Proving the definition of abs. value

[cmurphy]

I need to show that the absolute value of x = max {x, -x}. Of course I know this is true, but I must show this. How would I go about doing such a thing?

[arildno]

The absolute value is always positive, right?
Use that fact.

[dextercioby]

BTW,a definition cannot be proved...

Lemmas,theorems,properties,propositions,corolaries ,but not definitions...

Daniel.