The concept of an axiom

The axiom (other Greek-ἀξίωμα "statement, position") or postulate is the starting position of any theory accepted within the framework of this theory to be true without the requirement of proof and used in proving other of its positions, which in turn are called theorems.

Axiom is an assertion that is accepted without proof.

Assignment of axioms

To draw any conclusions and give evidence, one must rely on some statements. A set of basic statements within any science or scientific theory that are accepted without evidence and constitutes its basis.

Theorem and its proof

The word "theorem" is literally translated from Greek as "consider, think".

Axiom is an assertion that is accepted without proof.

A theorem is an assertion, which is proved. The proof uses both axioms and previously proved theorems.

The statement of the theorem contains the condition (this is what is given) and the conclusion (what must be proved in the theorem).

A theorem is an assertion, in the truth of which one is convinced with the help of a proof.