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Solved: Prove that given a real number x there exist
Chapter 8, Problem 21E(choose chapter or problem)
QUESTION:
Problem 21E
Prove that given a real number x there exist unique numbers n and ϵ such that x = n – ϵ, n is an integer, and 0 ≤ ϵ<1.
Questions & Answers
QUESTION:
Problem 21E
Prove that given a real number x there exist unique numbers n and ϵ such that x = n – ϵ, n is an integer, and 0 ≤ ϵ<1.
ANSWER:
Solution:
Step1
Given that
We have to prove that given a real number x there exist unique numbers n and ϵ such that x = n – ϵ, n is an integer, and 0 ≤ ϵ<1.
Step2