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gsenviro eNotes educator| Certified Educator

Set, in simplest terms, is a collection of similar elements or members.

It is most commonly used in mathematics while studying set theory. In mathematics, a set is generally a collection of numbers. For example, set of even numbers will be {2,4,6,8,.....}, set of prime numbers would be {2,3,5,7,.....}.

Part of a set is known as a subset, as long as the set contains all the elements of the subset.

A number of operations, such as Union, Intersection, etc. can be carried out for two sets.

Hope this helps.

Nolan McShea | Student

A set is used to describe a group of things. For example, a set can be the list of classes you have, a list of all of your friends, or a list of food! Delicious!

Let's take the set of food. So, a set of food can look like this: {pizza, chicken, salad, ...}. This is a notation of that set. A notation is when you list out the elements (every object) of that set in a pair of brackets. You can see a notation example with numbers labeled in the image below. 

There are both infinite and finite sets. Infinite sets are sets that go on and on forever. An example of an infinite set would be odd numbers. The notation for that set would look like this: {1,3,5,7,9, ...}, with the ... (ellipsis) indicating that the set goes on forever. A finite set is a set that does end. For example, for the set of numbers ranging from 1-5: {1,2,3,4,5}. If it is the set of numbers ranging from 1-50: {1,2,3,4,5, ..., 47,48,49,50}. The ... can be used in the middle of the set in this case so you don't have to write all the extra numbers. In other words, it's to save time. 

Hope I helped!

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kspcr111 | Student

We often use a single word to denote the collection or a group of objects such as 

    -> A class of students

    -> A family of people

    -> A football Team

    -> An army of soldiers etc. 

But in Mathematics, we use the word "SET" for a collection of objects which are well defined and distinct.

Definition:  SET is a well defined collection of objects. And the objects in the set are called the elements or members of the SET.

For better understanding let us see some collection which are sets and which are not sets.

Collection which are sets:

1) A collection of even numbers greater than 4 and less than 10 

2) A collection of football team players.

3) A collection of prime numbers between 30 and 50 

Collection which are not sets:

1) The collection of most interesting books in the library in your school.

2) The collection of clever girls in Des moines.

3) The collection of handsome boys in New York.

Usually a set is denoted by capital letters such as set A, set B, set X etc.

In order to define the elements in a set all the elements of the set are written in a row, separate by commas and then enclosed by flower brackets.

Ex:- A set consisting of elements as the even numbers from  0 to 10

set A ={2,4,6,8,10}

Note: In a set there will be no repetition of elements for more than one time 

for ex:- The elements given to form a set are " a,a,b,b,b,c,d,d,d,d,d,"

Then the set consists of the elements

                set A ={a,b,c,d}