Absolute inequalities

  • #1

Main Question or Discussion Point

prove the folowing and state when the inequality holds...

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

i was thinking that i consider all the possible cases, ie x is positive, y positive, z positive; then the various combinations with negative as well.....
is there another shorter method of doing it?
help.....
 

Answers and Replies

  • #2
mathman
Science Advisor
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You can start with 2 terms first. |x+y|<=|x|+|y|. (I am assuming you are talking about real numbers). Equal if the same sign, less if opposite. Then the 3 term case can be proven in two steps using the 2 term case.
 

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