Infinity isn't a number, but it is an ordinal (and the answer does mention how you can have an even/odd property on the ordinals)

The difference, explained by ChatGPT:

A number is a mathematical concept used to represent a quantity or value. Numbers can be whole numbers (integers), fractions, decimals, or even complex numbers, and they are used in various mathematical operations like addition, subtraction, multiplication, and division.

On the other hand, an ordinal is a term used to indicate the position or order of an element within a set or a sequence. Ordinals are generally expressed using words like first, second, third, or numerals with suffixes like 1st, 2nd, 3rd, etc. Ordinals are used to describe the rank or placement of an item in relation to others, rather than representing a specific quantity or value like numbers do.

In summary, numbers represent a quantity or value, while ordinals represent a position or rank in a sequence.

Which is also incorrect. See https://en.wikipedia.org/wiki/Ordinal_numeral vs https://en.wikipedia.org/wiki/Ordinal_number.

Cardinal numbers (size) and ordinal numbers (ordering) are both numbers. The numbers we're familiar with represent both concepts, sometimes simultaneously.

I really don't think that block quoting ChatGPT is a good contribution.

> I really don't think that block quoting ChatGPT is a good contribution.

It's the first time I've done it. I agree with you. But didn't know until I tried!

I agree. It's an interesting intellectual exercise, but I am not sure if we would miss out on anything if we just had a symbol(s) for specific really large discrete numbers.

Sometimes I wonder if there's a better math language waiting to be invented that eschews the non-discrete.

There is a definition for an infinite ordinal, omega.

https://en.wikipedia.org/wiki/Ordinal_number

The concept of "number" has a lot of definitions in mathematics. I agree with this [0] more in depth explanation that calling infinity strictly not a number is not useful (though it certainly is not e.g. a natural number). But more importantly, the concept of evenness readily generalizes to ordinals, so as long as we specify that we are in (or move into) that context, then the question is well formed and interesting.

[0]: https://math.stackexchange.com/a/36298