- #1
natasha d
- 19
- 0
whats an infinite intersection of open sets? how is it different from finite intersection of open sets
and why is it a closed set in the case of ∞ intersection but open in case of finite. To quote kingwinner, is it being defined as a limit?
it really does look look like a limit in the case of ∞ intersections, as in the sets are tending towards their intersection but not actually attaining it . Consider the intersection of the sets
∞
π (1-1/n, 2+ 1/n)
n=1
would the smallest set be an infinitesimally small ε on either side of the closed set [1,2], which would hence be their infinite intersection?
and why is it a closed set in the case of ∞ intersection but open in case of finite. To quote kingwinner, is it being defined as a limit?
it really does look look like a limit in the case of ∞ intersections, as in the sets are tending towards their intersection but not actually attaining it . Consider the intersection of the sets
∞
π (1-1/n, 2+ 1/n)
n=1
would the smallest set be an infinitesimally small ε on either side of the closed set [1,2], which would hence be their infinite intersection?