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Does a metric space have an origin? That is, does it have $(0,0)$.

Does a vector space have an origin?

It seems whatever you can do in a metric space can also be done in a vector space. Is this true?

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    They are entirely different concepts. As to an origin, a general metric space does not have anything that behaves like the ordinary number zero does. A vector space does have a unique "zero-like" object, that is, a vector, that we often call $0$, such that $0+v=v+0=v$ for any vector $v$ in the space. Although the concepts of vector space and metric space are entirely different, some familiar spaces, uch as $\mathbb{R^3}$, are simultaneously vector spaces and metric spaces, and there is interaction between the vector structure and the metric structure.2012-02-29
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    The answers below tell the tale, but I am interested to know what you mean by the penultimate sentence in your question. What sort of things have you seen done in metric spaces that can (apparently) also be done in vector spaces?2012-02-29

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