# Thread: Proof Question

1. ## Proof Question

Hi. I couldn't solve a proof problem, can you help me about this?
the question is:

thanks for any help =)

2. Originally Posted by dpb
Hi. I couldn't solve a proof problem, can you help me about this?
the question is:

thanks for any help =)
The contrapositive to "$\displaystyle \text{If } |x| > 1 \text{, then either }x > 1 \text{ or }x < -1$" is:
"$\displaystyle \text{If } -1 < x < 1 \text{, then } |x| < 1$"

Does this help?

-Dan

3. actually i need a full proof but i don't know how to proof thats my problem

4. Originally Posted by dpb
actually i need a full proof but i don't know how to proof thats my problem
Do you know the interpretation of $\displaystyle |x|$ on the number line? $\displaystyle |x|$ is the distance of the point x from the origin. Does this help?

-Dan

5. i know that but i dont know how to prove it in mathematical way =)

6. Originally Posted by dpb
i know that but i dont know how to prove it in mathematical way =)
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

7. i get it, thanks

8. i can't understand how to proof by cases (it says i need to use proof by cases)

9. Originally Posted by dpb
i can't understand how to proof by cases (it says i need to use proof by cases)
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

10. so what should i do in my case?