Axioms

What are the axioms in math? We dream that we will find that the French Academy of Mathematique has compiled a list of 179 axioms list in the order that they are needed…

Mathigon.org has an excellent article about axioms. It lists nine axioms.

Every area of math has its own set of axioms.

Some things that we could call axioms are instead called definitions. A definition is something you brought into existence. It can’t be wrong; at worst it might be deemed as “not helpful”.

Appendix A

Here is an axiom that we would expect to find: if it is true that for any two points on something there is always a point between those two points then it is also true that for any two points on that something there is an infinite number of points.