The document defines cardinality of sets as the number of elements in a set. A finite set is one that can be counted and has a last element, while an infinite set has an unlimited number of elements. Examples are provided of finite sets with their cardinalities identified, such as the set of counting numbers less than 30 having a cardinality of 29. Infinite sets are also illustrated, like the set of points on a given line. The document concludes by asking the reader to identify whether example sets are finite or infinite, and if finite, to provide the cardinality.

1. Cardinality of
sets
Module 3

2. WHAT IS A CARDINALITY OF
SETS?
• Consider the sets 𝑋, and 𝑌:
𝑋 = 5, 10, 15, 20, 25, 30
𝑌 =
How many elements does set 𝑿 have?
How many elements does set 𝒀 have?

3. • The cardinality of Set X is
6 and Set Y is 0, and is
denoted by,
𝑋 = 6
𝑌 = 0

4. Finite vs. Infinite
• Finite set – is a set whose elements
can be counted and has last element.
1. C = b, o, y  C = 3
Example:
 N = 5
 D = 10
2. N = 5, 10, 15, 20
3. D = 1, 3, 5, … , 19

5. • Infinite set – has an unlimited
number of elements.
1. A = 5, 10, 15, 20 …
Example:
2. X =
3. W = 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑒𝑛𝑑𝑖𝑛𝑔 𝑖𝑛 0

6. Identify whether the set is finite or
infinite. If finite, give its cardinality.
1. The counting numbers less than 30.
 FINITE
1, 2, 3, 4, … , 29
 The Cardinality of the set is 29.

7.  INFINITE
2. The points on a given line.
3. The female presidents of the
Philippines.
 FINITE
 The Cardinality of the set is 2.
𝐴𝑞𝑢𝑖𝑛𝑜, 𝐴𝑟𝑟𝑜𝑦𝑜

8. 4. Integers greater than or equal to 13.
13, 14, 15, 16, …
 INFINITE