Determining a Set's Cardinal Number

Definition

• Cardinal Number/Cardinality: Refers to the number of distinct elements in a set.
  • Represented as n(A) for a set A, read as "n of A".
  • Repeated elements do not change the cardinality.

Calculating Cardinality

• General Rule: Count the distinct elements in the set.

Examples

Example 1: Set D

• Set D: {3, 7, 15, 18, 21}
  • Contains 5 distinct elements.
  • Cardinality: n(D) = 5

Example 2: Set B

• Set B: {0}
  • Contains 1 element.
  • Cardinality: n(B) = 1

Example 3: Set E

• Set E: {15, 16, 17, ..., 31, 32}
  • Includes numbers 18 to 30, making a total of 18 elements.
  • Cardinality: n(E) = 18

Example 4: Empty Set

• Empty Set: No elements.
  • Cardinality: n(Empty Set) = 0

Key Points

• The cardinal number provides a way to quantify the size of a set in terms of its distinct elements.
• For infinite sets, the concept of cardinality can extend beyond simple counting.
• The empty set always has a cardinality of 0.