Theorem

The initial premises on which all theorems are based are called axioms. An axiom, or postulate, is a basic fact which is not subject to formal proof. For example, the statement that there is an infinite number of even integers is a simple axiom. Another is that two points can be joined to form a line. When developing a theorem, mathematicians choose axioms, which seem most reliable based on their experience. In this way, they can be certain that the theorems are proved as near to the truth as possible. However, absolute truth is not possible because axioms are not absolutely true.

To develop theorems, mathematicians also use definitions. Definitions state the meaning of lengthy concepts in a single word or phrase. In this way, when we talk about a figure made by the set of all points which are a certain distance from a central point, we can just use the word circle.