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Affine set

Euclidean space without distance and anglesIn ⁠R3{\displaystyle \mathbb {R} ^{3}}⁠, the upper plane (in blue) P2{\displaystyle P_{2}} is not a vector subspace, since 0∉P2{\displaystyle \mathbf {0} otin P_{2}} and ⁠a+b∉P2{\displaystyle \mathbf {a} +\mathbf {b} otin P_{2}}⁠; it is an affine subspace.

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