Amanani a-natural

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 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 0 (such as −1) are not natural numbers.

Amanani a-natural, asoloko ebizwa ngokuba ngamanani okubala, nganmanani asetyenziselwa ukubala izinto. Maxa wambi inani elilodwa elingu-zero kuthiwa nalo linanieli-natural. Maxa wambi u-inye ubizwa ngokuba lelona nani li-natural lakhe lalincinane. Amanani a-natural asoloko engamanani a-pheleleyo azii-(integers) kwaye akasokuze abe ngaphantsi kuka-zero.

Akukho nani li-natural likhe libe lelona likhulu kunamanye. Inanani eli-natural elinokulandela lingafumaneka kuphela ngokuthi kongezwe u-1 kwelo nani li-natural nelikhoyo ngaloo mzuzu, kutsho kwenzeke amanani ayakuqhubeka evela "umphelo". Akukho nani lingathi li-natural liphinde libe-infinite. Naliphi na inani eli-natural lingafumaneka ngokongeza u-1 kwinani eli-natural nekulelona lakhe lalincinane.

ipanslavism

Amanani angekho natural

Ezi ntlobo zamanani zilandelayo akungomanani a-natural:

Amanani angaphantsi ko-0 (amanani a-negative), umzekelo, −2 −1
ii-Fractions, umzekelo, ½ 3¼
ii-Decimals, umzekelo, 7.675
amanani a-Irrational, umzekelo, ${\sqrt {2}}$ , $\pi$ (pi)
amanani a-Imaginary, umzekelo, ${\sqrt {-1}}$ (i)
i-infinity, umzekelo, $\infty$ $\aleph _{0}$

Basic operations

Ukudibanisa/ukongeza; Isiphumo somdibaniso wamanani amabini a-natural siba linani eli- natural. $l+m=n$ $l+m=n$
- $l+n=n+l$
- $n+0=n$
- $(l+m)+n=l+(m+n)$
Multiplication": Isiphumo sophinda-phindo lwamanani amabini a-natural siba linani eli-natural. $l\times m=n$
- $l\times m=m\times n$
- $n\times 0=0$
- $n\times 1=n$
- $(l\times m)\times n=l\times (m\times n)$
- $l\times (m+n)=(l\times m)+(l\times n)$

Ulandelelwaniso: lwamanani amabini a-natural, ukuba akafani, ngoko ke elinye likhulu kunelinye, lize elinye libe lincinane. m = n or m > n or m < n
- Ukuba u- l > m ke u-l + n > m + n aze yena u-l x n > l x m
- U-Zero lelona nani lincinane kuwo onke amanani a-natural: 0 = n or 0 < n
- Kumanani a-natural akukho nani likhulu ukodlula amanye amanani n < n + 1

"Ukuthabatha okanye ukuphungula": ukuba u-n mncinane kuno-m then u-m minus n linani eli-natural. Ukuba If n < m then m - n = p.
- Ukuba u-l - m = n then l = n + m
- ukuba u-n mkhulu kuno-m, then u-m minus n akulonani li-natural
- Ukuba u-i = m - n no-p < n then l > m - p

Ukwahlula-hlula: Ukuba $l\times m=n$ then $n/m=l$

I-Mathematical induction: ukuba ezi zinto zimbini ziyinyaniso yayo nayiphi na i-property P yamanani a-natural, then u-P uyinyaniso yalo lonke inani eli-natural

Amanani a-natural ngokukodwa

Ii-Even numbers: Ukuba u-n = m x 2, then u-n uyi-even number
- Ii-even numbers ngoo-0, 2, 4, 6, njalo najlo. U-Zero uyeyona even number incinane (yokuqala).
Ii-Odd numbers: Ukuba u-n = m x 2 +1, then u-n uyi-odd number
- Inani lisenokuba even okanye libe-odd kodwa alinakubanazo zombini ezi mpawu.
- Ii-odd numbers ngoo-1, 3, 5, 7,njalo njalo.
Ii-Composite numbers: Ukuba u-n = m x l, no-m kunye no-l abango-0 okanye 1, then u-n uyi-composite number.
- Ii-composite numbers ngoo-4, 6, 8, 9, 10, 12, 14, 15,16,18,21 njalo njalo.
Ii-Prime numbers: ukuba inani alingo-0, 1, libe lingeyo-composite number, then liyi-prime number
- Ii-prime numbers ngoo-2, 3, 5, 7, 11, 13, 17, njalo njalo. Isibini silelona nani lincinane (okanye lokuqala) le-prime number. Isibini kukuphela kwenani eliyi-even prime number.
- Akukho prime number yongamele ezinye ngobukhulu.
Ii-Square numbers: ukuba u-n = m x m, then u-n usi-square. u-n usi-square sika-m.
- Izi-squares ngoo-0, 1, 4, 9, 16, 25,36,49 and so on.