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Every point in space will have a unique such vector, so there's no ambiguity if I said something like "the vector for the point P". But it works the other way, too, in that if I take any arrow that starts at the origin, it is associated with a unique point in space (the tip of the arrow). So there's no ambiguity if I say, "the point for the vector V". Since there's a one-to-one dictionary ...
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