Do You Know What Sets Are?

In mathematics, a set can be defined as the collection of simple distinct objects which form a group. The sets can include any type of collection such as the collection of weeks, days, the collection of vehicles, phones, and so on. Each and every quantity or number in the group is said to be an element of the set. The brackets which are curly in shape are used while we write the sets. Some examples of it are as follows: {2, 4, 6, 8, 9} , {1, 2, 4, 6, 8,} etc. You must remember that this can only be written till the number 10. All the natural numbers till 10 can be included in the collection. Natural numbers can be defined as the numbers which can be counted such as 1, 3, 5, 6, 8, and so on. In this article, we will try to cover some basic concepts regarding sets such as representation, types, and a brief analysis.

Representation of the Sets

Basically, there are some types of notations given for various sets which represent them differently. The difference is created by the way those elements mentioned in sets are listed. Generally, there are three types of representation of sets. 

• The first type of representation of sets signifies a statement: what are the elements of a set which are listed in it. This representation is known as the semantic form of sets. Let us take an example so that your concept is clear about the topic. The first set or set signifies the first ten odd numbers is a type of semantic form.
• The second type of representation of sets is the most common way of expressing it, as it involves the elements of a set in curly brackets which are segregated by the help of commas. This representation is known as the roster form. There are two types of roster forms: the infinite roster and the finite roster form. Examples of finite roster forms are as follows: 1, 3, 5, 7, 9; these numbers are the first five odd numbers. Examples of infinite roster forms are as follows: 6, 12, 18, 24, 30, and so on, these numbers are the multiple of 6 which are infinite.
• This representation of set describes the statement that specifically represents the basic features of the above two representations: roster and semantic form. It is known as the set builder form.

Different Types of Sets

Sets questions even appear in IMO, so it is pretty safe to say that having knowledge about the same would be of use one way or the other.

As mentioned above, the set can be defined as the collection of simple distinct objects which form a group. There are various different types of sets that possess different properties. The following points analyze the types of sets in brief. 

1. A type of set that consists of only one element can be defined as the unit set or singleton set.
2. A type of set which includes finite numbers of elements can be defined as the finite set.
3. A type of set which includes infinite numbers of elements can be defined as infinite sets.
4. A set that doesn’t contain any element in the list, they are known as the null or empty set.
5. Whenever two sets have the same number of elements in them, they are considered equal sets. Similarly, when they have an unequal number of elements listed, they are defined as unequal sets.

Cuemath Website

There are some topics in mathematics that are quite difficult to understand, one of them is sets. But you shall not worry, Cuemath is there to help you. If you want to learn about topics like sets in a detailed, fun, and interactive manner, visit the Cuemath website.