Sets – Definition, Notations & Symbols

Sets are an essential concept in mathematics that helps us organize and categorize objects or elements.

They are a fundamental building block in various areas of mathematics and have applications in many fields, including computer science, physics, and economics.

Here, we will explore the basics of sets, their notation, and how they are used.

 

What is a Set?

A set is a collection of distinct objects or elements. These objects can be anything: numbers, letters, colors, shapes, or even other sets.

For example, a set can contain numbers like {1, 2, 3}, letters like {a, b, c}, or even a combination of both like {1, a, 3, b}.

Important Note: The order of the elements in a set does not matter, and each element appears only once within a set.

 

Notations & Symbols

• Sets are commonly represented using curly braces { }.
• If an element “a” belongs to a set “A,” it is represented using the membership symbol “∈.”

The notation,

a ∈ A denotes that the element “a” is a member of the set “A.”

(In other words, “a” is one of the objects or elements included in the set “A.”)

Example

If we have a set “A” containing the numbers {1, 2, 3}, and we want to indicate that the number 2 belongs to set “A,” we would write it as “2 ∈ A.”

• Conversely, if an element does not belong to a set, we use the symbol “∉.”

For instance, if we want to indicate that the number 4 does not belong to set “A,” we would write it as “4 ∉ A.” This notation signifies that element 4 is not included in the set “A.”

 

Examples

1. A set of even numbers can be written as {2, 4, 6, 8, …}, where the ellipsis (…) represents that the pattern continues indefinitely.
2. The set of vowels can be written as {a, e, i, o, u}.