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> But "even" and "odd" are all about whether you can partition something into an equal number of pairs or not.

Sez you. I can just as easily define even and odd in terms of whether or not I can arrive at a given position in a (potentially infinite) sequence taking by taking two steps at a time.



Of course you cannot actually end up at ω by taking two steps at a time, but your point is still well taken.


Yes, I know. ω is odd :-)




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