- #1
carlosbgois
- 68
- 0
Homework Statement
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]
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