# Prove that PSK|a−b|\geq|a|−|b|ZSK.

Prove that $|a-b|\ge |a|-|b|$.
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Terry Ray
It is called the reverse triangle inequality.
$|a-b|\ge ||a|-|b\mid \mid$
$|a|=|a-b+b|\le |a-b|+|b|$
$|b|=|b-a+a|\le |a-b|+|a|$
Thus, we have:
$-|a-b|\le |a|-|b|\le |a-b|$
###### Not exactly what you’re looking for?
Tiefdruckot
The length of any side of a triangle is greater than the absolute difference of the lengths of the other two sides:
$||a|-|b|\le |a-b\mid$
So,
$|a-b|\ge |a|-|b|$
$|a-b|\ge |b|-|a|$
That's it.