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.
- The red apple is an element of the set.
- The green apple is also a member of the set.
- 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 $A$.