Basic concepts of Mathematics

In this article, we explore some basic concepts which are used almost in every area of mathematics. 

Axiom

A self-evident statement which needs not to be proved and can be used as basis of the argument.

Lemma

A lemma is a minor theorem which needs to be proved in the process of proving a major theorem.

Theorem 

A theorem is a statement which can be shown true by logical deduction from definitions, axioms or already established theorems.

Proof

An argument or a finite sequence of established formulas or proved statements which lead to validate the theorem or the formula.

Corollary 

A theorem of less importance which can be readliy proved from the theorem. 

Remark

A statement which highlights the important features of a theorem or explore the connections between different mathematical concepts.

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