In mathematics, a Grothendieck universe is a set with the following properties:
If x ∈ U and if y ∈ x, then y ∈ U.
If x,y ∈ U, then {x,y} ∈ U.
If x ∈ U, then P(x) ∈ U. (P(x) is the power set of x.)
If is a family of elements of U, and if I ∈U, then the union is an element of U.
A Grothendieck universe is meant to provide a set in which all of mathematics can be performed. (In fact, it provides a model for set theory.) As an example, we will prove an easy proposition...
