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.
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)
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.