Recent content by Bedrich

Thank you very much, but is it proving that ##f## is totally computable? Not just partialy computable?

I would keep running ##g(n)## for every possible ##n## (##g(3), g(4), g(5)##...) until an output pair would be ##(42, y)##.

For every pair ##(x, y)## check if that pair is in the graph and if yes, then ##y## of that pair is ##f(n)##? If that is not nonsence.

Hello, I'm trying to prove following problem. 1. Homework Statement Graph of function ƒ : ℕ→ℕ is set {(x, ƒ(x)), x ∈ ℕ and ƒ(x) ≠ ⊥} ⊆ ℕ2. Prove that function ƒ is totally computable when ƒ(x) is defined for every x ∈ ℕ and his graph is recursively enumerable set Homework Equations The...

Thank you for your answer. Can you please clarify the examples of functions. I can't really imagine how they could prove that ƒ-1 is recursively enumerable. There is nothing said about that functions from ℕ → ℕ have computable inverses.

Hello, I am stuck on deciding if given sets are recursive or recursively enumerable and why. Those sets are: set ƒ(A) = {y, ∃ x ∈ A ƒ(x) = y} and the second is set ƒ-1(A) = {x, ƒ(x) ∈ A} where A is a recursive set and ƒ : ℕ → ℕ is a computable function. I am new to computability theory and any...