Is the usual metric defined on R - {0}?

[tylerc1991]

Homework Statement

I was working on a problem and think I might have run across an issue. Is the usual metric defined on R - {0}? (Where R is the real numbers) Reworded, can I say that I have a space R - {0} with the usual metric on it? Thank you.

 

[lanedance]

I think you do almost whatever you want really ;)

however as the metric still satisfies all the metric consditions, it is still a metric space
http://en.wikipedia.org/wiki/Metric_space

however it will no lonegr be complete as it doesn't contain all its limit points