Proof Methods 2

There are a few proof methods not covered here, and even more that will not be. But we should discuss a few more proof types so you can see the most basic proofs.

Construction

A proof by construction involves constructing (building) the thing that is being proven. Usually, this is an algorithm that will construct the object. We also need to prove this construction method works. The following video gives a few examples

Rude Proofs?

The following video talks about an interesting proofs that converts ideas to numbers.

Proof, Theory, and Conjecture

A statement can only be considered a theorem if it has a mathematical proofs. Statements we believe to be true, but haven't formally proven, are known as conjectures.

One such conjecture is the twin prime conjecture. A twin prime is a set of primes that are only two apart. For example, 17 and 19 are twin primes. We believe there to be an infinite number of twin primes, and this is the conjecture. However, this has not been proven, so we cannot state it as fact, or use it as a part of another proof.

The very popular Riemann Hypothesis is also a conjecture. It is too complex to discuss here, but an interesting topic.