Question about infinity

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A 6 year old with autism who my sister knows keeps asking if infinity is even or odd. Does anybody know?

I personally can't visualize how it could be either, but I really don't know and I've never really thought about it before.

"Infinity" never ends, so I don't believe it can't be determined whether it is an odd or even number. In fact, I don't believe it is even a "number" in the absolute sense.

I'm sure mathematicians will chime in soon.

That's exactly what I've been thinking. If it doesn't end then it wouldn't end on an odd or even number, right? Yet for some reason there is something nagging in the back of my head that says infinity is even, but I have no idea how that thought could be in my head.

I guess we'll just wait for the mathematicians.

Infinity is an even number. A definition of even numbers is a number with no remainder when divided by 2.

10/2 = 5 + Remainder 0 (even)
7/2 = 3 + Remainder 1 (odd)

You can therefore define infinity because:

infinity/2 = infinity + Remainder 0 (even)

But isn't it true that one doesn't actually know the "number" which infinity represents?

I guess this means that it's an even number by default.

Infinity is not a number. It really means "unbounded" -- that is, there is no limit.

Suppose that infinity is a number. Assign X to be infinity. Then since X is a number, then X+1 exists and is also a number. However, then X cannot be infinity.

Thus infinity is not a number. Since infinity is not a number, it is neither even nor odd.

This. Infinity is, for some purposes, treated as a 'quasi-number', but it is not formally a number and shouldn't be thought of as one, but rather the lack of a limit.