Axioms (together with definitions) forms the basis of mathematical theorems. Every mathematical theorem is only proven inside its axiom system.

All mathematics is a sort of if - then language, only true inside the appropriate axiom system.

And there are different sets of axiom systems: Euclidean plane geometry, the Zermelo-Fraenkel axioms for set theory, Kolmogorov's axioms for probability theory and so on....

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Posts tagged Axiom