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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