The Number System
This page contains concise explanations of commonly used types
Natural numbers are the numbers 1, 2, 3, ... .
All natural numbers are integers, but also 0, -1, -2, ... .
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.
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),
the ratio of a circle's perimeter to its diameter, and the
square root of 2, which is
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 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
Transcendental numbers are real numbers that are not algebraic.
are transcendental (and real).
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