 At the level of function fields we therefore have

While a typical point "v" of "V" is φ("u") with "u" in "V"′, from "v" lying in "K"("V") we can conclude typically only that the coordinates of "u" come from solving a degree "e" equation over "K".The whole object of the theory of thin sets is then to understand that the solubility in question is a rare event.This reformulates in more geometric terms the classical Hilbert irreducibility theorem.