(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

d) Show that [itex]\left|x-y\right| \leq \left|x\right|+\left|y\right|[/itex]

e) Show that [itex]\left|x\right|-\left|y\right| \leq \left|x-y\right|[/itex]

3. The attempt at a solution

For item d) I've tried some approaches but none was promising.

For item e), I tried squaring [itex]\left|x-y\right|[/itex] to get

[itex](\left|x-y\right|)^{2} \geq (\left|x\right|-\left|y\right|)^{2}[/itex]

But if I take the square roots, the right side may not always be positive, then I don't have a proof, right?

Thanks

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# Homework Help: Spivak 1-12de (inequalities)

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