Problem 21. Prove that a real number y is computable if and only if there is a computable function f : Z+ → {0, 1} such that a(f(0)f(1)f(2)...) = y mod 1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
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Problem 21. Prove that a real number y is computable if and only if there is a computable function
f : Z+ → {0, 1} such that
x(f(0)f(1)f(2)....) = y mod 1.
Transcribed Image Text:Problem 21. Prove that a real number y is computable if and only if there is a computable function f : Z+ → {0, 1} such that x(f(0)f(1)f(2)....) = y mod 1.
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