- #1

- 57

- 0

## Homework Statement

I am trying to understand why

**ℕ**the set of natural numbers is considered a Closed Set.

**2. Relevant definition**

A Set

*S*in

**R**is closed iff its complement,

^{m}*S*=

^{c}**R**-

^{m}*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:

*-*

*S*R^{c}=^{m}**ℕ**is open because in so doing, we have removed the only boundary point of 0

Therefore, per definition,

**ℕ**or in this case,

**is closed.**

*S*Am I close?

Last edited: