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The UTM theorem
Let ℕ denote the set of natural numbers. Let A × B denote the Cartesian product of A and B. Let A ⇀ B denote the set of partial functions from A to B.
The UTM theorem says that there exists a computable function u : ℕ × ℕ ⇀ ℕ such that, for every computable function f : ℕ ⇀ ℕ, the...