Comment author:Z._M._Davis
11 January 2008 03:39:27AM
1 point
[-]

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 re채rrange 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.

## Comments (128)

OldCumulant, I think the idea behind "infinite set atheism" is not that limits don't exist, but that that infinities are acceptable

onlyas limits approached in a specified way. On this view, limits are not aconsequenceof 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

thinkI 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 re채rrange the terms, the Banach-Tarski paradox,&c.,&c.), but I'm not sure you can give up infinite sets withoutalsogiving up the real numbers (as others have touched on above), which seemsverywrong.