Linear subspace and Affine subspace I am currently reading a paper titled "Another view of division property" and encountered the terms "Affine subspace" and "Linear subspace". I am new to the field and having some difficulties to understand the topics. Can anyone describeb or give any reference about it so that I can read that.
In general an affine subspace is not a subspace, it's just a translate (coset) of a subspace. This is because normally we expect $0$ to be in a subspace $V$, since due to closure $x-x \in V.$

If $a+V$ is an affine subspace for $a\neq 0,$ and $V$ a subspace then automatically $a$ is required to be not in $V.$ Otherwise $a+V=V.$