# Is this a closed set?

1. Sep 17, 2009

### AxiomOfChoice

The set $\{1,2,3,4,5\ldots\}$...is it closed as a subset of $\mathbb{R}$? I'm thinking "yes," but I'm unsure of myself for some reason. (And yes, this is just the set of positive integers.

2. Sep 17, 2009

### Office_Shredder

Staff Emeritus
The definition of closed is the complement of an open set. So is the set

$$( - \infty,1) \cup (1,2) \cup (2,3) \cup (3,4)...$$ open?

3. Sep 17, 2009

### Petek

Can you show that its complement is open in $\mathbb{R}$?

4. Sep 17, 2009