what are Cardinal number of a set
Answers
Answer:
Here, we formalize these relationships between sets and whole numbers.
Sets of Numbers: The set of natural numbers (or counting numbers) is the set N = {1, 2, 3, …}.
The set of whole numbers is the set W = {0, 1, 2, 3, …}.
Cardinal Number of a Set: The number of elements in a set is the cardinal number of that set.
Notation: If a set A is equivalent to the set {1, 2, 3, …, N}, we write n(A) = N and say “The cardinal number of set A is N.”
Also, n(Ø) = 0. The cardinal number for an empty set is zero.
Example: Let C = {#, $, %, &}. Show n(C) = 4.
# $ % &
| | | |
1 2 3 4
Hence, C is equivalent to {1, 2, 3, 4} and n(C) = 4 since a 1-1 correspondence can be setup between C and {1, 2, 3, 4}.
Example: For M = {red, blue, green, yellow, orange}, n(M) = 5.
The symbol “n(M) = 5” is read, “The cardinal number of set M is equal to 5.”
Take the time to set up a 1-1 correspondence between M and {1, 2, 3, 4, 5}.
Example: For T = {2, 4, 6, 8, 10, 12, 14, 16}, n(T) = 8.
On a sheet of paper, set up a 1-1 correspondence between T and {1, 2, 3, 4, 5, 6, 7, 8}.
Example: In this picture, the circles represent sets A and B. The dots inside are the elements of the sets. We need to make sure we look at an entire circle, even though the circles overlap.
Venn Diagram
n(A) = 5 n(B) = 8
Step-by-step explanation:
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