Really difficult about metric space

**analysis** · December 16th 2011, 11:04 AM

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

**girdav** · December 16th 2011, 11:54 AM

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

**vincisonfire** · December 16th 2011, 11:58 AM

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.

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