Related to Real Analysis course 6. Let f, 9 : R → R be continuous functions and defineS = {x € R: f(x) - g(x) € Z},where Z stands for the set of all integers. Let (r,) be a convergent sequence in S and let x =lim,+x *n. Can we say that a E S? Would your answer change if we replace Z with the set Q of allrational numbers? Justify your answer.

It is given that, f, g : ℝ → ℝ are the continuous functions. And, S = x∈ℝ : f(x)-g(x) ∈ ℤ. Let…

Answered: 6. Let f.g: RR be continuous functions…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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