Elements of a Set

An object that forms a set is called an element (or a member) of a set.

Introduction

The objects are collected on the basis of one or more common factors for defining a set in mathematics and every object is called an element of the set. It is also called as a member of a set. Now, let’s learn the concept of members of a set from three understandable examples.

Basic example

In general, we buy or sell or carry the objects in closed packets. For example, three apples are collected in a closed geometric shape for a purpose. The collection of them formed a set. In this set, each object is called an element or a member.

1. The red apple is an element of the set.
2. The green apple is also a member of the set.
3. The yellow apple is also an element of the set.

Numerical example

Mathematics is all about numbers. So, let’s understand the concept of elements or members of a set from a numerical example.

The objects $2$, $4$, $6$ and $8$ are basically numbers and they are collected to form a set. Actually, the four objects are even numbers and the set is denoted by a letter $E$.

In the set $E$, the objects $2$, $4$, $6$ and $8$ are called the elements of a set. They are also called as the members of the set $E$.

Advanced example

In advanced mathematics, we use letters instead of numbers. Hence, the objects are denoted by the small (or lowercase) letters in set theory.

The objects $a$, $b$, $c$, $d$ and $e$ are five alphabets. The collection of them is formed a set $A$.

Now, the lowercase letters $a$, $b$, $c$, $d$ and $e$ are called the elements of set $A$. Similarly, they are also called as the members of the set $A$.