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Is infinity an odd or even number? (2011)

math.stackexchange.com

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Re: Is infinity an odd or even number? (2011)

#71

Post by amelius »

dkarl wrote: post #55
irrational wrote: post #14

>To explain the idea to a child, I would focus on the principal idea: whether finite or infinite, a number is even when it can be divided into pairs. For finite sets, this is the same as the ability to divide the set into two sets of equal size, since one may consider the first element of each pair and the second element of each pair. The answer this quote came from is amazingly obtuse, but it does make me think that…

In mathematics, you can define things in different ways to get different answers. Ways of defining things tend to be highlighted as true (in at least some context) if they are interesting and useful, and ignored if not. I don't think the definition based on "dividing into pairs" is particularly interesting or useful in the context of the child's understanding of numbers, because it's too vague to be useful, and it do…

An even more honest thing to say is that infinity when used as a number is a hack introduced by mathematicians to make notation and reasoning simple in some cases, but that it can be dangerous in other cases, like any other hack. If you want to use infinity in a safe way, then use limits around your expressions.

(And this quickly resolves the case of this article, since lim x->inf x-2*floor(x/2) does not exist).

Re: Is infinity an odd or even number? (2011)

#72

Post by bhk »

alexb_ wrote: post #12
warent wrote: post #10

In my experience with children, one of the easiest-to-grasp concepts of infinity is provided by the transfinite ordinals, since it can be viewed as a continuation of the usual counting manner of children, but proceeding into the transfinite: 1,2,3,⋯,ω,ω+1,ω+2,⋯,ω+ω=ω⋅2,ω⋅2+1,⋯,ω⋅3,⋯,ω2,ω2+1,⋯,ω2+ω,⋯⋯ Presumably this person has no experience with 6 year olds? This explanation is horrendous haha

No it isn't. If you ask a child what comes after infinity, "Infinity + 1" is pretty much the default answer. Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". The answer of "Infinity TIMES Infinity" is also popular for kids to say when they know a number bigger than their friend (who just proclaimed infinity is the largest number).

I thought that most of us learn at an early age, as a result of this kind of exchange, that "infinity" is not "the biggest number" or even a number at all, as far as the ordinary notion of "number" goes.

Re: Is infinity an odd or even number? (2011)

#73

Post by anotherhue »

alexb_ wrote: post #12
warent wrote: post #10

In my experience with children, one of the easiest-to-grasp concepts of infinity is provided by the transfinite ordinals, since it can be viewed as a continuation of the usual counting manner of children, but proceeding into the transfinite: 1,2,3,⋯,ω,ω+1,ω+2,⋯,ω+ω=ω⋅2,ω⋅2+1,⋯,ω⋅3,⋯,ω2,ω2+1,⋯,ω2+ω,⋯⋯ Presumably this person has no experience with 6 year olds? This explanation is horrendous haha

No it isn't. If you ask a child what comes after infinity, "Infinity + 1" is pretty much the default answer. Any kid who knows multiplication knows "Infinity + Infinity" is the same as "Infinity Times Two". The answer of "Infinity TIMES Infinity" is also popular for kids to say when they know a number bigger than their friend (who just proclaimed infinity is the largest number).

One of my favourite SMBCs: https://www.smbc-comics.com/comic/2014-02-16

Re: Is infinity an odd or even number? (2011)

#74

Post by Sharlin »

have_faith wrote: post #22

In JavaScript we're spoiled by having both. There's Number.NEGATIVE_INFINITY and Number.POSITIVE_INFINITY.

Those are simply the bog-standard IEEE/IEC.754 floating point infinities, so they're the same thing in essentially every mainstream language.

Re: Is infinity an odd or even number? (2011)

#75

Post by version_five »

warent wrote: post #10

In my experience with children, one of the easiest-to-grasp concepts of infinity is provided by the transfinite ordinals, since it can be viewed as a continuation of the usual counting manner of children, but proceeding into the transfinite: 1,2,3,⋯,ω,ω+1,ω+2,⋯,ω+ω=ω⋅2,ω⋅2+1,⋯,ω⋅3,⋯,ω2,ω2+1,⋯,ω2+ω,⋯⋯ Presumably this person has no experience with 6 year olds? This explanation is horrendous haha

Also my first thought. I assume he's writing this to other people who know what transfinite ordinals are (I don't understand the explanation) and would frame it differently with an actual kid. Even in context it's a hilarious quote though, I think it's possible this was on purpose

Re: Is infinity an odd or even number? (2011)

#76

Post by Cruncharoo »

bitL wrote: post #41

I really hate these mathematical technicalities spawned from material implication, chosen way of making a definition and vacuous truth - why can't we even consider some questions to be marked as non-sense/non-relevant like in relevance logic?

Not to be obtuse but isn't all of mathematics spawned from a chosen way of making a definition and vacuous truth?

Re: Is infinity an odd or even number? (2011)

#78

Post by ndsipa_pomu »

jstimpfle wrote: post #66
compressedgas wrote: post #23

Infinity is equal to the product of all the primes. It is even because it has 2 as a factor.

I find that primes are an odd thing to bring into the discussion, not even mildly relevant.

More worryingly, it raises the question of whether infinity is prime.

I suppose that if it's even, then it won't be prime, but then again infinity/2 is still infinity so we can't assume that division works the same way.

Re: Is infinity an odd or even number? (2011)

#80

Post by ftxbro »

Eisenstein wrote: post #9

I want to know if there are more decimal numbers between 0 and 1 than there are integers between 0 and infinity.

If you thought of this question from no real math training then that's pretty interesting. You should have been a mathematician. Your question is one of the most important and concisely stated questions about infinity that you can ask!
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