Summary of high school mathematics collection knowledge, senior one mathematics collection knowledge

Mathematics in the first year of high school is the knowledge of the set, so let me tell you the knowledge points of the collection of mathematics in the first year of high school, so that you can learn better.

Concept: To learn sets, you must first understand the concept of sets and know what sets are. A set is a totality of things of a specific nature.

Relationship between elements and sets: The things that make up a set are called elements. There are only two types of relationships between elements and collections: belonging and non-belonging.

The relationship between sets and sets: There must be more than one kind of object with a particular property, so there is more than one kind of set. The properties between sets and sets have a relation of subset, true subset. The specific relationship is shown in the figure.

Nature: There are 4 properties of the set, which are qualitative, mutual, independent, and disorderly. These properties are indispensable, otherwise they would not be a collection. The details are as follows.

As follows:

1. Given a set, any element that belongs to or does not belong to the set must be one of the two, and no ambiguity is allowed.

2. In a set, any two elements are considered to be different, that is, each element can only appear once. Sometimes you need to characterize the situation where the same element appears more than once, you can use a multiset where the element is allowed to appear more than once.

3. As an element of a set, it must be determined, that is, an object that cannot be determined cannot constitute a set, that is, given a set, whether any object is an element of the set is also determined.

4. For a given set, the elements in the set must be different (or different), that is, any two elements in the set are different objects, and the same object can only be counted as one element of the set when it is grouped into the same set.

5. A set with a finite number of elements is called a finite set, and a set with an infinite number of elements is called an infinite set.

The knowledge points of the first year of high school mathematics are as follows:1. Some specified objects are grouped together to form a set, referred to as a set, and each object is called an element. For example, if the first and second classes of high school are assembled, then all the students of the first and second classes of high school constitute a set, and each student is called the element of this set.

Second, it is common to use uppercase letters to represent collections, and lowercase letters to represent elements.

3. In a set, the status of each element is the same, and the elements are disordered among themselves.

Fourth, the foundation of set theory was laid by the German mathematician Cantor in the 70s of the 19th century, after a large number of scientists for half a century of efforts, by the 20s of the 20th century has established its basic position in the system of modern mathematical theory, it can be said that almost all the achievements of various branches of modern mathematics are built on strict set theory.

5. The number of elements in a set is called the cardinality of the set, and the cardinality of set A is denoted as card(a). When it is finitely large, set A is called a finite set, and vice versa is an infinite set. In general, a set with a finite number of elements is called a finite set, and a set with an infinite number of elements is called an infinite set.

As follows:

1. Sets and elements of sets are two different concepts, which are given by description in textbooks, which is similar to the concept of points and straight lines in plane geometry.

2. The elements in the set are deterministic, heterogeneous, and disordered.

3. The set has two meanings, namely: all eligible objects are its elements; As long as it is its element, it must be symbolic conditional.

4. Sets are a basic concept in mathematics. The underlying concept is one that cannot be defined by other concepts. The concept of a set can be "defined" in an intuitive, axiomatic way.

5. A set is to bring together some definite and distinguishable objects in people's intuition or thinking to make it a whole (or a monomer), and this whole is a set. Those objects that make up a set are called elements (or simply metas) of the set.

Quality. For any set a, the empty set is a subset of a: a: a.

For any set a, the union of the empty set and a is a: a:a a.

For any non-empty set a, the empty set is a true subset of a: a, and if a ≠ , then true is contained in a.

For any set a, the intersection of the empty set and a is an empty set: a, a

For any set a, the Cartesian product of the empty set and a is a empty set: a, a

The only subset of the empty set is the empty set itself: a, if a a, then a= a, if a= then a a.