We learn to be patient and bear. But there is always an eternal desire in our hearts. It is an eagle, flying in the sky! It's a good horse, galloping across the territory! Stand upright! Work hard! Hold on! Work hard! Success! Let's take a look at the compulsory knowledge point of senior one mathematics in Beijing Normal University Edition: the meaning and expression of set, which is prepared for everyone by No Senior One Channel. I hope it will help your study!

The concept of 1. set

Generally speaking, some identifiable different objects are regarded as a whole, that is, the whole is a set (or collection) composed of all these objects; Each object that constitutes a set is called an element (or member) of this set. The elements of a collection can be all kinds of things we see, hear, smell, touch and think of, or some abstract symbols.

2. Characteristics of set elements

From the two key words "definite" and "different" in the concept of set, we can know that set elements have two characteristics:

⑴ Deterministic characteristics: The elements in the set must be clear, and vague and inconclusive statements are not allowed.

Given a set, if there is a specific object, it is either an element or not, and the two will live together.

One, and only one.

⑵ Heterogeneity: The elements in the set must be different from each other. If a set is given, its elements refer to the different elements contained in it. When the same object belongs to the same collection, it can only be regarded as an element in the collection.

3. The relationship between sets and elements

There is only "attribution" or "non-attribution" between a set and an element. For example, it is an element of a set, recorded as "belonging" and pronounced as "belonging"; Elements that are not collections are recorded as "not belonging".

4. Classification of sets

Sets can be divided into finite sets and infinite sets according to the number of elements. In particular, a set that does not contain any elements is called an empty set.

5. Representation method of set

(1) enumeration method is a method of listing elements one by one without repetition and sequence, which is very intuitive and clear at a glance.

⑵ Feature attribute description is a set representation that describes the features of elements in a set with certain conditions.

For example, a set can be described as {} by its characteristic properties, which means that any element belonging to the set has properties in the set, while all elements not belonging to the set have no properties.

In addition, in the second year of high school, the set is often represented by Wayne diagram, which is a method of representing the set by points inside a closed curve (sometimes some elements in the set are also determined by lowercase letters)

Synchronous exercise questions

1. describes the set {1, 5, 9, 13, 17}, and the correct one is ().

A.{x|x is a positive odd number less than 18}

B.{x|x=4k+ 1, k∈Z and k.