Mathematically speaking, what is an ‘Axiom’?
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Have you ever seen a child repeatedly ask a parent “why?”?
“Why do I have to wear a raincoat?” So you don’t get wet. “Why would I get wet?”
Because it’s raining. “Why is it raining?” BECAUSE IT IS!
That last one is an axiom. It’s raining, and there is no reason for it.
In math we can make a statement like “The square root of a prime number greater than 1 is always irrational.” Then you ask “why?”. Some Mathematician gives you a proof and for each step of the proof you ask “why?”, so he gives you proofs for each step and again you as “why?” At some point the mathematician runs out of reasons and says “because that’s the way math is.” That thing that doesn’t have a reason is an axiom.
There are a limited number of axioms. They are the building blocks for math. All math is made of combinations of those axioms.
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