Math Homework. Do It Faster, Learn It Better.


In modern mathematics, just about everything rests on the very important concept of the set .

A set is just a collection of elements, or members. For instance, you could have a set of friends:

F = {Abdul, Gretchen, Hubert, Jabari, Xiomara}

or a set of numbers:

Y = { 3.4 , 12 , 9999 }

There are two methods of representing a set :

(i) Roster or tabular form

(ii) Set-builder form.

Roster or tabular form: In roster form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces { }.

For Example:

Z = the set of all integers = { , 3 , 2 , 1 , 0 , 1 , 2 , 3 , }

Set-builder form: In the set builder form, all the elements of the set, must possess a single property to become the member of that set.

For Example:

Z = { x : x is an integer }

You can read Z = { x : x is an integer } as "The set Z equals all the values of x such that x is an integer."

M = { x | x > 3 }

(This last notation means "all real numbers x such that x is greater than 3 ." So, for example, 3.1 is in the set M , but 2 is not. The vertical bar | means "such that".)

You can also have a set which has no elements at all. This special set is called the empty set, and we write it with the special symbol .

If x is a element of a set A , we write x A , and if x is not an element of A we write x A .

So, using the sets defined above,

862 Z , since 862 is an integer, and

2.9 M , since 2.9 is not greater than 3 .

See also subsets and operations on sets .