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Comment by marzell | Hacker News Reader

infinity is not a number.

It is a transfinite ordinal number, and the linked text explains how "even" and "odd" are defined for those.

"Infinity is a transfinite ordinal number" is a lot more definitive of a claim than you can justify making. There are different systems and they use different infinite quantities. Nonstandard analysis doesn't bother with ordinal numbers, but it has plenty of infinite numbers.

"Infinity" without further specification seems more likely to refer to the concept in the extended reals (where there are exactly two infinite numbers) than to refer to the concept of infinite ordinal numbers. The obvious analysis would appear to be that, not being an integer, it cannot be considered either even or odd, but there might be a convention I don't know about.

Since most reals are not either even and odd, I don’t know why you find the extended reals the more likely interpretation of “infinity” in the context of that question. In any case, the GGP objected to infinity being a number, but however you slice it, it is either an ordinal or cardinal number. And the GGGGP claimed that infinity is both even and odd, but however you slice it, it is at most one of those. I found it being either even or odd, as in the ordinals, more interesting, that’s why I gave that link.

> I don’t know why you find the extended reals the more likely interpretation of “infinity” in the context of that question.

Simple, that's the only sense of "infinity" that most people know.

On the other hand, typeof NaN === 'number'

Is it? To me it's more like a concept.

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