"The Concept of Sets" (the concept of sets and several common number sets in the first lesson) PPT

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"The Concept of Sets" (the concept of sets and several common number sets in the first lesson) PPT

Part One: Explanation of Curriculum Standards

1. Understand the meaning of sets through examples.

2. Master the three characteristics of elements in the set.

3. Understand the "belonging" relationship between elements and sets.

4. Remember commonly used number sets and their notation

The concept of set PPT, part 2: inquiry learning

1. The concepts of elements and sets

1. Dear classmate, congratulations on becoming a high school student! When you walk into this campus, everything is so fresh:

① All the buildings on campus are of different shapes; ② The teachers who teach your class are knowledgeable; ③ All the students in the class are energetic, including male and female students; ④ There are some taller students in the class , some students are more handsome; ⑤ There are many big trees on campus...

(1) What are the objects to be explained in each of the above sentences?

Tips: ① All the buildings on campus; ② Teachers who teach various subjects in your class; ③ All students in the class, male and female; ④ Taller students, more handsome students; ⑤ Big trees.

(2) Which statement involves an uncertain object? Why?

Tip: The objects involved in ④⑤ are uncertain. Because there are no clear criteria for classifying taller, handsomer, and big trees.

2. Fill in the blanks

Generally, we refer to the research objects as elements, usually represented by the lowercase Latin letters a, b, c,.... The totality of some elements is called a set (referred to as a set), usually represented by the uppercase Latin letters A, B, C, … represents a set.

2. Characteristics of elements in a collection

1. (1) Can the taller students in our class form a group? Can the students in our class whose height is no less than 180 cm form a group? What problem does this illustrate?

Tips: Taller students cannot form a group because the standard of "relatively taller" is uncertain; students with a height of no less than 180 cm can form a group because the standard of "height of no less than 180 cm" is determined. For any student in the class , whether "the height is not less than 180 cm" is clear. It means that the elements in the set are deterministic.

(2) The school supermarket purchased goods twice in one day. The first purchase included gel pens, mineral water, and bread, and the second purchase included ham, mineral water, and instant noodles. The goods purchased on this day formed a set. How many elements are there in the set? What does it mean?

Tip: There are 5 elements, namely gel pen, mineral water, bread, ham sausage, and instant noodles. This shows that the elements in the set are mutually exclusive. Repeated elements can only be counted as one. In other words, the elements in the set are not repeated. appeared.

(3) Our whole class forms a group. If the seats are adjusted once in the class, will the group of the class change? What does it mean?

Tip: The set has not changed because the elements are the same. This indicates that the elements in the set are disordered.

2. Fill in the blanks

(1) The three major characteristics of elements in a set: certainty, mutuality, and disorder.

(2) As long as the elements that make up two sets are the same, we say that the two sets are equal.

3. The relationship between elements and sets

1. (1) All the students in your class form a group. If you randomly designate a classmate, what is the relationship between this classmate and this class group?

Tip: Any given student either belongs to this class or does not belong. That is, there are only two relationships between elements and sets: belonging and not belonging.

(2) A set consisting of numbers greater than 1 is called set A. What is the relationship between 1 and 2 and set A?

Tip: Because 2>1 is true, 2 is an element in set A, that is, 2 belongs to set A; because 1>1 is not true, so 1 is not an element in set A, that is, 1 does not belong to set A.

2. Fill in the blanks

3. Do it

It is known that the element x in set A satisfies x-1<√3, then the following formulas are correct ()

A.3∈A and -3∉A B.3∈A and -3∈A

C.3∉A and -3∉A D.3∉A and -3∈A

Answer:D

4. Commonly used number sets and their notation

1. (1) Is 0 a natural number? Is 0 a positive integer? Is 0 an integer?

Tip: 0 is a natural number, an integer, not a positive integer.

(2) What is the difference between the set of natural numbers and the set of positive integers?

Tip: The set of natural numbers contains 0, and the set of positive integers does not contain 0.

(3) What are rational numbers? What are irrational numbers?

Tip: Numbers such as positive integers, 0, negative integers, positive fractions, and negative fractions are called rational numbers; irrational numbers are also called infinite non-repeating decimals and cannot be written as the ratio of two integers.

2. Fill in the blanks

The concept of set PPT, the third part: analysis of examples

collection concept

Example 1 gives the following sets of objects:

① The taller students in our class; ② The total number of numbers infinitely close to 0; ③ The total number of relatively small positive integers; ④ The total number of points on the plane whose distance from point O is equal to 1; ⑤ The total number of equilateral triangles; ⑥ The entire set of approximations of .

Among them, those that can form a set include ()

A.1 B.2 C.3 D.4

Analysis: To judge whether a group of objects can form a set depends on whether the judgment criteria are clear.

Analysis: ①②③⑥ cannot form a set because there is no clear judgment standard; ④⑤ can form a set. "The point on the plane whose distance from point O is equal to 1" and "equilateral triangle" have clear judgment standards.

Answer:B

Variation training 1 (multiple choice question) Which of the following groups of objects can form a set ()

A. All integers greater than 6

B. All difficult problems in high school mathematics

C. All integers divided by 3 with remainder 2

D. All points on the graph of function y=1/x

Analysis: The elements in options A, C, and D conform to the certainty of the elements in the set; while in option B, the "dilemma" has no clear standard and does not conform to the certainty of the elements in the set, so it cannot constitute a set.

Answer:ACD

PPT on the concept of assembly, part 4: practice in class

1. The objects given below can form a set ()

A. All very large numbers B. Numbers infinitely close to zero

C. A smart person D. The real roots of the equation x2=2

Analysis: The objects given in options A, B, and C are all uncertain, so they cannot form a set; the real root of the equation x2=2 in option D is x=-√2 or x=√2, which is deterministic. So it can form a set.

3. It is known that the three elements a, b, and c in the set S are the three side lengths of △ABC, then △ABC must not be ()

A. Acute triangle B. Obtuse triangle C. Right triangle D. Isosceles triangle

Analysis: From the mutuality of the elements in the set, we know that a, b, and c are not equal, so △ABC must not be an isosceles triangle.

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For more information about the PPT courseware "Sets and Commonly Used Logical Terms, The Concept of Sets, The Concept of Sets, and Several Common Number Sets", please click on the "Sets and Commonly Used Logical Terms, The Concept of Sets, ppt, The Concept of Sets, and Several Common Number Sets" ppt tags .

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Update Time: 2024-09-29

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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