Mathematically speaking, what is an ‘Axiom’?
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You can’t make any claim without making at least 1 assumption.
That initial assumption is an Axiom (or a postulate). You can’t explain why this is the case, but it’s just a starting point to build logic off of.
For a math example:
1 + 2 is the same as 2 + 1
Why are these the same? There’s no reason. “It is, because it is”. No matter what order you add two numbers together in, they equal the same thing.
Axioms in math often seem like “no duh” rules, because they’re some of the first things we learn in preschool.
A few Axioms given by Euclid’s Elements include:
1) It is possible to draw a straight line from any point to any other point.
2) It is possible to extend a line segment continuously in both directions.
3) It is possible to describe a circle with any center and any radius.
4) It is true that all right angles are equal to one another.
If anyone asks “why” about any of these, you just say “because we said so”.
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