Re:Is infinity an odd or even number? (2011)
by adverbly on Tuesday May 02, 2023 @02:43PM
(#35792286)
> we can...prove infinity is even....and prove infinity is odd...
> maybe I'm missing something
The answer said:
> the usual definition is that an ordinal number 𝛼 is even if... Otherwise, it is odd.
In other words, if a number could be proved to be even, it is even. If not, it is odd.
Using their definition, there is no such thing as "proving a number is odd". You'd have to do it by failing to prove it's evenness. In the case of infinity, because we can successfully prove evenness, it's even and not odd.
> maybe I'm missing something
The answer said:
> the usual definition is that an ordinal number 𝛼 is even if... Otherwise, it is odd.
In other words, if a number could be proved to be even, it is even. If not, it is odd.
Using their definition, there is no such thing as "proving a number is odd". You'd have to do it by failing to prove it's evenness. In the case of infinity, because we can successfully prove evenness, it's even and not odd.