  In this paper we will prove that all the elements in the smallest ideal
K($\beta$N) in the semigroup of the Stone Cech compactification ($\beta$N,.) of
the discrete semigroup of natural numbers N under multiplication constitute a
single equivalence class under the mid extension divisibility relation. And all
the elements in the closure of the smallest ideal Cl($\beta$N) constitute a
single equivalence class under the tilde extension divisibility relation.
