The Axiom of Choice.

In 1904 an seemingly inoffensive axiom was introduced in the new branch of mathematics of Set Theory. And although seemingly inoffensive, it is one of the most controversial principles of all mathematics.

[flyingbicycles]

I really like the axiom of choice. “If you have a nonempty set, you can pick an element from it” is very intuitive and obvious. If you couldn’t pick an element from it, it wouldn’t be nonempty! Sure there is no function to define how you pick an element, but that has the very easy real life analogue of blindly picking something out of a bag.

Then there’s the Banak Tarski paradox. Not really a paradox. Any real sphere has a finite number of atoms and a discrete structure. But why do mathematically perfect spheres need to follow this rule? We do physically impossible things with mathematical constructs all the time!

[srghma]

unbelieveble
the "picking function" exists, but it exists in CantGoTo (Cantor Godel Turing) universe (the "diagonal universe", David Deutsch, Beginning of Infinity)

[mzimmer]

This was really good content, but next time please use a different computer voice. Thanks!

[JxH]

The Universe (at T=0) probably looked at 'The Axiom of Choice', and was forced to include the 'Pauli Exclusion Principle' as a work-around.

🙂

[xyz.ijk.]

Can't take the computer voice, sorry.