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

 Basic operations 
 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 
 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.

Category:Amanani