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CARDINAL NUMBERS

Cardinal Numbers

Definition Of Cardinal Numbers

The total number of elements/items in a set is called its Cardinal Number.

More about Cardinal Numbers

Order of elements does not matter in a set.
A cardinal number is a nonnegative integer.

Example of Cardinal Numbers

The cardinal number of the set A = {2, 3, 5, 7, 9} is 5.

Video Examples:Surveys and Cardinal Numbers

Solved Example on cardinal numbers

Ques: If set A = {23, c, #, II, %, 91}, then find its cardinal number.

Choices:

A. 5
B. 23
C. 91
D. 6
Correct Answer: D

Solution:

Step 1: The number of elements in a set is called its cardinal number. [Definition]
Step 2: So, cardinal number of set A is 6.

Quick Summary

  • The cardinal number represents the size of a set.
  • Order of elements in a set does not affect its cardinal number.
  • Cardinal numbers are non-negative integers.
\[ N(A) = n, where A is a set and n is the number of elements in A. \]

🍎 Teacher Insights

Use visual aids like Venn diagrams to illustrate sets and their cardinal numbers. Emphasize that each unique element is counted only once.

🎓 Prerequisites

  • Sets
  • Elements of a Set
  • Integers

Check Your Knowledge

Q1: What is the cardinal number of the set {a, b, c, d}?

Q2: What is the cardinal number of the set {1, 2, 2, 3}?

Q3: If set A = {23, c, #, II, %, 91}, then find its cardinal number.

Frequently Asked Questions

Q: Does the order of elements matter when determining the cardinal number?
A: No, the order of elements in a set does not affect its cardinal number. Only the unique elements are counted.

Q: Can a set have a cardinal number of 0?
A: Yes, an empty set (a set with no elements) has a cardinal number of 0.

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