There are a number
of major sets of numbers.
Firstly, there are the natural numbers
or counting numbers
. These begin with either one
, and continue upwards with all whole numbers
greater than one
(depending on the definition). There are infinite
These are any 'whole numbers', including negative numbers, natural numbers, and zero if not counted already.
Examples: (all above plus) -1
These are any numbers which can be written as
where p and q are integers. p and q are the usual letters used. This therefore includes all types of fraction
s, whether proper
or not, all decimals (including those which are recurring
). There are infinitely many rational numbers between any two different integers.
Examples: (all above plus) 0.2
These are all numbers which can exist from performing any form of arithmetic operation on any set of real numbers. These include irrational
numbers, which include pi
, and the square root
of any natural number which is not a perfect square
. There are infinitely many of these between any two different rational numbers.
Examples: (all above plus) pi
These are all known numbers, which are used to calculate the square root of -1, which is defined as i
. With this, a whole new set of mathematics occurred, including fractal
s. Complex numbers that are not real are imaginary
Examples: (all above plus) i
(((((A: natural)B: integer)C: rational)D: real)E: complex)
anything in B but not A is negative
anything in C but not B is a fraction
anything in D but not C is irrational
anything in E but not D is imaginary
Help wanted: /msg me!