Axiom: Equal quantities are equal to each other. Equal amount plus equal amount, the sum is equal. Equal amount MINUS equal amount, the difference is equal.

In mathematics, the word axiom is used in two related but different meanings-logical axiom and illogical axiom. In both senses, axioms are the starting point for deducing other propositions.

Unlike theorems, an axiom (unless it is redundant) cannot be deduced from other axioms, otherwise it is not the starting point itself, but some kind of result that can be obtained from the starting point-it can be simply classified as a theorem.

The logical deduction method from premise (original knowledge) to conclusion (new knowledge) through reliable argumentation (syllogism and inference rules) was developed by the ancient Greeks and has become the core principle of modern mathematics. If there is no hypothesis, nothing can be deduced except tautology.

Axiom is the basic assumption that leads to a specific set of deductive knowledge. Axioms are self-evident, and all other assertions (theorems if we are talking about mathematics) must be proved by these basic assumptions.

However, there are different interpretations of mathematical knowledge from ancient times to the present, and finally the word "axiom" has a slightly different meaning in the eyes of today's mathematicians, Aristotle and Euclid.