Finite Sets & 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.

Infinite Vs. Finite Number Sets

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

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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}

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

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How To Classify Finite And Infinite Number Sets?

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Sets Worksheets

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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