# I really do not get proofs AT ALL.

1. Jul 12, 2010

### 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$$\leq$$4."

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 any one of them. How do I approach those equations, and how do I know which proof I need to use??

Last edited by a moderator: Jul 12, 2010
2. Jul 12, 2010

### EnumaElish

3. Jul 12, 2010

### Hurkyl

Staff Emeritus
Re: proofs

I've edited out some whining and language. :grumpy:

4. Jul 12, 2010

### Hurkyl

Staff Emeritus
Re: proofs

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?