Comment by ridiculous_fish

I have no background in combinatory logic, and so I've predictably never understood fixed-point combinators:

1. Every function has a fixed point.

2. A fixed-point combinator will compute it.

So what is the fixed point of f(x) = x + 1?

Also why doesn't this give us mathematical superpowers? Define f(x) = x iff x is a non-trivial zero of the Riemann zeta function...