The Number System
This page contains concise explanations of commonly used types
of numbers.
Natural Numbers
Natural numbers are the numbers 1, 2, 3, ... .
Integers
All natural numbers are integers, but also 0, -1, -2, ... .
Rational numbers
Rational numbers are fractions p/q where q
is non-zero and p and q are both integer.
For example, all integers are rational (pick q =1).
Other examples of rational numbers are
3/2, -5/7, -1232321/74567467.
Real numbers
Without getting technical, real numbers are all numbers that can
be written as a possibly never repeating decimal fraction. For
example, all rational numbers are real. Their decimal
representations do repeat. Decimal fractions whose
representation do not repeat are irrational. Example
of irrational real numbers include
e = 2.71828...
(the base of the natural logarithm),
pi=3.14...,
the ratio of a circle's perimeter to its diameter, and the
square root of 2, which is
1.4142...
.
Complex numbers
Complex numbers are numbers of the form
where a and b are real numbers and i
is the square root of negative 1, i.e.,
.
The symbol i is called the imaginary unit.
Algebraic numbers
Algebraic numbers are complex numbers that can be obtained as
the root of a polynomial with integer coefficients. For
example, rational numbers are algebraic, and so are roots of
integers.
Transcendental numbers
Transcendental numbers are real numbers that are not algebraic.
For example
e
and
pi
are transcendental (and real).
Fine print, your comments, more links, Peter Alfeld,
PA1UM
[16-Aug-1996]