Amanani a-natural

**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. <math> l \times m = n</math>*
** 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  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 
** Ukuba u-i = m - n no-p  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.