Another math question

[Farmer]

Show that |x| = max{ -x,x }

I'm sorry, but what does 'max{ x,-x}' mean?

 

[TerribleTerryTate]

it should mean the maximum of the set of numbers between -x and x, inclusive

 

[RedCOMET]

Originally posted by: TerribleTerryTate
it should mean the maximum of the set of numbers between -x and x, inclusive

Gee, i didn't know that, i guess i should have paid more attention in my calc classes.

 

[akubi]

just means you take the larger of the two.

so max{-1,0} = 0, max{32,1000}=1000, max{-10,10}=10

basically max{-x,x} intuitively says you take the positive value of the two.
(i.e. if x is negative, -x will be positive so you take that. if x is pos, x will be positive so you take that)

so you just consider abs as piecewise linear function
from (-inf,0) |x|=-x, for [0,inf) |x|=x
... (-inf,0) max{-x,x}=-x, for [0,inf) max{-x,x}=x (so they are equivalent)