# Math Help - Really difficult about metric space

1. ## Really difficult about metric space

Let $(R,d)$ be a metric space. Is it true, that for any metric $d$, from $d(x_{n},x)\longrightarrow 0$ follows $d(x_{n}-x,0)$ converges, when $n\longrightarrow\infty$?
Actually, it is not true, but it is terribly difficult to find counterexample

2. ## Re: Really difficult about metric space

How is $x_n-x$ defined on a metric space?

3. ## Re: Really difficult about metric space

Originally Posted by girdav
How is $x_n-x$ defined on a metric space?
I guess you could add what is 0 in your metric space.