Any of you q-hackers know how to use theta-function asymptotics to prove that (q^0+q^1+q^3+q^6+...) - (sqrt(2))(q^0+q^1+q^4+q^9+...) converges to (sqrt(2))/2 as q goes to 1 from the left? (I'm interested in the other two as well, but this struck me as the hardest of the trio.) Are there places where the relevant expansions can be found? Jim Propp On Sunday, September 4, 2016, James Propp <jamespropp@gmail.com> wrote:

I'd welcome math-funsters' comments on http://mathoverflow.net/questions/248994/comparing- sizes-of-sets-of-natural-numbers .

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