prove-that-if-x-1-x-0-then-x-1-

Question Number 75936 by Rio Michael last updated on 21/Dec/19

p r o v e t h a t i f [\frac{x + 1}{x}] = 0 t h e n x ⩽ - 1

Commented by turbo msup by abdo last updated on 21/Dec/19

[\frac{x + 1}{x}] = 0 \Rightarrow [1 + \frac{1}{x}] = 0 \Rightarrow

1 + [\frac{1}{x}] = 0 \Rightarrow [\frac{1}{x}] = - 1 \Rightarrow

- 1 ⩽ \frac{1}{x} < 0 \Rightarrow 0 < - \frac{1}{x} ⩽ - 1 \Rightarrow

\Rightarrow - x ⩾ - 1 \Rightarrow x ⩽ - 1

Commented by Rio Michael last updated on 21/Dec/19

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