2 ms·

Colin, is this submitted for disagreement, or because you think the author is really on to something?

• ColinWright 12y ago
  It's submitted because it's interesting. My point of view is that AC is neither "True" nor "False" - maths at this level isn't really about "Truth". There are choices to make, and we make choices that are convenient and useful. The question with AC is that to make the choice that it's "true" is to allow things that seem intuitively wrong, but similarly, making the choice that AC is "false" is to prevent things that intuitively seem like they should be allowed. This article is explaining clearly one of the consequences of choosing to accept the AC, and pointing out that, in the opinion of the author, the consequences are just too much to permit.
• gus_massa 12y ago
  The axiom of choice is very interesting. It’s independent of the other (more intuitive axioms), so you can do math with it and with it’s negation. It’s useful to prove some “intuitive” results and some “paradox”, so it’s polemic. The canonical “paradox” is the Banach–Tarski paradox, but it’s a very strange result and it can be “ignored” as a weird corner case. I didn’t know this “paradox”. This “paradox” looks more innocent. It’s easy to explain. Most of the steps are easy and intuitive. I have to read this five times to be sure that this has no obvious error, and I’m a mathematician. This is not a ground braking result that will change math forever, it’s just another example of the polemic state of the axiom of choice. But the article is interesting and I’ll remember this example because it can be useful to discuss the topic with the students.