let's have a computable binary function $\phi_e(x,y)$, from the canonical ordering. Is it possible to have such $e$, that $\phi_e(x,y)=\phi_x(y)$?
2026-03-29 08:13:33.1774772013
Is it possible for a binary computable function to "execute" an unary computable function?
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That the answer is yes is the statement of the Universal Turing Machine (UTM) theorem. The indices $e$ with this property are exactly the indices of UTMs.