A set is a group, and it has several properties, all of which are in this textbook. In addition, the set of senior three tends to do problems, and the rest are minor problems. You should be able to grasp the following points: the whole set of specified objects is called a set. On the whole, a set of definite, definite and distinguishable things is called a set, and each thing is called an element or element of the set. Such as (1) different Chinese characters appearing in the true story of Ah Q (2) all English capital letters. Any set is a subset of itself. Generally speaking, if some identifiable different objects are regarded as a whole, it is said that the whole is a collection (or collection) composed of all these objects. Each object that constitutes a set is called an element (or member) of this set. The relationship between elements and sets can be divided into two types: attribution and non-attribution. The relationship between sets. When some specified objects are grouped together, they become a collection of symbols, which contains finite elements and infinite elements. An empty set is a set without any elements, and it is recorded as φ. An empty set is a subset of any set and a proper subset of any non-empty set. Any set is a subset of itself. Subsets and proper subset are transitive. Explanation: If all elements of set A are elements of set B at the same time, call A a subset of B, and write A? B. If A is a subset of B and A is not equal to B, then A is called proper subset of B, which is generally written as A? B. What will be in the middle school textbook? A ≠ symbol (as shown on the right) is added below the symbol, so don't confuse it. The exam should be based on the textbook. A collection of all people is a collection of all people, proper subset. Several algorithms for the union of sets: A set whose elements belong to A or B is called the union (set) of A and B, marked as A∪B (or B∪A) and pronounced as A and B (or B and A), that is, A ∪ B = {x | x ∈. Pronounced as "A across B" (or "B across A"), that is, A∩B={x|x∈A, x∈B} For example, Complete Works U = {1, 2,3,4,5 5} A = {65438+}. Then because both A and B have 1, 5, A ∩ B = {1, 5}. Let's take another look. Both contain 1, 2, 3, 5, no matter how much, either you have it or I have it. Then say a ∪ b = {1, 2, 3, 5}. The shaded part in the picture is a ∩ B. Interestingly; For example, how many numbers in 1 to 105 are not integer multiples of 3, 5 and 7? The result is that the subtraction set of each item of 3, 5 and 7 is 1 and then multiplied. 48. Symmetric difference set: Let A and B be sets, and the symmetric difference set A of A and B? The definition of b is: a? B =(A-B)∩(B-A) For example: A={a, b, c}, B={b, d}, then A? Another definition of B={a, c, d} symmetric difference operation is: a? B =(A∪B)-(A∪B) Infinite set: Definition: A set containing infinite elements in a set is called an infinite set finite set: let N* be a positive integer, N_n={ 1, 2, 3, ..., n}, if there is a positive integer n, the difference is that the elements belong to. Note: An empty set is contained in any set, but it cannot be said that "an empty set belongs to any set". Complement set is a concept derived from difference set, which means that a set composed of elements belonging to complete set U but not to set A is called the complement set of set A, and it is denoted as CuA, that is, an empty set with CuA={x|x∈U and x not belonging to A} is also considered as a finite set. For example, if the complete sets U = {1, 2, 3, 4, 5} and A = {1, 2, 5}, then 3,4 in the complete set but not in A is CuA, which is the complement of A. CuA = {3,4}. In information technology, Determinism: Every object can decide whether it is an element of a set. Without certainty, it cannot be a set. For example, "tall classmates" and "very few" cannot form a set. This property is mainly used to judge whether a set can constitute a set. 2. Independence: The number of elements in the set and the number of the set itself must be natural numbers. 3. Relevance: Any two elements in the set are different objects. If written as {1, 1, 2}, it is equivalent to {1, 2}. Being different from each other makes the elements in the collection not repeat. When two identical objects are in the same set, they can only be counted as an element of this set. 4. Disorder: {a, B, c}{c, B, a} are the same set. 5. Purity: The purity of the so-called set is represented by an example. Set a = {x | x

Intersection, union, complement, empty set, subset element enumerator combined with predicate logic, binary relational function algebra system, array mapping semi-group intersection, union, complement, empty set, subset element enumerator combined with predicate logic, binary relational function algebra system, array mapping semigroup string algorithm, vector recursive greedy algorithm, Map Hashmap Arraylist. The entries in Baidu Encyclopedia are for reference only. If you need to solve specific problems (especially in the fields of law and medicine), it is recommended to consult professionals in related fields. The entry 4456 helps me to add search and sharing: co-editors: Zhuang Lintai, Encyclopedia Robot, Meikao, Encyclopedia Fenghua, Hao Chen 95, Bailiyi, bieiloveyou, etc. If you think this entry needs further improvement, Encyclopedia welcomes you to participate in editing the entry. Before editing, you can also learn how to edit an entry. If you want to complain, please go to Baidu Encyclopedia Complaint Center. If you want to make comments and suggestions, please go to Baidu Encyclopedia.