3 ms·

It isn't clear to me infinity is a number in the first place. Reification and category mistakes are as much a danger in math as anywhere.

snotrockets 4y ago
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)
- breck 4y ago
  [flagged]
  - yjk 4y ago
    Which is also incorrect. See https://en.wikipedia.org/wiki/Ordinal_numeral https://en.wikipedia.org/wiki/Ordinal_numeral vs https://en.wikipedia.org/wiki/Ordinal_number https://en.wikipedia.org/wiki/Ordinal_number.
  - NegativeK 4y ago
    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.
    - breck 4y ago
      > 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!
breck 4y ago
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.
paulddraper 4y ago
There is a definition for an infinite ordinal, omega. https://en.wikipedia.org/wiki/Ordinal_number https://en.wikipedia.org/wiki/Ordinal_number
r0uv3n 4y ago
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 https://math.stackexchange.com/a/36298

snotrockets 4y ago

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)

breck 4y ago
[flagged]
- yjk 4y ago
  Which is also incorrect. See https://en.wikipedia.org/wiki/Ordinal_numeral https://en.wikipedia.org/wiki/Ordinal_numeral vs https://en.wikipedia.org/wiki/Ordinal_number https://en.wikipedia.org/wiki/Ordinal_number.
- NegativeK 4y ago
  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.
  - breck 4y ago
    > 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!

breck 4y ago

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.

paulddraper 4y ago

There is a definition for an infinite ordinal, omega. https://en.wikipedia.org/wiki/Ordinal_number https://en.wikipedia.org/wiki/Ordinal_number

r0uv3n 4y ago

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 https://math.stackexchange.com/a/36298