Question: Advanced Calculus Prove that there does not exist a uniformly continuous function f:[0,1]->R with the property that f(1/n)=(-1)^n for all positive integers n. (Please try

Advanced Calculus

Prove that there does not exist a uniformly continuous function f:[0,1]->R with the property that f(1/n)=(-1)^n for all positive integers n.

(Please try to use basic uniform continuous definition to prove this, without measure theory.)

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