Mathematically speaking, what is an ‘Axiom’?

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Mathematically speaking, what is an ‘Axiom’?

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A logic system is roughly like a Lego set. You have bricks, and you have ways to connect the bricks into bigger assemblies. In logic you have rules of inference that tell you how to connect smaller things into bigger things, and axioms are the ground truths, the bricks you get out of the box.

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