# Mathematical Proof/Methods of Proof/Other Proof Types

# Other kinds of Proof[edit | edit source]

Some Proofs do not fall into any of the categories listed above. For example, a non constructive existence proof is a method which demonstrates the existence of a mathematical entity, without actually constructing it.

## Non Constructive Existence Proofs[edit | edit source]

For example, proofs exist which show the existence of nonconstructible numbers (numbers which can not be created using any combination of algebraic operations). These proofs can clearly not be constructive.

## Proof By Exhaustion[edit | edit source]

Proofs which analyse and document every instance of an assertion in a case-wise analysis can be used in finite cases. This is a cumbersome method of proof and is really only suitable when dealing with fairly small sets. A more involved use of proof by exhaustion is the proof of the Four-Colour Theorem. The proof has broken down the four-colour problem into subsets and a four-colour proof was applied to each of these by a computer. This proof has not currently been verified by a human and is hence not considered fully proven.