Numbers

See also: prime numbers, GCD and LCM, significant figures and scientific notation

In Mathematics, a number can be classified into different types. They are complex numbers, imaginary numbers, real numbers, rational numbers, irrational numbers, integers and natural numbers.

Natural Number (ℕ)
Also called counting number or whole number. There are two definitions of natural number.
  • an element of the set { 1, 2, 3, 4, ... }
  • an element of the set { 0, 1, 2, 3, 4, ... }
That is, one definition includes zero and the other excludes zero. Unfortunately, there is no general agreement until now. To be more precise, the terms positive integers (without 0) and nonnegative integers (includes 0) are recommended.
Example: 1, 2, 4, 7, etc.
Integer (ℤ)
Number that can be written without a fractional or decimal component. The set of integers consists of natural numbers, their negatives and the number zero.
ℤ = { ..., -2, -1, 0, 1, 2, ... }. The symbol ℤ stands for Zahlen (German for numbers).
Example: -12,-3, 0, 4, 5 etc.
Rational Number (ℚ)
Number that can be expressed as a fraction. The symbol ℚ stands for quotient.
Example: -23,-3.5, 0, 2, 2¾, 4.7, etc.
Irrational Number
Number that cannot be expressed as a fraction.
Example: √2, √3, π, e, etc.
Real Number (ℝ)
Number that is in one-to-one correspondence with the points on the infinite number line. The set of real numbers consists of rational and irrational numbers.
Example: √2, -3.4, 1, etc.
Imaginary Number
Number whose square is a negative real number. It's denoted by the symbol i, where i = √-1.
Example: 2i, -4i, 5i, etc.
Complex Number (ℂ)
Number of the form a + bi, where a and b are real numbers and i is the imaginary unit (i = √-1).
Example: 2 + 3i.

See also: prime numbers, GCD and LCM, significant figures and scientific notation