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Finite Sets & Infinite 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.

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.

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).


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.
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}

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

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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