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Prove : If $a < b$ then $-b < -a$

My proof :

$a + (-b) < b + (-b) $

$a - b < 0$

$a - b + (-a) < 0 + (-a)$

$a + (-a) -b < -a$

$-b < -a$

Is my proof correct?

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    $\begingroup$ It looks fine to me. $\endgroup$ May 25 '20 at 7:36
  • $\begingroup$ well yea it's totally correct $\endgroup$
    – Mathsisfun
    May 25 '20 at 8:03
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Direct alternative proof.
$a < b $
$-a + a - b < -a + b - b $
$-b < -a$

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