  # no genius

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8

• Lepton

## no genius's Achievements 10

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1. 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"
2. $\left( \Psi \left( x+1 \right) -\Psi \left( x-1 \right) \right) {x \choose 2}$
3. $\sum _{i=1}^{\infty }A_{{i}}=5$ nice. i <3 maple's latex converter.
4. 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.
5. 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?
6. no no no. you cant prove something by listing a finite number of numerical examples. i'm no genius, but i know that much
7. 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
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