"Obviously, the intersection of an arbitrary collection of affine sets is again affine. Therefore, given any $S \subset R^{n}$ there exists a unique smallest affine set containing $S$ (namely, the intersection of collection of affine sets M such that $S \subset M$. This is called the affine hull of S. "
This is a paragraph from "convex analysis" by rockafeller (page - 6). My question is why, given every $S \subset R^{n}$ there exists a unique smallest affine set containing S ? Why it should be so ? (just to clear another doubt, is $S$ here any subset of $R^n$ or does it mean only subspace of $R^n$? Nothing is mentioned in the book)