>So it should be possible to define f() and g() such that neither of those are computable, but the truth of f(x) < g(x) is computable, but not so much for f(x)

>So it should be possible to define f() and g() such that neither of those are computable, but the truth of f(x) < g(x) is computable, but not so much for f(x) < g(y). The difficulty is really just defining an uncomputable function that has a definite value for some domain, but this can be done. Let's call one h. f(x): -abs(h(x)) g(x): -f(x) Gives your second inequality.