Any general rules as to when an affine space is a vector subspace and when it's not?
Because Wikipedia example:
https://en.wikipedia.org/wiki/Affine_space#/media/File:Affine_space_R3.png
says that in that case $P_2$ is not a subspace.
However the article gives in many parts that an affine space is a subspace. However, does this not even imply that it could be a vector/linear subspace in some cases?
The article also write:
Any vector space may be considered as an affine space
So this means that affine spaces can be vector spaces without the null vector property?
An affine space is a linear subspace if and only if the affine space contains the null vector.
The nomenclature makes sense if you think about an affine function. If it goes through 0, it is a linear function.