> One of the consequences of this axiom is that every subset of the real numbers has a least element according to some ordering. An even weirder consequence of

> One of the consequences of this axiom is that every subset of the real numbers has a least element according to some ordering. An even weirder consequence of AC is the Banach-Tarski paradox [1]. Other examples of how mathematicians come up with alternative perspectives are non-Euclidean geometries that replace the parallel postulate of the common Euclidean geometry, e.g. Lobachevskian [2] and Riemannian geometry [3]. [1] https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox [2] https://en.wikipedia.org/wiki/Hyperbolic_geometry https://en.wikipedia.org/wiki/Hyperbolic_geometry [3] https://en.wikipedia.org/wiki/Elliptic_geometry https://en.wikipedia.org/wiki/Elliptic_geometry