Warning: Some posts on this platform may contain adult material intended for mature audiences only. Viewer discretion is advised. By clicking ‘Continue’, you confirm that you are 18 years or older and consent to viewing explicit content.
Well that’s interesting: in order to define unmeasurable sets, you relied on the axiom of choice… I suppose it might be possible to define unmeasurable sets without AC, but maybe not!
Every time I encounter the axiom of choice implying a bunch of crazy stuff, it always loop back to requiring AC. It’s like a bunch of evidence against AC!
I find it interesting that the basic description of AC sounds very plausible, but I’m still convinced mathematicians might have made the wrong choice… (See what i did there? 😄)
It’s required, but nontrivially so. It has been proven that ZF + dependent choice is consistent with the assumption that all sets of reals are Lebesgue measurable.
Well that’s interesting: in order to define unmeasurable sets, you relied on the axiom of choice… I suppose it might be possible to define unmeasurable sets without AC, but maybe not!
Every time I encounter the axiom of choice implying a bunch of crazy stuff, it always loop back to requiring AC. It’s like a bunch of evidence against AC!
I find it interesting that the basic description of AC sounds very plausible, but I’m still convinced mathematicians might have made the wrong choice… (See what i did there? 😄)
It’s required, but nontrivially so. It has been proven that ZF + dependent choice is consistent with the assumption that all sets of reals are Lebesgue measurable.