Hi. I couldn't solve a proof problem, can you help me about this?
the question is:
thanks for any help =)
I think you are thinking this is a very hard thing to do and thus you are making it hard.
Look at the definition of $\displaystyle |x|$:
$\displaystyle f(x)=|x|=\left\{\begin{array}{rr}x,\text{ if }x>0\\
-x,\text{ if }x<0\\
0,\text{ if }x=0\end{array}\right.$
(with thanks to Krizalid. I always forget how to code this one for some reason!)
From this we know that if $\displaystyle |x| < 1$ that $\displaystyle -1 < x < 1$ by definition.
-Dan
topsquark's definition gave you the cases. you consider when x is less than zero, greater than zero, and equal to zero. all these are taken care of in topsquark's definition. it could be broken down into two as suggested though: x greater than or equal to zero, and x less than zero