Finite Sets And Infinite Sets
In these lessons, we will learn about finite sets and infinite sets.
Related Pages
Describing Sets
Venn Diagrams
More Lessons On 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
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.
How To Classify Finite And Infinite Number Sets?
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