On 30 May 2012, at 16:08, Stephen P. King wrote:

On 5/30/2012 4:45 AM, Bruno Marchal wrote:


On 30 May 2012, at 08:12, Stephen P. King wrote:


Hi Brent,

Yes, that is a very good point! The axiom of choice is a suspect here. Banach and Tarsky proved a paradox of the axiom of choice, it is the "scalar field" of mathematics, IMHO; you can get from it anything you want.



Banach and Tarski proved an amazing theorem with the axiom of choice, but it is not a paradox, in the sense that it contradicts nothing, and you can't get anything from it.

Bruno

The axiom of choice allows for violation of conservation laws, if it where to be a physical law.

The axiom of choice is not a physical law.

Bruno


http://iridia.ulb.ac.be/~marchal/



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