Affine Subspaces $\mathbf{a} + V = \{ \mathbf{a} + \mathbf{w} : \mathbf{w} \in V\}$: Adding/Subtracting Non-Set Objects (Vector Elements) from Sets?

Question

The following article seems to show non-set objects (in this case, vectors) being subtracted from sets:

https://en.m.wikipedia.org/wiki/Affine_space#Affine_subspaces_and_parallelism

I’m wondering what’s going on here, since, as far as I’ve learned, this is not a valid mathematical operation?

I would appreciate it if people could please take the time to clarify this.