In article <firstname.lastname@example.org> WM <email@example.com> writes: ... > Therefore the vase is never empty -
Similar in the sequence 1/n the elements value is never zero.
> and the only error is your > assertion it would be empty after the last step and there was a state > of the vase "at infinity".
Never heard about limits? We may consider the following for limits of sets (X_n etc are sets): lim sup X_n: x in lim sup X_n if and only if x in infinitely many X_n lim inf X_n: x in lim inf X_n if there is some n0 such that x in X_n for n > n0 lim X_n: exists when lim sup X_n = lim inf X_n and in that case is equal to them.
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. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/