In this lesson, we will learn about finite sets and infinite sets.

Related Topics:

Other Topics on Sets

Sets and Venn Diagrams Games

**Finite sets** are sets that have a finite number of members. If the elements of a finite set are listed one after another, the process will eventually “run out” of elements to list.

Example:

* A* = {0, 2, 4, 6, 8, …, 100}

*C* = {*x* : *x* is an integer, 1 < *x* < 10}

An **infinite set** is a set which is not finite. It is not possible to explicitly list out all the elements of an infinite set.

**Example:**

* T = * {*x* : *x* is a triangle}

* N * is the set of natural numbers
* A* is the set of fractions

The **number of elements **in a finite set *A* is denoted by **n( A)**

**Example: **

If *A* is the set of positive integers less than 12 then

*A* = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and * n*(*A*) = 11

If *C* is the set of numbers which are also multiples of 3 then

*C* = {3, 6, 9, …} and *C* is an infinite set

If *D* is the set of integers *x* defined by –3 < *x* < 6 then

*D* = {–2, –1, 0, 1, 2, 3, 4, 5} and * n*(*D*) = 8

If *Q* is the set of letters in the word *‘HELLO’ *then

*Q * = {*H, E, L, O *} , n(*Q*) = 4 ← ‘*L*’ is not repeated.

This video lesson is Part 1 of 2 on Infinite vs. Finite Number Sets

This video lesson is Part 2 of 2 on Infinite vs. Finite Number Sets

The following video describes sets and gives more examples of finite and infinite sets.

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