# Math Help - Proving a set closed

1. ## Proving a set closed

Consider the metric space (R,d) with d(x,y) := |x - y| whenver x,y $\in$ R. Show that the set N is closed.

2. If x is not natural, there exists a natura number n such that

n<x<n+1

This clearly implies that there exists an open set containing x and not lying N.