difference between algebraic set and affine algebraic set in hartshorne my question is basically already in the title. I just started to read the Algebraic Geometry book by Hartshorne where he defines an algebraic set but in some propositions a bit later talks about affine algebraic sets. So does he mean the same thing because i didn't see him define affine algebraic sets?
Thank you!

an algebraic set (or variety) is the zero set of a polynomial whose 
coefficients belong to a given
field k, considered as a subset of k^n.
if k contains R k^n may be considered affine space,
in the sense that it is closed under u,v-->au+(1-a)v for all a in R,
and then the algebraic set may be called affine.
some authors use variety only to mean na irreducible algebraic set.
