Number Sets

Natural Numbers

ℕ = \{0, 1, 2, 3, 4, 5, 6 \cdot \cdot \cdot\}

Integers

ℤ = \{\cdot \cdot \cdot, - 3, - 2, - 1, 0, 1, 2, 3, \cdot \cdot \cdot\}

Rational Numbers

ℚ = \{\frac{p}{q} | p, q \in ℤ, q \neq 0\}

A rational number is any number that can be expressed as fraction of two integers.

Irrational Numbers

ℚ^{*} = \{\cdot \cdot \cdot, - \sqrt{3}, \sqrt{2}, π, e, \cdot \cdot \cdot\}

Irrational number is any number that cannot be expressed as a ratio between two integers.

Real Numbers

ℝ = ℚ \cup ℚ^{*}

All Rational and Irrational numbers.

Complex Numbers

ℂ = \{a + i b | a, b \in ℝ, i = \sqrt{- 1}\}

Relation Between Number Sets

ℕ \subset ℤ \subset ℚ \subset ℝ \subset ℂ

Keywords: number sets, natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers, relation between number sets

General Information
Symbols, and relationships in mathematics
Number theory
Number Sets
Prime Numbers - Prime Factorization
Divisibility Rules
Greatest Common Divisor (factor) - Least Common Multiple
Operations with rational numbers
Binomial theorem
Binomial theorem
Combinatorics
Permutations
Combination
Variation
Sets
Operations on Sets
Cardinality of sets
Fundamental laws of set algebra
Cartesian product
Relation
Logic
Logical Operations and Truth Tables
Properties of Logical Operators
Graph Theory
Graph Theory - definitions, relationships