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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.

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.




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
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}


 
The following video describes sets and gives more examples of finite and infinite sets.
Set of objects, Natural numbers, Real numbers and how to find distance between two points.
How to classify Finite and Infinite Number Sets?
What is a set? Finite Sets, Infinite Sets, and the Null Set

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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