Amanani a-natural

From Wikipedia
Jump to: navigation, search
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 68   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.

Amanani angekho natural [tshintsha | edit source]

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, , (pi)
  • amanani a-Imaginary, umzekelo, (i)
  • i-infinity, umzekelo,

Basic operations[tshintsha | edit source]

  • Ukudibanisa/ukongeza; Isiphumo somdibaniso wamanani amabini a-natural siba linani eli- natural.
  • Multiplication": Isiphumo sophinda-phindo  lwamanani amabini a-natural siba linani eli-natural.
  • 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 then
  • 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[tshintsha | edit source]

  • 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.