Maths Definitions

Proof

A series of logical steps which we use to solve a theorem

Axiom

A statement accepted without proof, as a basis for an argument, e.g. axiom 1 (two points axiom)

Theorem

A statement deduced from the axioms by logical argument

Corollary

A statement that follows readily from a theorem. Often a statement of a theorem in a more specific context.

Converse

The reverse of a theorem

Proof by contradiction

Where we assume that a statement is false and then prove that this assumption contradicts another statement that is known to be true