Let be a Vector Space over a Field , and let be a nonempty Set. Now define addition for any Vector and element subject to the conditions

- 1. ,
- 2. ,
- 3. For any , there Exists a unique Vector such that .

In an affine space, it is possible to fix a point and coordinate axis such that every point in the Space can be represented as an -tuple of its coordinates. Every ordered pair of points and in an affine space is then associated with a Vector .

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1999-05-25