Really difficult about metric space

Let $\displaystyle (R,d)$ be a metric space. Is it true, that for any metric $\displaystyle d$, from $\displaystyle d(x_{n},x)\longrightarrow 0$ follows $\displaystyle d(x_{n}-x,0)$ converges, when $\displaystyle n\longrightarrow\infty$?

Actually, it is not true, but it is terribly difficult to find counterexample

Re: Really difficult about metric space

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

Re: Really difficult about metric space

Quote:

Originally Posted by

**girdav** How is $\displaystyle x_n-x$ defined on a metric space?

I guess you could add what is 0 in your metric space.