In article <firstname.lastname@example.org> WM <email@example.com> writes: > On 27 Nov., 17:02, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: ... > > > Therefore the vase is never empty - > > > > Similar in the sequence 1/n the elements value is never zero. > > Correct. But in the sequence 1,1,1... the limit is 1 with no doubt.
Yes, so what?
> > You may verify that in the case you proposed lim X_n does exist and is > > equal to the empty set. > > > > Note: > > 1 = lim |X_n| != |lim X_n| = 0 > > but that should not come as a surprise. > > Let one ball rest in the vase in eternity. The limit will be 1.
The limit of the sequence of set of balls is the single ball that stays there forever. And so in that case we have: 1 = lim |X_n| = |lim X_n| = 1 and so what?
> Consider the sequence 1, 101, 1, 101, 1, 101, ... There is no limit.
> Nevertheless the sequence of minima
Minima of what?
> 1,1,1,... has limit 1 as before.
Yes, so what?
> Therefore the result of set theory shows that set theory is not > mathematics.
I have no idea how you come to that conclusion.
I think you are confusing the limit of a sequence of sets (which is a set) and the limit of the sequence of the cardinalities of sets ( which is a cardinality). In general: the limit of the cardinalities is not necessarily the cardinality of the limit, however much you would like that to be the case. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/