Prove that a nonzero number and its reciprocal have the same sign.

by RoRi

June 30, 2015

If $a \neq 0$ , then $a$ and $1/a$ have the same sign.

Proof.
First, since $a \neq 0$ , we know $1/a$ exists and $a(1/a) = 1 > 0$ . By Theorem I.24, this means $a$ and $1/a$ are both positive or both negative $. \qquad \blacksquare$

Stumbling Robot

Prove that a nonzero number and its reciprocal have the same sign.

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