##
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]