# Representation of Sets in Mathematics

**Topic discussed in this video:**

- Representation of sets in math
- Roster form / Listing Method
- Set-builder form / Property Method

To understand the representation of sets, let’s get back to its definition.

**A set is a well-defined collection of objects of the same kind.**

Here, the phrase collection of objects gives us the idea that we can make a list of all the objects. That’s why the first method is known as the listing method. The other name for the listing method is the roster form of the set.

Secondly, the phrase objects of the same kind give us the idea that all the objects in that collection possess a common property and we can represent the set by that common property. That’s why the second method is known as the property method. The other name for the property method is the set-builder form of the set.

Let’s take an example “** a collection of the first five natural numbers**” to understand the two forms in detail.

As we know, ** a collection of the first five natural numbers** will always have 1, 2, 3, 4, and 5. In roster form, we make a list of these objects like this:

Objects are also known as elements of sets. In roster form, elements are always separated by commas and always enclosed within curly braces {}.

Generally, we usually denote sets by capital letters and elements by small letters. So, if I denote the set by

**A**, then the roster form will look like this:

Before we discuss the set-builder form, there are two important points regarding the roster form that you should remember……