Mathematically speaking, what is an ‘Axiom’?
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An axiom is simply something you assume to be true. You can put together any number of axioms you like and proceed. If your axioms contradict in any way you have an uninteresting and useless system. If they do not you can start proposing and trying to prove things from the axioms. If you look into geometry you can see alternative systems can coexist and illuminate truths in the proper context.
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