An _affine space_ is an $n$-dimensional [space](Spaces.md) over a field, $\mathbb{F}$, containing an infinite number of elements - and these elements are _points_ identified by $n$ elements that [span](Affine%20span.md) this space. # Vector Spaces If we were to choose an _origin_ (i.e. a point that's considered a $\mathbf{0}$ vector), the space would no longer be considered an affine space but instead would be a [vector space](Vector%20spaces.md). # Affine subspace --- # Proofs and Examples %%discussion on stack exchange discussion here https://math.stackexchange.com/questions/884666/what-are-differences-between-affine-space-and-vector-space %% %%See also notes here https://people.eecs.ku.edu/~jrmiller/Courses/VectorGeometry/ %% #MathematicalFoundations/Geometry