Proof by contradiction


by Bill Abrams
Tags: contradiction, proof
Char. Limit
Char. Limit is offline
#2
Feb24-11, 05:12 PM
PF Gold
Char. Limit's Avatar
P: 1,930
Well, a^2-b^2 = (a+b)(a-b), right? Then consider the cases of a and b even, and a and b odd (if only one is even, then the left side is odd and the right side is even, a contradiction). You'll find that (a+b) is even AND (a-b) is ALSO even, and thus the left side is divisible by four, while the right side cannot be divisible by four. Again, contradiction.
Char. Limit
Char. Limit is offline
#3
Feb24-11, 05:14 PM
PF Gold
Char. Limit's Avatar
P: 1,930
Quote Quote by Dick View Post
The usual trick for problems like this use modular arithmetic. What are the possible values of a^2 mod 4?
I assumed by the title that he was looking for a proof by contradiction, but we're probably working toward the same thing anyway.

Dick
Dick is offline
#4
Feb24-11, 05:16 PM
Sci Advisor
HW Helper
Thanks
P: 25,170

Proof by contradiction


Quote Quote by Char. Limit View Post
I assumed by the title that he was looking for a proof by contradiction, but we're probably working toward the same thing anyway.
Right. That's why I deleted my post. We are talking about the same thing but your wording is more likely what the problem is looking for.
Bill Abrams
Bill Abrams is offline
#5
Feb24-11, 05:23 PM
P: 2
Thanks. I tried this before but I must have messed up the algebra or something


Register to reply

Related Discussions
proof by contradiction Calculus & Beyond Homework 1
proof by contradiction Precalculus Mathematics Homework 1
Proof By Contradiction Calculus & Beyond Homework 7
Proof by contradiction? General Math 12
Proof by Contradiction Calculus 7