- #1

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## Homework Statement

abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement

## Homework Equations

Triangle inequality?

## The Attempt at a Solution

I have nothing :/

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- Thread starter lepton123
- Start date

- #1

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abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement

Triangle inequality?

I have nothing :/

- #2

UltrafastPED

Science Advisor

Gold Member

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So make a table with all of the possible cases and see what happens!

- #3

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- #4

UltrafastPED

Science Advisor

Gold Member

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So once you have carried out the detailed work you can apply your own standards of elegance and cleverness ... and write something elegant!

- #5

verty

Homework Helper

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- #6

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x + y + z <= |x| + |y| + |z|

- x - y - z <= |x| + |y| + |z|

(definition of the absolute value)

- x - y - z <= |x| + |y| + |z|

(definition of the absolute value)

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