Finite Sets And Infinite Sets


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




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Describing Sets
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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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