I really do not get proofs AT ALL.

[XodoX]

I really do not get proofs AT ALL. Stuff like this...

"Prove that (n+1)^{2 \geq}3ⁿ if n is a positive integer with n\leq4."

Proof by exhaustion would be applied here.. what the book tells me.




"Show that there are no solutions in integers x and y of x²+3y²=8."

Then there's also "Constructive Existence Proof" and "Nonconstructive proof". No idea how to do anyone of them. How do I approach those equations, and how do I know which proof I need to use??

 

[EnumaElish]

For the first problem, "by exhaustion" means "case by case."

(Non-) Constructive proof: http://en.wikipedia.org/wiki/Constructive_proof

 

[Hurkyl]

I've edited out some whining and language.

 

[Hurkyl]

Something is a (formal) proof if and only if it adheres to a certain set of directions. (the rules of logic)

There is a wide variety of proofs, because the rules of logic allow many different possibilities at each step of the proof.

The "game" of proving things is to find a proof that starts with a useful hypothesis and ends with a useful conclusion. (And in this problem, you're told what the hypothesis and the conclusion are)



Now, what do the rules of logic say a "proof by exhaustion" is?