Ginti

Ginti, Mathematics ke ek concept hae, jiske kaam me laae ke giina aur naapa jaae hae. Ginti khaatir 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 ke kaam me laawa jaae hae. Ginti ke sab se sahaj namuna hae natural numbers 1, 2, 3, 4, 5, ..... Ek-ek number ke koi bhasa me  number sabd, nai to number symbols, jiske numerals bola jaawe hae, me likha jaae sake hae; jaise ki, "paanch" ek number sabd aur "5" iske  numeral hae. Kaaheki khaali thorraa symbol ke yaad karaa jaae sake hae , basic numerals ke numeral system me arrange karaa jaae hae, jon ek number ke represent kare ke  organized way hae. Sab se jaada kaam me laawe waala  numeral system Hindu–Arabic numeral system hae, jisme koi non-negative integer ke ten fundamental numeric symbols adj. and n. </ref> Naape aur giine ke alaawa , ginti ke   labels (jaise telephone numbers),  order kare ke khaatir (as with serial numbers), and for codes (as with ISBNs). Sadharan kaam me  numeral ke the number se ditinguish nai karaa jaae sake hae. 

Mathematics me,  number ke idea ke kuchh sau saal me barrhae ke  zero (0) ke saamil karaa gais hae, negative numbers, rational number jaise one half , real number jaise square root of 2  aur , aur complex numbers jon real numbers ke extend kare hae square root of  (and its combinations with real numbers by adding or subtracting its multiples). Numbers se [Calculation]]  arithmetical operations se karaa jaawe hae, jisme se sab se jaana maana hae addition, subtraction, multiplication, division, aur exponentiation. Iske adhyan aur kaam ke  arithmetic bola jaawe hae, ek sabd jiske  number theory ke khaatir kaam me bhi laawa jaawe hae, jon number ke properties ke adhyan hae.

Itihaas

Ginti ke sab se pahile kaam me laana
Haddi aur duusra chij ke paawa gais hae, jisme mark kaata gais hae, jiske biswas karaa jaawe hae ki  tally marks hae. Kuchh itihaas ke parrhe waale ii suggest karis hae ki Lebombo bone (dated about 43,000 years ago) aur Ishango bone (dated about 22,000 to 30,000 years ago) sab se puraana arithmetic chij hae, lekin ii  interpretation ke dispute karaa jaawe hae. Ii tally marks ke saait time ke jiine ke khaatir kaam me laawa gais rahaa, jaise ketna roj bitaa hae, chandarma ke cycles nai to quantities, jaise ketna jaanwar hae ke gine ke khaatir.  Ek perceptual system for quantity jiske numeracy ke underly kare ke socha jaawe hae, jaise  phylogenetic distribution jon suggest kare hae ki ii bhasa se pahile rahaa. 

Ek tallying system me place value (as in modern decimal notation) ke koi concept nai rahe hae, jon isse brraa ginti likhe nai de hae. Lekin  tallying systems ke pahila rakam ke  abstract numeral system maana jaawe hae.

Sab se puraana unambiguous ginti, archaeological record me Mesopotamian base 60 system hae( BC); jisme place value  3rd millennium BCE me aais rahaa. Sab se puraana, jaana jaawe waala base 10 system  3100 BC me Egypt me suruu karaa gais rahaa.

Numerals
Numbers, numerals se different hae. Numerals uu chinh hae jisse ginti ke likha jaawe hae. Egyptian log pahila  ciphered numeral system ke banae rahin, aur Greeks iske baad rahin jon gine waala number ke  Ionian aur Doric alphabets me mal kare rahin. Roman numerals, ek system hae  Roman alphabet ke letters ke kaam me laawe hae, Europe me sab se jaada kaam me laawa jaawat rahaa,  Hindu–Arabic numeral system ke  late 14th century me dunia bhar me faile se pahile, aur Hindu–Arabic numeral system abhi sab se jaada kaam me laawe waala system hae.  Ii  system  ke khaas gun ii hae ki isme  zero ke khaatir chinh hae, jiske puraana Indian mathematicians lagbhag 500 AD me develop kare rahin.

Zero
Pahila dafe jab zero ke kaam me laawa gais rahaa,  AD 628 me rahaa, aur ii Brāhmasphuṭasiddhānta me likha hae, t Indian mathematician Brahmagupta ke khaas kaam. Uud 0 ke ek number ke ruup me kaam me laais rahaa aue iske  operations ke discuss karis rahaa, jismedivision by zero bhi hae. Ii time talak (the 7th century), ii concept  Cambodia pahunch gais rahaa,   Khmer numerals me, aur iske baare me documentation dekhae hae ki idea baad me s China aur Islamic dunia talak faila rahaa.


Brahmagupta ke Brāhmasphuṭasiddhānta pahila book hae jon zero ke ek  number ke ruup me batae hae, tab Brahmagupta ke jaada kar ke pahila jan maana jaawe hae jon concept of zero ke formulate karis rahaa. Uu zero ke kaam me laae ke niyam diis hae, negative aur positive numbers ke saathe, jaise "zero ke jab ek positive number se jorra jaawe hae tab answer ek  positive number rahe hae, aur jab negative number ke zero se jorraa jaawe hae tab answe ek   negative number" rahe hae. Brāhmasphuṭasiddhānta sabse puraana book hae jon  zero ke ek number ke ruup me kaam me laawe hae.

vibhag:G
vibhag: Arithmetic