A complete set means that a set contains all the elements involved in the problem we are studying, so it is called a complete set, usually expressed 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.

Any set can be a complete set. When a specific set is studied, it is a complete set. If we study real numbers, then the set of all real numbers, the real number line R, is a complete set. This is the default complete works when Cantor first developed modern naive set theory and set potential with real analysis in1870s and1880s. Cantor initially only cared about a subset of r.

Extended data

The nature of the set:

1, certainty

Given a set, any element, whether it belongs to the set or not, must be one of them, and there is no ambiguity.

2. Interrelation

Any two elements in a collection are considered different, that is, each element can only appear once. Sometimes it is necessary to describe the situation that the same element appears many times. You can use multiset, which allows the element to appear many times [6]? .

3. Chaos

In a set, the state of each element is the same and the elements are out of order. You can define an order relation on the set. After defining the order relation, you can sort the elements according to the order relation. But as far as the characteristics of the set itself are concerned, there is no necessary order between elements.

Baidu Encyclopedia-Complete Works