer to the first question is "it depends"; there are lots of different contexts in which you might formulate the question, and they give different answers. I have no idea why Borges would think the middle page should have no reverse. --Trovatore 19:33, 31 July 2006 (UTC)
replies: text: The book with an infinite number of pages appears to be an analogy for the real number line.  The weight of each individual page must be zero, or else the book would be infinitely heavy.  The product of a finite number of 0s is 0 but the product of an infinite number of 0s is undefined.  The pages on the left side of the book correspond to negative numbers and those on the right to positive numbers.  The page number 0, if it existed, would be in the middle of the book with no counterpart.Awis 00:22, 10 August 2006 (UTC)
thread_title:  Negative infinity plus infinity? / The middle of infinity? [Borges] 

message: 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)
replies: text: There is no consensus on any of the three options as yet. See shape of the Universe and ultimate fate of the universe. EdC 14:53, 28 August 2006 (UTC)

text: Not as such; big bang cosmology is compatible with the universe being flat or open. EdC 03:09, 29 August 2006 (UTC)
thread_title:  {{Tl|Fact}} tag for Cosmology 

message: ∞/2 = ∞
*Is this logical or illogical? (Simonapro 09:32, 29 August 2006 (UTC)
replies: text: An example of cardinality and bijection from set theory might help. Consider N, the set of all naturals {0,1,2,3,...}, and E, the set of even naturals {0,2,4,6,...}. We can define a bijection between the two sets, f(e) = e/2, for every e in E. Clearly, every member e in E is mapped to a unique member e/2 in N. It's also clear that both E and N are infinite sets. So that's one way of thinking about ∞/2 = ∞. — Loadmaster 00:16, 31 October 2006 (UTC)
thread_title:  ∞/2 = ∞.  

message: 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.
::eh? 86.16.223.203 14:51, 25 October 2006 (UTC)
thread_title:  a strange varient 

message: 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)
replies: text: Fractal would be nice but I think Pi, like all irrational numbers, can be represented with infinite number of non-repeating decimals. So I'm not sure what you exactly mean by infinite scope of mathematical entities such as Pi.ExterayT.C 02:23, 13 September 2006 (UTC)

text: So, does 1/3 have "infinite scope" too? —Keenan Pepper 03:26, 14 September 2006 (UTC)

text: Well, there you go. —Keenan Pepper 01:52, 15 September 2006 (UTC)
thread_title:  Pi and Fractals 

message: I'd love to read about the fact that there are at least two kinds of infinites:
*one is that of natural numbers and rational numbers
*and the other is that of real numbers.
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)
replies: text: Look at Countable set.  I added the link to the article as well. CMummert 13:53, 25 October 2006 (UTC)

text: There are infinitely many different infinite cardinal numbers. The two you are referring to are aleph-null and the cardinality of the continuum. --Zundark 14:01, 25 October 2006 (UTC)

text: Hm. I don't think that works. Consider: the Cantor set is a disconnected dust but of cardinality C, while the rationals are dense on the reals but of cardinality \aleph_0. EdC 22:03, 31 October 2006 (UTC)
replies: text:  Cantor dust is a good counter-argument. It is also, if I'm not mistaken, non-integratable. But I don't think a countably dense set (the rationals) is a good counter-example to integration of a countinuous function. But I could be wrong. (Are there continuous functions, other than trivial ones like f(x)=1, that contain only rational values?) — Loadmaster 23:58, 6 November 2006 (UTC)
replies: text:  In the reals, no; but in the rationals f: \mathbb{Q} \rarr \mathbb{Q}: x \mapsto x is continuous, assuming the standard topology on \mathbb{Q}.  Similarly, the Lebesgue integral doesn't exist on \mathbb{Q}, but (I think) one can use the Daniell integral to construct an integral on \mathbb{Q}. EdC 12:05, 7 November 2006 (UTC)
replies: text: These seem to be special cases not usually encountered by calculus students. So I think my point is valid, that we can in general distinguish between countable infinite using summation and uncountable infinity using intgration. Even if it's not 100% technically correct, it can still be used to introduce the difference between the two types to beginner-level students. — Loadmaster 23:33, 7 November 2006 (UTC)
thread_title:  At least two different infinites in mathematics 

message: 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)
replies: text: One source for many of the equations is Affinely Extended Real Numbers from Wolfram MathWorld. -- Schapel 15:21, 15 November 2006 (UTC)
thread_title:  Source? 

message: 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?
* Hilbert's paradox of the Grand Hotel
:There is a bit of information at 0.999...#p-adic numbers and Infinity plus one. If you'd like detailed answers to your questions, this isn't the best forum; try Wikipedia:Reference desk/Mathematics. Melchoir 01:30, 13 December 2006 (UTC)
thread_title:  Unrelative infinity 

message: 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)
replies: text: Eh, delete it. It's better placed in the article on photographic lens. –EdC 05:04, 3 January 2007 (UTC)
thread_title: Photography/lens material in lead

message: 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????
:As with so many other things, this is context-dependent.  In the context of the extended real number line, 1/∞ is indeed zero. But you're correct that this means that, in that context, a/b=c no longer means exactly the same thing as a=bc. --Trovatore 19:01, 9 January 2007 (UTC)
thread_title:  one divinded into infinity does not equal 0! 

message: 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)
thread_title:  Introduction image 

message: 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)
thread_title:  Infinity and Ethics 

message: 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)
thread_title:  Symbol for infinity 

message: 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 , 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)
thread_title:  Lazy Eight in fields outside of Mathematics 

message: 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)
thread_title:  re: [[Octopus card#Name and logo]], [[∞]] and the [[Möbius strip]]. 

message: 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)
thread_title:  A "simple" example of positive and negative infinitely large numbers? 

message: 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)
thread_title: Expand this article

message: 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.
<BR>
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)
replies: text: Absolutely; IIRC cardinals express the intuition that the size of a set is unchanged if its elements are reordered; which is more obviously the case in some instances than in others.  But still, we don't want to get bogged down in detail; rigorous definition can be deferred to the appropriate articles. –EdC 22:22, 23 May 2007 (UTC)
thread_title:  Size and Cardinality