There are a
number of major sets of numbers.
Natural Numbers.
Firstly, there are the
natural numbers or
counting numbers. These begin with either
one or
zero, and continue upwards with all
whole numbers greater than
one or
zero (depending on the definition). There are
infinitely many.
Examples: (
0?),
1,
2,
3,
4,
5,
42,
69,
666,
1701,
2600.
These are any 'whole numbers', including negative numbers, natural numbers, and zero if not counted already.
Examples: (all above plus)
-1,
-2,
-5,
-999.
These are any numbers which can be written as
p/
q
where p and q are integers. p and q are the usual letters used. This therefore includes all types of
fractions, 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,
4/5,
66/9,
-12.2.
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,
e, 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,
e, sqrt(12.21).
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
fractals. Complex numbers that are not real are
imaginary.
Examples: (all above plus)
i,
3i+4.
Venn diagrams.
(((((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!