Finite and Infinite Sets

Finite and Infinite Sets

Finite Set

A set having finite number of elements is called finite set, i.e. elements of a finite set are countable.

Examples:

1. The set {2, 4, 6, 8}
2. The set of vowels.

Infinite Set

A set having infinite number of elements is called infinite set, i.e. elements of a finite set are uncountable.

Examples:

1. The set all even numbers.
2. The sets R, W, N, Z, Q and C
   1. R = set of real numbers = {x : x is either rational or irrational number}
   2. W = set of whole numbers = {0, 1, 2, 3, ...}
   3. N = set of natural numbers = {1, 2, 3, 4, ...}
   4. Z = set of integers= {... , -3, -2, -1, 0, 1, 2, 3, ...}
   5. Q = set of rational numbers = \( \{\frac{p}{q} : p, q \in Z, q \neq 0\} \)
   6. C = set of complex numbers = \( \{a + ib : a, b \in R, b \neq 0\} \)