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Let A be a set and let a € A. Suppose that f: A→ A satisfies (a) a = f (a), (b) if x Ey then f (x) = f (y), for all x and y in A. Let hw→A be as stated in Recursion Theorem. Prove that h (n) = h (n+) for all n E w.

Let A be a set and let a € A. Suppose that f: A→ A satisfies (a) a = f (a), (b) if x Ey then f (x) = f (y), for all x and y in A. Let hw→A be as stated in Recursion Theorem. Prove that h (n) = h (n+) for all n E w.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...
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Let A be a set and let a € A. Suppose that f: A→ A satisfies (a) a ≤ f (a), (b) if x Ey then f (x) = f (y), for all x and y in A. Let hw→A be as stated in Recursion Theorem. Prove that h (n) ≤ h (n+) for all n E w.
Transcribed Image Text:Let A be a set and let a € A. Suppose that f: A→ A satisfies (a) a ≤ f (a), (b) if x Ey then f (x) = f (y), for all x and y in A. Let hw→A be as stated in Recursion Theorem. Prove that h (n) ≤ h (n+) for all n E w.
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