In mathematics, a set is a collection of distinct elements. Note that a set can be considered an element in its own right.  The elements in a set may be anything: numbers, people, letters of the alphabet, other sets, and so on.  Conventionally, sets are symbolized by capital letters.  

 

In order for us to attain a clearer understanding of sets, we may look at some basic examples:

Suppose A is the set of the first four positive even integers.

Suppose B is the set of colors of the American flag.

Hence, A={2,4,6,8}

                B={red, white, blue}

Note that these sets are finite.

 

The key relation between sets is membership. It is possible to have one set be an element of another. We may look at a simple example. Suppose C is the infinite set of all non-negative integers. We denote this as C={0,1,2,3,4,5,……}. Moreover, let D be the set of positive integers that are strictly less than 5. We denote this as D={1,2,3,4}.

Here is some analysis about these two sets:

0 is an element of C but it is not an element of D.

1 is an element of C and 1 is an element of D.

 

Here are some questions:

1)What is another element  of C that is not a member of D?

2) What is an element that is contained in both C and D?

 

Answers:  

1)      Any integer greater than or equal to 5 and 0.

2)      2, 3, or 4.