-|x|<=x<=|x|
-|y|<=-y<=|y|
deduce by adding: |x-y|<=|x|+|y|
|x-y|-|y|<=|x|
insert x=y-z and you get:
|z|-|y|<=|y-z|=|z-y|
Q.E.D
I am trying to prove one of the triangle inequalities.
[] are going to be my absolute value symbols, sorry, i don't have mathematica on this computer with the symbols.
I am proving that [[x]-[y]]<=[x-y].
i tried this: we know -[x]<=x<=[x] and -[y]<=y<=[y]
if i subtract these i get: -[x]--[y]<=x-y<=[x]-[y]
then you simplify and get -([x]-[y])<=x-y<=([x]-[y])
so, [x-y]<=[[x]-[y]].
I thought i was on the right track but then i realized that the inequality was pointing in the wrong direction. Did i make some computational error or am i going about this the wrong way? I appreciate any hints on where I might start. thanks!