Let $x\in\mathbb{R}$ and assume that for all $\epsilon > 0$, $|x|< \epsilon$. Prove that $x = 0$. Use a proof by contradiction.

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score 1 · Answer 1 · answered Feb 16 '17 at 06:55

1

Suppose $x\neq0$ and take $\epsilon=\frac{\vert x\vert}{2}$. Then you see that $\vert x\vert\ge\epsilon$ (and even $>$).

Hence $x=0$.

answered Feb 16 '17 at 06:55

Adren

1 Answers1