# Understand Sets in Maths with Cuemath

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When the talk comes to mathematics, the concepts are very wide. Right from the start, the student is told about different types of mathematical concepts that will be used in the other concepts in the higher classes. One of the very common concepts of maths is sets. Almost every student learns this in school. Sets in math are the collection of the objects that are represented in the two forms i.e. set-builder or the roaster form.

The sets are mostly represented in curly brace {}. For example there is a set P = {2, 4, 6, 8}. The set is not complete until it does not close with the curly bracket. It is defined as the collection of well-defined objects that will not change from person to person. The set will always be represented with a capital letter and it will include different types of numbers.

For example there is set A = {1, 2, 3, 4, 5}. The name of the set is A which is a capital letter and it has elements 1, 2, 3, 4, 5 which are included in the set. There can be multiple elements in the set but make sure that there is no repetition of the element in the set. The sets can also be written as the set of the first five natural numbers.

There are different types of numbers included in a set which are stated below:

Set can include all Natural numbers which are presented by N.

Set can include all integers and it is represented by Z.

All the rations numbers are included in the set which is represented by R.

Even all the positive integers can be included in the set which is presented by Z+.

The order of the set will represent what the set has in it. The size of the set is represented by the cardinal number. For example, A = {1, 2, 3, 4, 5}. So the cardinal number will be 5 because it has five elements in it. The representation of the sets can be done in the following forms. Let’s have a look at them.

Statement form: In this form of representation, a well-defined description of the members of the sets and even it will be enclosed in the curly brackets. For example, there is a set A that includes all odd numbers less than 10. So it will be represented as A = {odd numbers less than 10}.

Roasted form: In this form, all the sets are represented in the form of numbers. For example, the set includes all the natural numbers less than 7. So the set will be stated as A = {1, 2, 3, 4, 5, 6}.

Set builder form: It is a little technical form of writing a set. The general form is, A = { x : property}. If the person wants to write the set A = {2, 4, 6, 8, 10} in the set builder form. A proper analysis of the common property will be taken out from it like in this all are multiple of 2 like 2 = 2*1, 4 = 2*2, 6= 2*3, 8= 2*4, and 10= 2*5. So in set-builder form, the set will be represented as A = { x: x= 2n, n N and 1 ≤ n ≤ 4}.

Even the sets can be easily represented in the form of Venn diagrams for better understanding. There are different types of stated below:

Empty set that does not have anything in it.

Singleton set that contains only one element in it.

Finite sets that contain a definite number of elements.

Infinite sets are sets that are not finite.

Equivalent sets are two sets of the same cardinal numbers.

Equal sets that have exactly the same elements.

A universal set is a set that contains all the elements present in different sets.

So, if any of the students want to have more information on this. They can easily take help from the visit website of Cuemath which is a great platform to learn the different concepts of numbers.

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