Explain what is a MATHEMATICAL axioM?

An axiom is a rule in mathematics that can not be proven correct. I think most of the time instead of being able to prove it correct, axioms can only be “not proven incorrect”. A lot of the time, we also just “feel” these to be correct, but we can’t exactly show why.

Here are a couple examples:

I think that a clear example is that through any two points there is exactly one line, which I can’t prove to be true, but I can’t find any issues with the statement. It’s inductive reasoning in a way


A mathematical proof comes from deductive reasoning, and can be proven to be true. There are no exceptions to a mathematical proof. It is a mathematical statement that is viewed to be correct and true. An example of this is that on any map or set of shapes, only four colours are needed to colour it so that no same colours are touching.

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