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: (

?),

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!