a consequence of the axiom of choice is that every set can be given a well ordering. and well orderings always have smallest elements, but they may not have largest elements.
so there is someone who is the least gay, but there may not be a single person who is the most gay.
I’m not sure if I understand. There might not be the “fully” gay person but there is person(s) who is more gay than anyone else, thus making them gayest
The axiom of choice doesn’t say one way or another whether the spectrum in “the standard order” (is there a standard definition of more/less gay?) is a well ordering, only that there is some well ordering.
yeah this is true. i should have clarified a bit better that a well ordering wouldn’t give you a “least gay” person in that sense of the word. it would be more correct to say there is a well ordering ⊰, and so there is a “⊰”-least gay person. but of course a “⊰”-least gay person could be in the middle of that spectrum.
but the number of people on earth is finite, so in fact the usual ordering is a well-ordering in this case. so i guess those two mistakes i made cancel each other out, and the axiom of choice isn’t even needed here.
a consequence of the axiom of choice is that every set can be given a well ordering. and well orderings always have smallest elements, but they may not have largest elements.
so there is someone who is the least gay, but there may not be a single person who is the most gay.
I’m not sure if I understand. There might not be the “fully” gay person but there is person(s) who is more gay than anyone else, thus making them gayest
oops. you’re completely right. i forgot there are only a finite number of people on earth. there is a gayest person
The axiom of choice doesn’t say one way or another whether the spectrum in “the standard order” (is there a standard definition of more/less gay?) is a well ordering, only that there is some well ordering.
yeah this is true. i should have clarified a bit better that a well ordering wouldn’t give you a “least gay” person in that sense of the word. it would be more correct to say there is a well ordering ⊰, and so there is a “⊰”-least gay person. but of course a “⊰”-least gay person could be in the middle of that spectrum.
but the number of people on earth is finite, so in fact the usual ordering is a well-ordering in this case. so i guess those two mistakes i made cancel each other out, and the axiom of choice isn’t even needed here.