Generally speaking, if a set contains all the elements involved in the problem we are studying, it is called a complete set, usually denoted as U. In mathematics, especially in the application of set theory and mathematical foundation, the whole class (if it is a set, it is a complete set) is about such a class, which (to some extent) contains all the research objects and sets.

Extended data

In general mathematics, SN can be accurately defined as a complete set; This is the model of Zermelo's set theory. Zemello's set theory is an axiomatic set theory first put forward by Ernst zermelo in 1908. The success of Zermelo's set theory lies entirely in its axiomatization of "general" mathematics and the completion of the project started by Cantor thirty years ago.

However, zermelo's set theory is not enough to further develop axiomatic set theory and other work in mathematical foundation, especially model theory. To give a dramatic example, the above description of superstructure cannot be completed independently in Zemelo's set theory.

The last step is to construct S as an axiom that is infinite and needs to be replaced. This axiom was added to the Zemello set theory in 1922 and became the general Zemello-frankl set theory. Therefore, although general mathematics can be carried out in SN, the discussion of SN is no longer "ordinary" and belongs to meta-mathematics.

Baidu Encyclopedia-Complete Works