Call a function f :N - N eventually nondecreasing if the set decr(f) {n eN|S(n+1) < f(n)} is finite. Prove: If f : N N is computable and eventually nondecreasing, then range f is decidable.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 51E
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Call a function f :N N eventually nondecreasing if the set
decr(f) = {n EN| f(n+1) < f(n)}
is finite. Prove: If f : N N is computable and eventually nondecreasing, then range f is
decidable.
Transcribed Image Text:Call a function f :N N eventually nondecreasing if the set decr(f) = {n EN| f(n+1) < f(n)} is finite. Prove: If f : N N is computable and eventually nondecreasing, then range f is decidable.
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