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. $l+m=n$
  • $l+n=n+l$
  • $n+0=n$
  • $(l+m)+n=l+(m+n)$
• 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.