hey guys
having a problem with a couple of calculus proofs...please help!
(1) prove that is odd iff is odd
i have done the <--- part of this, im just having a problem proving that is odd if is odd (the ---> part)
(2) Show that there exists no rational number such that = 3.
i have attempted to use proof by contradiction but im getting nowhere!
thanks
We have already shown that if n is odd, then n^2 is odd. Next, we have to show if n^2 is odd, then n is odd.
Contradiction: n^2 is odd and n is even.
Since n is even, 2|n, and since n^2 is odd,
.
But, we have 2|n. Therefore, we have reached a contradiction, and if n^2 is odd, then n is odd.