hi, I stumbled upon a simple demonstration but i can´t solve it:
||z|-|w|| <= |z-w|
Can someone help me?
The fact is, that any nonnegative number is equal to its absolute value. So if , then .
However, any negative number is less than its absolute value (since the absolute value is always nonnegative). So if , then .
So that means for any that .
A similar argument works the other way to show .
So that means .