hi, I stumbled upon a simple demonstration but i canīt solve it:

||z|-|w|| <= |z-w|

Can someone help me?

Pedro

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- Nov 24th 2010, 02:24 PMPedroProving ||z|-|w|| <= |z-w|
hi, I stumbled upon a simple demonstration but i canīt solve it:

||z|-|w|| <= |z-w|

Can someone help me?

Pedro - Nov 24th 2010, 02:29 PMProve It
- Nov 24th 2010, 03:25 PMPedro
ok, thank you!

- Nov 25th 2010, 07:37 AMPlato
This proof relies on this fact: .

So

Likewise

Thus we now have

Can you use the*fact*to finish? - Nov 27th 2010, 03:07 PMrcs
i understood what is discussed above... but i would like know how to explain and admit that

-|a| ≤ a ≤ |a|

and

-|b| ≤ b ≤ |b|

can anybody help me to prove this?

all i know is that a negative is of course less than a positive number - Nov 27th 2010, 03:35 PMPlato
**Please start a new thread for any new question.**

You said that you understand that

If you do, can we say that

If so then is it not true that - Nov 27th 2010, 04:33 PMProve It
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 . - Nov 27th 2010, 10:16 PMrcs
thanks you! so same in the -|b| ≤ b ≤ |b|.