Real Life Analogy:

Think of a set as a collection of distinct items, like a bag of marbles. The cardinality of the set would be the count of marbles in the bag.

Examples:

  1. Finite Set:
    • Set A = {1, 2, 3, 4, 5}
    • Cardinality of A: |A| = 5
  2. Infinite Set:
    • Set B = {1, 2, 3, 4, ...}
    • Cardinality of B: ∞ (infinity)
  3. Empty Set:
    • Set C = {}
    • Cardinality of C: |C| = 0

Real Life Examples:

  1. Class Attendance:
    • Set D = {students present in a class}
    • Cardinality of D represents the number of students in the class.
  2. Library Books:
    • Set E = {books in a library}
    • Cardinality of E is the count of books in the library.
  3. Shopping Cart:
    • Set F = {items in a shopping cart}
    • Cardinality of F is the number of items in the cart.

Important Points

  • Cardinality only considers distinct elements within a set.
  • Cardinality can be finite or infinite.
  • The cardinality of an empty set is always zero.
  • The order of elements in a set does not affect its cardinality.
  • Cardinality is often denoted by vertical bars (| |) around the set or by using the function n(A).
  • Sets with the same cardinality have the same number of elements, even if the elements themselves differ.

Further Reading