Sets
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:
{Abdul, Gretchen, Hubert, Jabari, Xiomara}
or a set of numbers:
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:
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:
You can read as "The set equals all the values of such that is an integer."
(This last notation means "all real numbers such that is greater than ." So, for example, is in the set , but 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 is a element of a set , we write , and if is not an element of we write .
So, using the sets defined above,
, since is an integer, and
, since is not greater than .
See also subsets and operations on sets .