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Natural number

number in the set of natural numbers (to clarify whether zero is included or not, use Q28920044 or Q28920052)
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).

Natural numbers, also called counting numbers, are the numbers used for counting things. Natural numbers are the numbers small children learn about when first starting to count. Natural numbers are always whole numbers (integers excluding Negative numbers) excluding zero. One is the smallest natural number.

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 "for ever". There is no infinite natural number. Any natural number can be reached by adding 1 enough times to the smallest natural number.

Non-natural numbersEdit

The following types of numbers are not natural numbers:

Basic operationsEdit

  • Addition; The sum of two natural numbers is a natural number.  
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  • Multiplication: The product of two natural numbers is a natural number.  
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  • Ordering: Of two natural numbers, if they are not the same, then one is bigger than the other, and the other is smaller. m = n or m > n or m < n
    • if l > m then l + n > m + n and l x n > l x m
    • Zero is the smallest natural number: 0 = n or 0 < n
    • There is no largest natural number n < n + 1
  • "Subtraction": If n is smaller than m then m minus n is a natural number. If n < m then m - n = p.
    • if l - m = n then l = n + m
    • if n is greater than m, then m minus n is not a natural number
    • if l = m - n and p < n then l > m - p
  • Division: If   then  
  • Mathematical induction: If these two things are true of any property P of natural numbers, then P is true of every natural number
  1. P is true of 1
  2. if P of n then P of n+1

Special natural numbersEdit

  • Even numbers: If n = m x 2, then n is an even number
    • The even numbers are 0, 2, 4, 6, and so on. Zero is the smallest (or first) even number.
  • Odd numbers: If n = m x 2 +1, then n is an odd number
    • A number is either even or odd but not both.
    • The odd numbers are 1, 3, 5, 7, and so on.
  • Composite numbers: If n = m x l, and m and l are not 0 or 1, then n is a composite number.
    • The composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21 and so on.
  • Prime numbers: If a number is not 0, 1, and not a composite number, then it is a prime number.
    • The prime numbers are 2, 3, 5, 7, 11, 13, 17 and so on. Two is the smallest (or first) prime number. Two is the only even prime number.
    • There is no biggest prime number.
  • Square numbers: If n = m x m, then n is a square. n is the square of m.
    • The squares are 0, 1, 4, 9, 16, 25, 36, 49 and so on.

How to write itEdit

  or   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
  Positive numbers, without zero
  Positive numbers without zero
  Positive numbers, with zero
  Positive numbers without zero
  Positive numbers without zero

Related pagesEdit