Mathematically speaking, what is an ‘Axiom’?

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Mathematically speaking, what is an ‘Axiom’?

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An axiom is a rule or a statement that is considered true without proof. For example, in planimetry you can’t draw two or more lines through two points, only one. Why? Well, because that’s how it is.

Another example is that if an object one is equal to object zero, then object zero is equal to object one.

All of mathematics rests upon such axioms.

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