On 27 Nov., 17:02, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > In article <ac583807-eb9d-4ae4-86f2-37f329692...@k17g2000yqh.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes: > ... > > 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.
> 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. Consider the sequence 1, 101, 1, 101, 1, 101, ... There is no limit. Nevertheless the sequence of minima 1,1,1,... has limit 1 as before. Therefore the result of set theory shows that set theory is not mathematics.