**Related Pages**

Describing Sets

Venn Diagrams

More Lessons On Sets

In these lessons, we will learn about finite sets and infinite sets.

**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.

**Examples:**

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.

**Examples:**

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)**

**Examples:**

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.

The word finite means

- having bounds.
- a set that contains a countable number of elements.
- the set starts and stops.

The word infinite means

- the set in which the number of elements cannot be counted or determined (never ending)
- the set can continue forever in the beginning, or the end, or both

**Examples of Infinite and Finite Number Sets**

Errata (submitted by Tim): At 3:20, the set {x ∈ whole numbers: 0 < x < 10} should be {1, 2, 3, 4, 5, 6, 7, 8, 9}

Set of objects, Natural numbers, Real numbers and how to find distance between two points.

Set Notations

A quiz to test your knowledge of set notations: intersection, union, subset, etc.

Elements in a Set

Determine whether an element is a member of a given set and the number of members in a given set.

Types of Sets

Determine whether a given set is an infinite set, finite set or empty set.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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