Cumulant, I think the idea behind “infinite set atheism” is not that limits don’t exist, but that that infinities are acceptable only as limits approached in a specified way. On this view, limits are not a consequence of infinite sets, as you contend; rather, only the limit exists, and the infinite set or sequence is merely a sloppy way of thinking about the limit.
Eliezer, I’ll second Matthew’s suggestion above that you write a post on infinite set atheism; it looks as if we don’t understand you.
I think I understand the motive for rejecting infinite sets (viz., that whenever you deal with infinites you get all sorts of ridiculously counterintuitive results—sums coming out different when you reärrange the terms, the Banach-Tarski paradox, &c., &c.), but I’m not sure you can give up infinite sets without also giving up the real numbers (as others have touched on above), which seems very wrong.
Cumulant, I think the idea behind “infinite set atheism” is not that limits don’t exist, but that that infinities are acceptable only as limits approached in a specified way. On this view, limits are not a consequence of infinite sets, as you contend; rather, only the limit exists, and the infinite set or sequence is merely a sloppy way of thinking about the limit.
Eliezer, I’ll second Matthew’s suggestion above that you write a post on infinite set atheism; it looks as if we don’t understand you.
I think I understand the motive for rejecting infinite sets (viz., that whenever you deal with infinites you get all sorts of ridiculously counterintuitive results—sums coming out different when you reärrange the terms, the Banach-Tarski paradox, &c., &c.), but I’m not sure you can give up infinite sets without also giving up the real numbers (as others have touched on above), which seems very wrong.