6. Let f,g: R→ R. be continuous functions and define S = {r ER: f(x) = g(x) = Z}, where Z stands for the set of all integers. Let (n) be a convergent sequence in S and let z = limn→∞ n. Can we say that ES? Would your answer change if we replace Z with the set Q of all rational numbers? Justify your answer.
6. Let f,g: R→ R. be continuous functions and define S = {r ER: f(x) = g(x) = Z}, where Z stands for the set of all integers. Let (n) be a convergent sequence in S and let z = limn→∞ n. Can we say that ES? Would your answer change if we replace Z with the set Q of all rational numbers? Justify your answer.
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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