It's worded confusingly; it certainly can be that `S` has an even number of elements. (For a silly example, if `f(S) = 1` identically, then `f(∅) = 1` even tho

It's worded confusingly; it certainly can be that `S` has an even number of elements. (For a silly example, if `f(S) = 1` identically, then `f(∅) = 1` even though `∅` has an even number of elements.) What cannot be is that `f(S) = 1` is equivalent to `S` having an even number of elements (because, as the sibling thread https://news.ycombinator.com/item?id=23967766 https://news.ycombinator.com/item?id=23967766 by @ColinWright points out, that is not a monotone property … unless `n = 0`!)