Re:Parallels Between Math and Software Engineering
by avz on Sunday August 09, 2015 @10:42PM
(#10032407)
> 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].
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
[2] https://en.wikipedia.org/wiki/Hyperbolic_geometry
[3] https://en.wikipedia.org/wiki/Elliptic_geometry