# [SOLVED] direct proof and proof by contradiction

• Feb 27th 2010, 08:55 PM
SimonK
[SOLVED] direct proof and proof by contradiction
Hi Guys and Gals

I'm a serious newbie here so please be nice to me and excuse any ingnorance i may demonstrate.(Itwasntme)

Hoping some one can help me with this question.... "If X is a positive real number and X<1 then X^2<1" , i have to give both a direct proof and proof by contradiction for this statement. I have read up and understand what is meant by a direct proof and proof by contradiction but i cant really put it together.

Any help?(Worried)
PS. I think i posted this in the wrong topic area previously. Sorry about that.

• Feb 27th 2010, 09:36 PM
Jhevon
Quote:

Originally Posted by SimonK
Hi Guys and Gals

I'm a serious newbie here so please be nice to me and excuse any ingnorance i may demonstrate.(Itwasntme)

Hoping some one can help me with this question.... "If X is a positive real number and X<1 then X^2<1" , i have to give both a direct proof and proof by contradiction for this statement. I have read up and understand what is meant by a direct proof and proof by contradiction but i cant really put it together.

Any help?(Worried)
PS. I think i posted this in the wrong topic area previously. Sorry about that.

Ah, so you know that you are required to prove an implication here. That is, a statement of the form P => Q.

A direct proof means, you assume P and then show that Q follows from it.

A proof by contradiction means, you assume P and notQ and show that a contradiction follows from it.

How about you start your proofs and show where you are getting stuck. Both proofs are actually quite similar in this case. if you get one, you can get the other.
• Feb 27th 2010, 10:07 PM
SimonK
Thanks
Its under control now mate, sometimes it takes a while for things to sink in.

Thanks for responding.