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Re: ? 417 An implication of actual infinity
Posted:
Jan 11, 2014 6:54 PM


WM <wolfgang.mueckenheim@hsaugsburg.de> writes:
> Am Samstag, 11. Januar 2014 19:49:10 UTC+1 schrieb Ben Bacarisse: > >> > I said quite clearly that I consider only the terms of the sequence of >> > FISONs, not its limit. >> >> You also said of lim(n=1..)[ S_n ] "[i]n the infinite there is no limit >> set" (mesage ID: <8c904bde0087430dbf5b261c83ed0bd7@googlegroups.com>) > > Correct. >> >> Are you changing your mind? Does the limit set lim(n=1..)[ S_n ] exist? > > No. (But if set theory is the base of arguing, then all S_n must > exist.)
So, have we found the first thing where you'd tell the students a lie? In mathematics lim(n=1..)[ S_n ] = N but a student claiming that would be told it's not true?
(Oddly, lim(n=1..)[ S_n ] is the same as Union(n=1...)[ S_n ] which is equal N even in WMaths. In some definitions the limit is even defined in terms of unbounded unions and intersections.)
<snip>  Ben.



