Numbers in Mathematics: Integers to Irrationals

Integers (Z)

• Integers include all positive and negative whole numbers, and zero.
• Notation: {...−1, −2, 0, 1, 2,...}

Natural Numbers (N)

• Natural numbers are used for counting and are all positive integers.
• Notation: {0, 1, 2,...} (Note the inclusion of 0)

Real Numbers (R)

• Real numbers encompass all numbers on the number line.
• Examples: 15, √15, 0, −2

Rational Numbers (Q)

• Rational numbers can be expressed as a fraction (p/q) where p and q are integers and q ≠ 0.
• All integers are rational numbers (e.g., 1 = 1/1).
• Examples: 15, 5/1 ( = 5), 2/3, 3/2, 0/3 (= 0)

Irrational Numbers (I)

• Irrational numbers cannot be expressed as a fraction of two integers.
• They are all real numbers that are not rational.
• Examples: π, √2, √3