Question

if {kn} is a collection of nonempty compact sets in R and kn-1 contained in kn for all n in N, then the intersection of kn is not the empty set.

Answer 1

In mathematics, if we have a collection of nonempty compact sets in R such that the previous set is contained in the current set, then the intersection of all the sets in the collection is not empty.

Step-by-step explanation:

In mathematics, we have a collection of nonempty compact sets {kn} in R such that kn-1 is contained in kn for all n in the set of natural numbers N. If this condition holds, then the intersection of all the sets in the collection, denoted by ∩nkn, is not the empty set (∅).