triangle inequality intterpretation: |x + y| <= |x| + |y|

[transgalactic]

i know that the sum of two sides is always bigger then the third one

but in this formula
|x+y|=<|x| +|y|

on both sides i have a sum of two members
why the third side is |x+y| ??
and why there is an option for them to be equal??
(the sum of two sides is always bigger then the third one)

 

[pka]

Re: triangle inequality intterpretation..

No one knows for sure the origin of the term triangle inequality.
But clearly it reminds us all of that famous proposition from geometry concerning the lengths of two sides of a triangle relative to the third side.
That said, the triangle inequality is one of the most important ideas in mathematics. AND the possibility of equality is absolutely essential to the concept.
http://mathworld.wolfram.com/TriangleInequality.html