5 ms·
Some people, when confronted with a problem, think “I know, I'll use the Banach–Tarski Theorem.”
by sparky_z 11y ago
Some people, when confronted with a problem, think
“I know, I'll use the Banach–Tarski Theorem.”
- shoo 11y agoNow they have their original problem (assumed to contain a sphere), an additional sphere, and a dependency upon the axiom of choice.
- jordigh 11y agoTrue story, did you know you can have paradoxical sets without choice? You just need infinity. https://en.wikipedia.org/wiki/Paradoxical_set https://en.wikipedia.org/wiki/Paradoxical_set http://www.math.hmc.edu/~su/papers.dir/banachtarski.pdf http://www.math.hmc.edu/~su/papers.dir/banachtarski.pdf
- JadeNB 11y agoWhile I don't dispute your claim, neither of the links substantiates it. The Wikipedia article says that you only need the axiom of infinity, but mentions only Banach–Tarski (which does require choice); and the minor thesis says on p. 2 that "the philosophy adopted in ths paper will be the unquestioned acceptance of Choice as a useful foundation in our work". Do you have any other references for this? (I'm interested, not snarking.)
- jordigh 11y agoThe paper is kind of long. Look at Theorem 4 in it. https://www.math.hmc.edu/funfacts/ffiles/30001.1-2-8.shtml https://www.math.hmc.edu/funfacts/ffiles/30001.1-2-8.shtml