- #1
knowLittle
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Homework Statement
Prove that for every two real numbers x and y
##|x+y| \leq |x| + |y| ##
Homework Equations
The Attempt at a Solution
There are three cases. The easiest ones is when they are both positive and negative.
The third one I have problems with.
The numbers have different sign. Say x>0 and y<0
Divide this into two subcases:
case 3.1
## x+y \geq 0#### |x| +|y| = x+(-y) = x-y##
Now, so far so good, but my book states the following.
## |x| +|y| = x+(-y) = x-y > x+y = |x+y|##
How is it possible that x-y be ever greater than x+y?
case 3.2
## x+y < 0 ##
This one is easy too.