"The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes."


"The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" 


What are people's opinions on choice?


Proofs involving choice are often delightfully unenlightening or even paradoxical, but it does have uses.

Views: 19

Replies to This Discussion

The easiest way of seeing it outside of set theory is in linear algebra. The AC is logically equivalent to saying "every vector space has a basis".

AC can be used to construct non-measurable sets, which leads to the Banach-Tarski paradox, something that is well worth looking up!

RSS

Discussion Forum

Serious discussions of mathematics

Started by Charles Daney. Last reply by Joe Morgan Dec 9, 2012. 3 Replies

Fun teaser

Started by DWatts. Last reply by onyango makagutu Oct 24, 2012. 9 Replies

Basic Geometry

Started by Michel-san. Last reply by Joe Morgan Dec 9, 2012. 2 Replies

Choice...

Started by Michel-san. Last reply by Graham E. Lau Feb 10, 2010. 3 Replies

Events

Blog Posts

My Purity Ring

Posted by Michelle Varni on July 5, 2015 at 7:18pm 7 Comments

Services we love!

Advertise with ThinkAtheist.com

© 2015   Created by umar.

Badges  |  Report an Issue  |  Terms of Service