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First of I am not a math guru, so it might be a dumb question, but today in the metro I was bored, and started thinking what is the last number of the infinity, and came up with this theory, that the last number is a "whole", it is exact opposite to zero/void.

An examples of Whole, can be a peak of sinusoid, a number "1" in the range between 0 and 1, etc... Whole is basically where mathematics ends, while zero is where mathematics are absent.

Actually I have no question, but just would like to here what bright folks have to say about this.


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closed as not a real question by t.b., Listing, yunone, Rasmus, Willie Wong Jul 10 '11 at 14:35

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

As you said this is not a real question, therefore I voted to close. You should also make sure to check the related answers, infinity seems so fascinating that people ask about it every few days. If it is an odd number, whether it exists, and many more... –  Listing Jul 10 '11 at 8:44
There's enough of a hint at ordinals here that I think it makes sense to answer the question to support the OP in his thoughts -- I vote not to close. (That means the next close vote should be written here as a comment instead of a "real" vote, and cancels my vote.) –  joriki Jul 10 '11 at 8:47
I'm afraid your post doesn't make sense. What does "last number of the infinity" mean? What does it mean for math to "end" or "be absent", much less for "zero" or "Whole" to be where that occurs? Furthermore, as stated in the FAQ, if you don't have a well-defined, specific question, your post is not appropriate here. –  Zev Chonoles Jul 10 '11 at 8:48
@joriki: I was just about to close the question, but I will refrain if you feel you can give a productive answer. I am turned off by the OP's admission that he has no question. –  Zev Chonoles Jul 10 '11 at 8:49
I have a question too, but I dont know if its worthy here: Does math need the concept of infinity? What if every time you take the limit as x->inf instead use lim y->0 with x=1/y,is there anywhere in math a theorem cant be proved without a concept of infinity? –  user1708 Jul 10 '11 at 8:55

2 Answers 2

up vote 6 down vote accepted

Though the question is somewhat vague and open-ended (there's already a close vote after two minutes), there's one sense in which your ruminations correspond to something rigorous in mathematics. In studying infinity, mathematicians have come up with classifying different kinds of infinity which can be compared and sometimes even added and multiplied much like numbers. There are two different such classifications; in both of them, different kinds of infinity are treated as generalizations of the natural numbers. Cardinal numbers generalize the aspect of numbers that you can use them to count sets of things to measure their size (cardinality), and ordinal numbers generalize the aspect of numbers that you can use them to count things to put them in a certain order. Ordinal numbers are defined such that each ordinal number is the set of all ordinal numbers preceding it. (If that sounds rather abstract to you, that's because it is. :-) So your idea of "the last number of infinity" being "a whole" is actually not terribly far away from how the first infinite ordinal number is defined: it is precisely the "whole" set of all natural numbers, and in a sense it's the number that comes "at the end" of all of the natural numbers. However, it's not the last one by far -- in mathematics, there's an infinite hierarchy of ever-ascending infinities!

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its a good point about ever-ascending infinities, actually I thought about that too, that when you reach the infinity, your start all over again. In that sense, universe is counting till infinity, through time period it tries to gather all mass, reaches a tipping point, where all the physics laws stops existing and the next thing is "big bang" a start of ride down –  spacemonkey Jul 10 '11 at 9:28
@spacemonkey: Nowhere in joriki's post was any mention of the universe, physics, or existence. The fact that humans have decided to make certain definitions does not imply anything about reality. –  Zev Chonoles Jul 10 '11 at 11:25

Your theory of peak of a sinusoid's "whole" being equal to 1 reminds me of the supremum of a set. It seems like you are describing the edge of a bound, i.e., where the set $[0,1]$ "ends". Mathematicians generally don't think of this concept as "infinite", we are not generally concerned with boundaries when we think of infinity.

As joriki mentioned, there is a hierarchy of infinities and Cantor's theorem demonstrates that no matter which infinity you've got, you can always generate a bigger one. However, sometimes mathematicians like to think about infinities greater than those that can be proved to exist using the standard language.

To talk about them, all they do is simply extend their language to discuss these "bigger" infinities. They call these infinities large cardinals, and they are used in various (very advanced) areas of set theory.

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