Natural number

numbers examples
 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 52 53 54 55 56 57 58 59   60  
61 62 63 64 65 66 67 68 69   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 or equal to 0 (such as −1) are not natural numbers (rather integers).

The naturals (also called counting numbers or the whole numbers), are the numbers used for counting things. Natural numbers are the numbers small children learn about when they first start to count. Natural numbers are always whole numbers (integers) and exclude zero, so one is the smallest natural number. The set of natural numbers can be represented by the symbol .

There is no largest natural number. The next natural number can be found by adding 1 to the current natural number, producing numbers that go on "forever". There is no natural number that is infinite in size. Any natural number can be reached by adding 1 enough times to the smallest natural number.

Non-natural numbers
The following types of numbers are not natural numbers:
 Numbers less than 0 (negative numbers), for example, −2 and −1
 Fractions, for example,  and 
 Fractional numbers, for example, 7.675
 Irrational numbers, for example,  and   (pi)
 Imaginary numbers, for example,  (i)
 Complex numbers, for example, 
 infinities, for example,  and 

Basic operations

 Addition: The sum of two natural numbers is a natural number. 
 Subtraction: The difference of two natural numbers is a whole number
 if  is greater than , then  minus  is a natural number
 Multiplication: The product of two natural numbers is a natural number. 
 Division: The quotient of two natural numbers is a rational number

 Ordering: Of two natural numbers, if they are not the same, then one is bigger than the other, and the other is smaller.  , , or 
 if  then 
 if  and  then , which is the same as .
 One is the smallest natural number:  or 
 There is no largest natural number 

 Mathematical induction: If these two things are true of any property  of natural numbers, then  is true of every natural number
 if  is true of 1
 and if  of  then  of 
 then  is true of all natural numbers

Special natural numbers

 Even numbers: If , then  is an even number
 The first even natural numbers are 2, 4, 6, 8, and so on.
 Odd numbers: If , then  is an odd number
 A number is either even or odd but not both.
 The first odd natural numbers are 1, 3, 5, 7, and so on.
 Composite numbers: If , and  and  are not 0 or 1, then  is a composite number.
 The first composite (non-prime) natural numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21 and so on.
 Prime numbers: If a number is not 1, and not a composite number, then it is a prime number.
 The first prime (non-composite) natural numbers are 2, 3, 5, 7, 11, 13, 17 and so on. Two is the only even prime number.
 There is an infinite number of prime numbers. 
 Square numbers: If , then  is a square.  is the square of .
 The first natural squares are 1, 4, 9, 16, 25, 36, 49 and so on.

 How to write it 
 is the way to write the set of all natural numbers. While 0 is not a natural number, it is possible to create a set that includes both the set of natural numbers and the number zero. This set is written .

Related pages
 Integer

 References 

Category:Number theory
Category:Integers