Definition:Dimension (Geometry)

Informal Definition
The dimension of a (geometrical) space is the minimum number of coordinates needed to specify a point in it.

Affine Dimension
Let $\mathcal E$ be an affine space with difference space $E$.

The dimension of $\mathcal E$ is defined to be the dimension of the vector space $E$.

Also see

 * Dimension of Non-Empty Affine Space is Well Defined