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An Absolutely Trivial Inequality

In this post I will talk about the absolutely trivial inequality

x|x|.

This is easily seen. If x is positive, it is equal to its absolute value. If it is negative, it is of course less than its absolute value.

I have to admit that I probably didn’t understand the reverse triangle inequality

||x||y|||xy|

or at least I definitely did not think it through. But actually, as a weaker inequality,

|x||y||xy|.

Had I realised this sooner I probably would have spent less time banging my head against a simple problem.

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