Sets

2. 2. Finite & Infinite Sets

Sets can be finite or infinite. Intuitively, a set is finite if it consists of a specific number of different elements, i.e. if in counting the different members of the

set the counting process can come to an end. Otherwise a set is infinite. Lets look at some examples.

Example 4:1: Let M be the set of the days of the week. The M is finite

Example 4:2: Let N = {0,2,4,6,8........}. Then N is infinite

Example 4:3: Let P = {x< x is a river on the earth}. Although it maybe difficult to count the number of rivers in the world, P is still a finite set.

Exercise 1.3: Which sets are finite?

1. The months of the year

2. {1, 2, 3, ......... 99, 100}

3. The people living on the earth

4. {x | x is even}

5. {1, 2, 3,........}

Solution:

The first three sets are finite. Although physically it might be impossible to count the number of people on the earth, the set is still finite. The last two sets are infinite. If we ever try to count the even numbers, we would never come to the end.