What Are Sets?

What Are Sets?

It is a term in mathematics that is used to define the presentation of collected objects. In other words, it refers to the representation of a collection of objects. Sets are usually represented in mainly two forms, one is set-builder and the second one is roster form. When you will start studying sets then you will get to observe that these are represented by using curly brackets only. A = {5,7,9,11} is an example of sets.

Definition of sets

When the collected elements or objects are represented, such a representation is called a set. It would remain the same person to person, there won’t be any sort of change in it. The elements that are represented in a finite set are named cardinal numbers.

Let’s understand the properties of sets with the following example:

A = {3,5,7,9,11}, the alphabet ‘A’ is a set and the numbers that are written in curly brackets are the members or elements of sets. Any order can be used while writing these sets but one thing is to be considered and that is the elements of a set can not be repeated, in simple words, there should be no repetition in elements of sets.

We use different alphabets for different sets:

N for a set containing all natural numbers

Z for a set containing elements that are integers

Q for a set that has rational numbers only

R for a set that has real numbers only

Z+ for a set that has only positive integers

Order of sets

The element that assists in defining how many members that a set has is called the order of sets. It also helps in knowing the size of a set, it is also called cardinality.

Representation of sets

As already stated above, sets are represented in two forms mainly, statement form, set-builder form, or roster form.

Statement form

In this form, elements of a set are written in curly brackets and are written in a well-defined manner. Let’s say you want to write a set of odd numbers less than 21. Then you will write it as A = {odd numbers less than 21}.

Roster form

In this form only listed elements are written. Let say, you want to create a set of natural numbers less than 9. It will be represented as N = {1,2,3,4,5,6,7,8}. All these numbers are natural and less than 9.

Types of sets in Mathematics

There are many types of sets in mathematics. To gain knowledge of sets, you can visit the Cuemath website. There are various math experts who have explained sets in an easy manner. However, types of sets include equal sets, finite sets, infinite sets, proper sets, empty sets, etc.

Empty set

When a set does not include any element or member in it, such a set is known as an empty set. A null set or void set are also used to present an empty set. It is written as A = {} or ∅.

Singleton set

When in a set only one element or member is present, such a set is called a singleton set.

Finite set

When in a set there are a specified number of elements. That set is known as a finite set. For example, in a set of odd numbers up to 11. You know that there will be only limited numbers because the odd number has not to be more than 11. It will only include 1,3,5,7,9,11.

Infinite set

In this type of set, numbers of elements or members can not be restricted to a specified number. Let say, you want to write all even numbers in a set. Then it will include 2,4,6,8,10,……….. n. It can not be limited.

Equal sets

When two or more sets have an equal number of elements of equal values, irrespective of the series in which they have been written.

For example, set A = {2,4,6,8} and set B = {8,6,4,2}. These two sets are equal having equal number of elements with equal values but in a different sequence.

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