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

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, ${\displaystyle {\sqrt {2}}}$, ${\displaystyle \pi }$ (pi)
• amanani a-Imaginary, umzekelo, ${\displaystyle {\sqrt {-1}}}$ (i)
• i-infinity, umzekelo, ${\displaystyle \infty }$ ${\displaystyle \aleph _{0}}$

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

• 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 ${\displaystyle l\times m=n}$ then ${\displaystyle n/m=l}$

• 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

• 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.