More precisely, let "V" be an algebraic variety over "K" (assumptions here are: "V" is an irreducible set, a quasi-projective variety, and "K" has characteristic zero). A type I thin set is a subset of "V"("K") that is not Zariski-dense. That means it lies in an algebraic set that is a finite union of algebraic varieties of dimension lower than "d", the dimension of "V". A type II thin set is an image of an algebraic morphism (essentially a polynomial mapping) φ, applied to the "K"-points of some other "d"-dimensional algebraic variety "V"′, that maps essentially onto "V" as a ramified covering with degree "e" > 1. Saying this more technically, a thin set of type II is any subset of