It is the research object of set theory. The basic theory of set theory was not established until19th century. The simplest form is defined as primitive set theory, and naive set theory is defined as "a certain group of things".
The "things" in a set are called elements. The whole consisting of one or more recognized elements is called a set, and if X is a member of set A, it is recorded as X ∈ A. ..
A group of elements has three characteristics:
1, deterministic (the elements in the set must be deterministic).
2. Anisotropy (a group of elements is different). For example, if a = {1, a}, then a cannot be equal to 1).
3. Disorder (there is no element sequence in the set), for example, sets {3,4,5} and {3,5,4} are regarded as the same set.
Correlation characteristic
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 where the same element appears many times. You can use multiset, where elements are allowed to appear multiple times.
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.