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1-Prove-that-if-gt-0-and-a-x-R-then-a-x-lt-iff-x-lt-a-lt-x-help-

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Question Number 193078 by Mastermind last updated on 03/Jun/23
1) Prove that if ε>0 and a,x∈R, then ∣a−x∣<ε iff x−ε<a<x+ε help
1)Provethatifε>0anda,x∈R,then∣a−x∣<εiffx−ε<a<x+εhelp
Answered by Subhi last updated on 03/Jun/23
−ε<a−x<ε x−ε<a<x+ε
−ϵ<a−x<ϵx−ϵ<a<x+ϵ

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