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# Natural number

 Natural numbers example  (0) 1   2   3   4   5   6   7   8   9   10   11 12 13 14 15 16 17 18 19   20   21 22 23 24 25 26 27 28 29   30   31 32 33 34 35 36 37 38 39   40   41 42 43 44 45 46 47 48 49   50   51 42 53 54 55 56 57 58 59   60   61 62 63 64 65 66 67 68 68   70   71 72 73 74 75 76 77 78 79   80   81 82 83 84 85 86 87 88 89   90   91 92 93 94 95 96 97 98 99   100   200   300   400   500   600   700   800   900   1000   2000   3000   4000   5000   6000   7000   8000   9000   10,000   100,000   1,000,000   1,000,000,000   1,000,000,000,000   Numbers less than 0 (such as −1) are not natural numbers.

Natural numbers, also called counting numbers, are the numbers used for counting things. They are whole numbers (called integers), and never less than zero (i.e. positive numbers). The special number zero is sometimes considered a natural number. Examples of natural numbers can be seen in the box on the right. Whole numbers are the natural numbers, but whole numbers always include zero.

The next possible natural number can be found by adding 1 to the current natural number, producing a set of numbers that could continue "for ever".

## Non-natural numbers

The following types of number are not natural numbers:

• Numbers less than 0 (negative numbers), e.g. −2 −1
• Fractions, e.g. ½ 3¼
• Decimals, e.g. 3.125
• Irrational numbers, e.g. ${\displaystyle {\sqrt {2}}}$, ${\displaystyle \pi }$ (pi)
• Imaginary numbers, e.g. ${\displaystyle {\sqrt {-1}}}$ (i)

## How to write it

${\displaystyle \mathbf {N} }$ or ${\displaystyle \mathbb {N} }$ is the way to write the set of all natural numbers. Because some people say 0 is a natural number, and some people say it is not, people use the following symbols to talk about the natural numbers:

Symbol Meaning
${\displaystyle \mathbb {N} ^{+}}$ Positive numbers, without zero
${\displaystyle \mathbb {N} ^{*}}$ Positive numbers without zero
${\displaystyle \mathbb {N} _{0}}$ Positive numbers, with zero
${\displaystyle \mathbb {N} _{>0}}$ Positive numbers without zero
${\displaystyle \mathbb {N} \setminus \{0\}}$ Positive numbers without zero