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Proof

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Point of confusion

Colloquial use of "mathematical proof" The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something about everyday life, or when data used in an argument is numerical. It is sometimes also used to mean a "statistical proof" (below), especially when used to argue from data.


A proof is an argument which is logically correct, clearly showing the truth of a stated theorem.

Possible Components:

A theorem is statement of one or more steps which shows a mathematical claim to be true.

A lemma is a theorem where the result is proven elsewhere, when accepted it is used to show solved steps in other theorems or proofs.

A corollary is similar to the theorem's result which follows from the the details in a previous proof.
(unhappy need more reading)
Types of proofs: The long list: Contradiction. Contrapositive. Costructive. Inductive. Without words. (-- not great usually needs words useful explanation)