Counting with Your Fingers
Do you know how to count with your fingers?
OBJECTIVE: To learn about the cardinality of sets
In a previous lesson, you learned about basic set vocabulary and methods of naming sets.
Setting the Table: https://www.geogebra.org/m/eqajxyqr
In this lesson, you will expand your set vocabulary and learn about the Cardinality or Cardinal Number of sets.
SET VOCABULARY
Cardinality or cardinal number—number of elements in a set; n(A)—"the number of elements in set A"
Examples: A = {a, b, c, d, e, f, g, h, i, j} n(A) = 10
Z = { x | x is an integer greater than or equal to -3
and less than or equal to 3}
= {-3, -2, -1, 0, 1, 2, 3} n(Z) = 7
Empty set or null set—set with no elements, denoted by ∅ or { }; n( ) = 0
Examples: E = { } or ∅ n(E) = 0
F = {female popes in the Catholic Church} n(F) = 0
Unit set or singleton—set with only one element; n( ) = 1
Examples: E = {even prime number} = {2} n(E) = 1
W = {whole number between -1 and 1} = {0} n(W) = 1
Finite set—set with a limited number of elements; n( ) = x
Examples: T = {vertices of a triangle} n(T) = 3
M = {months of the year} n(M) = 12
C = {1, 2, 3, ... , 99, 100} n(C) = 100
Infinite set—set with an unlimited number of elements; n( ) = none
Examples: P = {points in a line} n(P) = none
N = {..., -5, -4, -3, -2, -1} n(N) = none
W = {0, 1, 2, 3, 4, ...} n(W) = none
Z = {..., -3, -2, -1, 0, 1, 2, 3, ...} n(Z) = none
In Sets C, N, W, and Z, the ellipses or three dots mean "the pattern continues until the next listed element."
Equal sets or identical sets—sets with exactly the same elements, denoted by A = B
Examples: A = {letters in the word "brake"}; B = {letters in the word "break"}. Therefore, A = B.
V = {vowels in the English alphabet}; F = {vowels in the word "facetious"}. Therefore, V = F.
Equivalent sets—sets with the same cardinality or the same number of elements, denoted by A ↔︎ B
Examples: L = {a, b, c}; N = {1, 2, 3}.
n(L) = n(N) = 3. Therefore, L ↔︎ N.
H = {letters in the word "hymn"}; S = {♣, ♦, ♥, ♥}.
n(H) = n(S) = 4. Therefore, H ↔︎ S.
NOTE: All equal sets are also equivalent, but not all equivalent sets are equal.
Below is a set of problems that require you to determine the cardinality of sets.
Cardinality of Sets
ANSWER BOX:
Check the Answer Box below for the correct answers.
In this lesson, you learned about the cardinality of sets and expanded your set vocabulary.
In succeeding lessons, you'll learn more set vocabulary, including subsets and operation on sets. Hope you had FUN today!