How do I prove $| x | - x \neq 0$ $|x|-x!=0$ ?

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Answer 1 · 2018-02-09T15:26:20

For $x \geq 0 :$ $x>=0:$

$| x | - x = x - x = 0$ $|x|-x=x-x=0$ wrong

For x<0:

$| x | - x = - x - x = - 2$ $|x|-x=-x-x=-2$ rignt

Then $| x | - x \neq 0 \forall x < 0$ $|x|−x≠0 AA x<0$

or $\exists x : | x | - x = 0$ $EE x: |x|−x=0$

How do I prove |x|−x≠0|x|-x!=0 ?