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Prove that the following functions are computable. n-m if nm (a) -:IN² →→ IN defined by n- m:= 0 (b) Rem : N² → N defined by Rem(n,m) := the unique r € {0,1,...m – 1} such that n = q • m+r if m #0; otherwise, Rem(n, m) := 0. otherwise.

Prove that the following functions are computable. n-m if nm (a) -:IN² →→ IN defined by n- m:= 0 (b) Rem : N² → N defined by Rem(n,m) := the unique r € {0,1,...m – 1} such that n = q • m+r if m #0; otherwise, Rem(n, m) := 0. otherwise.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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Prove that the following functions are computable. -{"- n-m if n>m otherwise. 0 - - : N² → N defined by n-m := (a) : N². (b) Rem : N² → N defined by Rem(n, m) := the unique r = {0, 1,...m-1} such that n = q · m +r if m # 0; otherwise, Rem(n, m) := 0.
Transcribed Image Text:Prove that the following functions are computable. -{"- n-m if n>m otherwise. 0 - - : N² → N defined by n-m := (a) : N². (b) Rem : N² → N defined by Rem(n, m) := the unique r = {0, 1,...m-1} such that n = q · m +r if m # 0; otherwise, Rem(n, m) := 0.
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