Definition: Generally, some specified objects are brought together to form a set.
Set: Set some specified objects together to form a set.
Characteristics of elements in a set
Certainty: given an element according to a clear standard, it is either in this set or not in this set, and there can be no ambiguity.
When it comes to belonging, that is, A is an element of set A, it is said that A belongs to A, and the set marked a∈A is usually represented by uppercase Latin letters, such as A, B, C, P, Q ... elements are usually represented by lowercase Latin letters, such as the opening directions of A, B, C, P, Q .. "∑" and A∑ "cannot be represented.
If A is not an element of the set A, it is said that A does not belong to A, and it is recorded as
Dependency: The elements in the collection are not duplicated.
Out-of-order: The elements in a collection have no definite order (usually written in normal order).
Representation of a set:
(1) enumeration method: the elements in the set are listed one by one with braces and separated by commas. Specifically, it is divided into the following three situations:
(1) when the number of elements is small and limited, all of them are listed; For example {1, 2, 3}
(2) When the number of elements is large and limited, you can list some elements with ellipsis in the middle, and it depends on whether you can see the law in general, which is called the middle ellipsis. For example, "all natural numbers from 1 to 10000" can be expressed as {1, 2,3, ..., 10000};
③ Thirdly, when the number of elements is infinite but regular, similar ellipsis can also be used for enumeration. For example, a set composed of natural numbers can be expressed as {0, 1, 2, 3, 4, ...}, and enumeration is omitted.
(2) Description method
It can be subdivided into text description and attribute description. In the former, the attributes of a set are written in braces. Because the brackets themselves contain the meaning of "all" and "all", similar quantifiers should be removed.