Is infinity even or odd?

Icebreaker

Is infinity even or odd? If it's even (or both), then it would mean there's a finitely largest prime.

By coarsely applying limit concepts, and lim(x->inf)x/2 does not yield a remainder.

cepheid

I'm no math Phd, but I do know this: infinity is not a number!

z-component

Infinity isn't a number; it's a concept used in mathematics.

Icebreaker

So, what, we can assume that there will ALWAYS be larger primes?

cepheid

You shouldn't assume anything in math. I seem to remember seeing a proof of that somewhere, but I can't remember any of the details. My memory could be wrong. Surely somebody will know though...

Hurkyl

Suppose there are finitely many primes. Can you find a number divisible by all of them? Can you find a number not divisible by any of them?

Chronos

Interesting. Is hydrogen male or female? The answer is similar.

Icebreaker

Wouldn't the question be: suppose there are finitely many primes, can a combination of their products be used to construct any integer?

Hurkyl

Would the answer to this answer your version?

mathwonk

infinity = 2 times infinity, hence infinity is even, which may seem odd.

shmoe

It's even odder since infinity=2*infinity+1, hence it's odd as well as even. (joking )

Seriously though, infinity is not a number that you can perform arithmetic with. You can add it to the reals and make what's often called the extended reals, but don't expect it to play nice with the rest of the numbers. Certainly don't expect it to have any nice properties like even or odd.

Icebreaker

What is the answer?

matt grime

Not every number can be formed from a product if primes if there were only a finite number of them: multipply them all together and add 1.

shmoe

The answer is yes. If you can find a number not divisible by all the primes, then you would have found a number that is not a combination of their products.

Suppose their are finitely many primes, [itex]p_1,p_2,\ldots,p_n[/itex]. Then consider their product [itex]M=p_{1}p_{2}\ldots p_{n}[/itex]. Then M is divisible by all the primes. This answers Hurkyl's first question (from post#6). Can you use it to answer the second?

edit:I type slower than matt!

moving finger

In another thread on this forum I've seen posts claiming that an integer cannot be infinite (ie only finite integers are allowed).

See http://www.physicsforums.com/showthr...006#post478006

Any thoughts on this subject anyone?

If an infinite integer is allowed, then it must also have an infinite number of digits, right?

matt grime

They aren't elements of [tex]\mathbb{Z}[/tex] or [tex]\mathbb{N}[/tex] by definition so your argument is baseless.

You are saying: if we assume that when cantor said the natural numbers he actually meant something entirely different then his argument is wrong. As he didn't mean something entirely different his argument is correct and you are wrong.

evthis

infinity is a description not a numerical value and since only numerical values can be odd or even, infinity is neither.