Question Number 193078 by Mastermind last updated on 03/Jun/23
$$\left.\mathrm{1}\right)\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\varepsilon>\mathrm{0}\:\mathrm{and}\:\mathrm{a},\mathrm{x}\in\mathbb{R},\:\mathrm{then} \\ $$$$\mid\mathrm{a}−\mathrm{x}\mid<\varepsilon\:\mathrm{iff}\:\mathrm{x}−\varepsilon<\mathrm{a}<\mathrm{x}+\varepsilon \\ $$$$ \\ $$$$\mathrm{help} \\ $$
Answered by Subhi last updated on 03/Jun/23
$$−\epsilon<{a}−{x}<\epsilon \\ $$$${x}−\epsilon<{a}<{x}+\epsilon \\ $$