User blog comment:Vel!/Hilbert ITTMs/@comment-10429372-20140724163701/@comment-10429372-20140724181958

Can you proof that there are Beth_1 functions from {0,1} to Z? I thought the following:

We can pick Beth_0 values for f(0), and Beth_0 values for f(1), so there are total Beth_0^2=Beth_0 functions from {0,1} to Z.

However there are Beth_1 functions form Z to {0,1}.