How do i geometrically visualise discrete metric space? This is a informal question i guess. Some metrics is easy to understand intuitively and draw some understandable diagrams denoting convergence or any metric property.How can i draw a discrete metric ?

A metric space is discrete iff there is no point a and    sequence of points {$a_j$}, none of which are a, for which   the sequence d(a,$a_j$) converges to 0.  
A space is discrete iff there is no point a and net n,
no points of which are a, for which n converges to a.   
If the space is first countable, then sequences instead
of nets can be used.
