no genius

its not because its a "mac" that it runs vista better.. its because its got the following inside of it:

"2.4-GHz Core 2 Duo T7700 processor, the maximum 4GB of RAM, a 160GB hard drive, and nVidia's new top-of-the-line notebook graphics card, the nVidia GeForce 8600M GT"

[math] \left( \Psi \left( x+1 \right) -\Psi \left( x-1 \right) \right) {x \choose 2}[/math]

[math]\sum _{i=1}^{\infty }A_{{i}}=5[/math]

nice. i <3 maple's latex converter.

my prof and my textbook (Discrete Mathematics and Its Applications, Rosen), make a distinction between "indirect proof" and "proof by contradiction". the proof by contradiction of this was part c) of the problem.

ok, i think i've got it. the original statement, which i've proven directly, was "if n is odd, then n^2 is odd". so basically a statement in the form p -> q. this is logically equivalent to ~p OR q.

so i can indirectly prove it by showing that ~p OR q is a tautology.

so ~p OR q = "Either n is even or n^2 is odd"

n is even OR n^2 is odd <=>

n = 2k OR n^2 = 2j + 1 <=>

n^2 = 2(2k^2) OR n^2 = 2j + 1 <=>

n^2 is even OR n^2 is odd <=> (which has the form "~q OR q")

T

correct?

anyone?

no no no. you cant prove something by listing a finite number of numerical examples. i'm no genius, but i know that much

i have an assignment question where i'm supposed to prove that the square of an odd number is an odd number using both a direct proof and an indirect proof.

the direct proof was easy enough, but i'm kinda stuck on the indirect part.

so basically i'm supposed to prove that "if n^2 is even then n is even."

so i started by stating that .

n^2 = 2k

n * n = 2k

n = 2 (k/n) and i'm saying that (k/n) is always an integer

but something doesnt seem right about this, especially since i'm not really sure how to justify that (k/n) is an integer.

can someone put me on the right path?

thank you