Definition of Set, and Set Notation

 

1. Introduction

Set theory is a fundamental part of mathematics education. Set theory may be used to study a wide range of mathematical topics more quickly and accurately. Sets and certain fundamental procedures using them were previously covered in junior high school, so you should be familiar with them. Because we'll be using sets in our math tutorials, we need to go over some basic concepts again.

2. Definition of a Set

In daily life, we often discuss the accumulation of items. For instance, a team of players, a group of pupils, or a bouquet of flowers. We used the term "set" to refer to a unique kind of collections.

Look at the following two collections:

1. January, February, March, April, May, June, July, August, September, October, November, December.
2. Angry people in your class.

The first example is the collection of the months in a year. Objects are clearly defined in the first example. 'Angry people' is a relative phrase in this case. Kojo may be angry per the view of Abena, while Charles may not think that to be the case. On this premise, we are unable to make a decision on whether or not to add Kojo in our class's collection of irate (angry) students.

Thus, set is a well-defined collection of objects of the same kind.

In the first example, we can definitely decide whether a given object belongs to a given collection or not. In the second example, collection is not well defined.

i) All boys in Form 2

ii) Days of a week

iii) Collection of the numbers 3, 5, 7.9

iv) Courageous people

Collections (i), (ii), and (iii) are sets but (iv) is not a set.

3. Set Notation

Set up conventionally denoted are represented by capital letters. For example, . etc and the members of a set are enclosed in curly brackets {} .

Members or elements of a set refer to the things that make up a set.. They can be anything, that is, numbers, people, letters of your favorite, other sets, and so on. For instance, if , then 3 is an element or a member of i.e. .

Additionally, .

The set notation means "is a member of" or "belongs to."

It can also be said that 8 does not belong to or it is not a member of P, written in set notation as:

The set notation means "does not belong to" or "not a member of."

The number of elements in set is 4 , and the set notation for that is .

The cardinality of a set is the total number of items in the set.

Thus, the cardinality of the set is .

Some sets, such as the set of natural numbers, on the other hand, have an unlimited number of members.

For detailed maths tutorial on the above subject, watch the video below.

 

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