Affine set

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(or affine manifold, affine variety, linear variety, flat.)

A set LaTeX: S that contains the line through any two of its points --i.e. LaTeX: x, y \in S implies LaTeX: ax + (1-a)y \in S for all LaTeX: a \in \mathbb{R}. The dimension of an affine set is that of the (unique) subspace parallel to it. Dimensions of 0, 1 and 2 are called points, lines and planes, respectively.

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