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.

Given: f:A→A a) a∈fa b) fx∈fy To find: Solution

Answered: Let A be a set and let a € A. Suppose…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.