[math-fun] Comparing sizes of sets of natural numbers

I'd welcome math-funsters' comments on http://mathoverflow.net/questions/248994/comparing-sizes-of-sets-of-natural-... . Teaser: The size of {0,2,4,6,...} exceeds the size of {1,3,5,7,...} by exactly 1/2. "From a certain point of view." Jim Propp