1 (getæl)

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ġecyndu ġetalu
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

Þā getalu þe læssa sind þonne oþþe gelīċ sind noll (swelċe −1) ne sind nā gecyndu getalu (ac ġehāl Ġetalu).

Þis geƿrit hæfþ ƿordcƿide on Nīƿenglisce.

Þā ġecyndan ġetalu, eac geciged tel-ġetalu oþþe ġecyndelīċan rīm, sind þā getælu þe man brȳcþ tō þinga telanne. Þā ġecyndan ġetalu sind þā getælu þe lȳtle cildru leorniaþ ymbe þonne hīe ǣrest ongunnon tō tellanne. Þā Ġecyndan ġetalu sind symle hāl ġetalu (ġehāl Ġetalu þā ne sind niþerlīċ) and oft ne healdiaþ nōll, on hwilcum gefealle ān is þæt læst ġecynde getæl. Þæt gefeall of ġecyndum getælum mæg bēon ātācnod mid þǣm tācne ℕ.

Nis nan mǣst gecyndelic rīm. Þæt æfterfylgende gecyndelic rīm mæg gefunden weorþan þurh ān tō þǣre nuwǣrran gecyndelican rīme, bringende rīm þā gāð on ēcnesse. Nis nan gecyndelic rīm þæt is ānfealdlic on mǣte. Ælc gecyndelic rīm mæg ġerǣht weorþan þurh ān ġenōg oft tō þǣm læst gecyndelican rīme.

Unġecynde ġetalu

Þæslicu getalu sindon ne gecyndelic getalu:

Getalu læssa þonne 0; niþerlīċ getalu (-2, -1)
Dǣlas (½, 3¼)
Tēoþisċ (7.675)
Undǣllic getalu (√2, 𝜋)
Ġehīewod getalu (i, -i)
Ungeendodlicnes (∞, ℵ₀)
0 (hwīlum)

Weorc

Addition; The sum of two natural numbers is a natural number. $l+m=n$
- $l+n=n+l$
- $n+0=n$
- $(l+m)+n=l+(m+n)$
Multiplication: The product of two natural numbers is a natural number. $l\times m=n$
- $l\times m=m\times n$
- $n\times 0=0$
- $n\times 1=n$
- $(l\times m)\times n=l\times (m\times n)$
- $l\times (m+n)=(l\times m)+(l\times n)$

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
- if l > m and l > 0 then 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 $l\times m=n$ then $n/m=l$

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

Special natural numbers

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 it

$\mathbf {N}$ or $\mathbb {N}$ 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
$\mathbb {N} ^{+}$	Positive numbers, without zero
$\mathbb {N} ^{*}$	Positive numbers without zero
$\mathbb {N} _{0}$	Positive numbers, with zero
$\mathbb {N} _{>0}$	Positive numbers without zero
$\mathbb {N} \setminus \{0\}$	Positive numbers without zero