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In mathematics, numbers are rigorously defined and separated into classes. The relationships between different
systems is very well illustrated below:
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N
is the system for natural
numbers. These
include numbers, such as 1, 2 and 3 and do not include zero.
For example 6 / 2 = 3
and 5 ^ 2 = 25
.
Z
is the system for integers
. The notation Z comes from
the German word Zahlen
, which means Numbers
. These
include positive and negative integers, such as -3, -2, -1, 0, 1, 2 and 3.
For example -12 / 3 = -4
and 8 ^ 2 = 64
.
Q
is the system of rational
numbers.
A rational number can be written as a fraction
.
The resulting decimal will be either repeating or terminating.
The denominator of the fraction cannot be zero.
The notation Q means Quotient
.
For example -13 / 9 = -1.444...
and 8 ^ -2 = 0.015625
.
I
is the system for any number that cannot be written as a fraction
where the numerator and denominator are integers.
Since irrational numbers cannot be expressed as a fraction they form decimals
that are neither repeating nor terminating.
For example Pi
and Sqrt( 7 )
.
R
is the real
numbers system and
includes the rational and irrational numbers.
The notation, such as Z*
means Z \ { 0 }
or Z excluding zero
.
Writing Z+
means only positive numbers of Z
. Consequently,
Z-
means only negative numbers of Z
.
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