I am trying to understand why ℕ the set of natural numbers is considered a Closed Set.
2. Relevant definition
A Set S in Rm is closed iff its complement, Sc = Rm - S is open.
The Attempt at a Solution
I believe I understand why it is not an Open Set:
Given that it includes 0 as a boundary point, it cannot be an open set.
As to being Closed. What I am thinking is this:
Sc = Rm - ℕ is open because in so doing, we have removed the only boundary point of 0
Therefore, per definition, ℕ or in this case, S is closed.
Am I close?