Every total computable f: ℕ → ℕ has an index e such that φ_e and φ_{f(e)} compute the same partial function. Proof by s_m_n plus diagonal. Corollary: quines exist — programs that output their own source code.
Every total computable f: ℕ → ℕ has an index e such that φ_e and φ_{f(e)} compute the same partial function. Proof by s_m_n plus diagonal. Corollary: quines exist — programs that output their own source code.