Thread: Proof by cases

I need to use a proof by cases to show that for all real numbers :

|xy| = |x| |y| Could someone please get me started.

I think if x >or = to 0 and y> or = 0 then |x| = x and |y| = y so xy = |xy|= |x| |y|
and if x< 0 and y<0 then |x| = -x and |y| = -y and since -x(-y) = xy I can go to same as above. Is this right????

Originally Posted by frostking2

I need to use a proof by cases to show that for all real numbers :
|xy| = |x| |y| Could someone please get me started.
I think if x >or = to 0 and y> or = 0 then |x| = x and |y| = y so xy = |xy|= |x| |y| and if x< 0 and y<0 then |x| = -x and |y| = -y and since -x(-y) = xy I can go to same as above. Is this right????

Yes it is correct.
Now finish: take one nonnegative and one negative.