Published on: July 2, 2007117: 24: 29 Source: Read (44) Comments (0) Report this article link:/292823213/blog/1.
Episode 3
1. 1 set
Teaching purpose: knowledge goal:
(1) enables students to have a preliminary understanding of the concept of set, and to know the concept and notation of common number set.
(2) Let students understand the meaning of "belonging" relationship.
(3) Make students understand the meaning of finite set, infinite set and empty set.
Ability goal:
(1) Attach importance to the teaching of basic knowledge, the training of basic skills and the cultivation of abilities;
(2) Inspire students to discover and ask questions, be good at independent thinking, and learn to analyze and solve problems creatively;
(3) Finding knowledge conclusions through teachers' guidance, and cultivating students' abstract generalization ability and logical thinking ability;
Teaching emphasis: the basic concept and expression method of set
Difficulties in teaching: Using two common representations of sets-enumeration method and description method to correctly represent some simple sets.
Teaching type: new teaching
Course arrangement: 2 hours
Teaching AIDS: multimedia, physical projector.
Teaching process:
First, check the import:
1. Introduce the development of number sets, and review the greatest common divisor and the least common multiple, the sum of prime numbers;
2. Introduction at the beginning of the textbook;
3. The founder of set theory-Cantor (German mathematician);
4. "Birds of a feather flock together" and "Birds of a feather flock together";
Second, the new lesson explanation:
Read the first part of the textbook. These questions are as follows:
1. What are the concepts? How is it defined?
2. What symbols are there? How is it expressed?
3. What are the characteristics of the elements in the set?
(1) Related concepts of set (see textbook for examples):
1, the concept of set
(1) set: Some specified objects are set together to form a set.
(2) Element: Each object in a set is called an element of this set.
For example, the set of all solutions of an equation can be expressed as {- 1, 1}.
Note: (1) Some sets can also be expressed as:
Set of all integers from 5 1 to 100: {5 1, 52,53, …, 100}
The set of all positive odd numbers: {1, 3, 5, 7, …}
(2)a is different from {a}: A represents an element, {a} represents a set, and a set has only one element.
Description: A method of indicating whether an object belongs to this set with a certain condition and writing this condition in braces to indicate the set.
Format: {x∈A| P(x)}
Meaning: Set X that satisfies the condition P(x) in Set A.
For example, the solution set of inequality can be expressed as: or
The set of all right triangles can be expressed as:
Note: (1) The vertical line and the left part can be omitted without confusion.
Such as: {right triangle}; {Real number greater than 104}
(2) Error expression: {real number set}; {All Real Numbers}
3. Venn diagram: a method of representing a set with the interior of a closed curve.
Note: When to use enumeration? When to use descriptive methods?
(1) The common attributes of some sets are not obvious, so it is difficult to generalize, and it is not convenient to express them by description, so enumeration can only be used.
assemble
(2) Some elements of the set cannot be listed one by one, or it is inconvenient and unnecessary to list them one by one, and descriptions are often used.
Such as: collection; Set the prime number within {1000}
Note: Are the set and the set the same set?
A: No.
A set is a point set, and set = a set of numbers.
(3) Finite sets and infinite sets
2. Common number sets and their representations.
(1) non-negative integer set (natural number set): the set of all non-negative integers. Write n
(2) Positive integer set: a set that does not contain 0 in the non-negative integer set. Write down N* or N+
(3) Integer set: the set of all integers. Write z
(4) Rational number set: the set of all rational numbers. Write q
(5) Real number set: the set of all real numbers. Record as r
Note: (1) natural number set is the same as non-negative integer set, that is, natural number set contains.
Count to 0.
(2) The set of non-negative integers does not contain the set of 0. Write N* or N+. Q, z, r, etc.
A set excluding 0 from a number set is also expressed in this way, such as a set excluding 0 from an integer set.
Settings, represented by Z*
3. The connection between elements and sets
(1) belongs to: If A is an element of the set A, it is said that A belongs to A and marked as A ∈ A.
(2) Does not belong to: 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
4. Characteristics of elements in the set
(1) Determinism: Given an element or in this set according to clear criteria,
(2) or not, not ambiguous.
(3) Reciprocity: the elements in the set are not repeated.
(4) Disorder: The elements in the set have no certain order (usually written in normal order).
Note: 1, the set is usually represented by capital Latin letters, such as A, B, C, P, Q. ...
Elements are usually represented by lowercase Latin letters, such as A, B, C, P, Q. ...
2. In the opening direction of "∈", a∈A cannot be written as A ∈ A in reverse. ..
practise
1. Can the following groups of objects determine a set?
(1) All very large real numbers. (uncertain)
(2) Good people. (uncertain)
(3) 1, 2, 2, 3, 4, 5. (copy)
Read the second part of the textbook. These questions are as follows:
How many representations are there for the 1. set? How is the difference defined?
2. What are the concepts of finite set, infinite set and empty set? Give an example of each.
(2) Representation of sets
1, enumeration method: list the elements in the collection one by one and write them in braces to represent the collection.
2. Finite set: a set containing finite elements.
3. Infinite set: a set containing infinite elements.
4. Empty set: a set without any elements. Record as φ, such as:
Exercise questions:
1. describes the following set.
①{ 1,4,7, 10, 13}
②{-2,-4,-6,-8,- 10}
2. Use enumeration to represent the following sets.
①{x∈N|x is the divisor of 15} {1, 3,5, 15}
②{(x，y)|x∈{ 1，2}，y∈{ 1，2}} {( 1， 1)，( 1，2)，(2， 1)(2，2)}
Note: It is forbidden to write {( 1, 2)} as {1, 2} or {x= 1, y=2}.
③
④ {- 1, 1}
⑤ {(0,8)(2,5),(4,2)}
⑥
{( 1, 1),( 1,2),( 1,4)(2, 1),(2,2),(2,4),(4, 1),(4,2),(4,4)}