aupcharik ganana

ganiteey tarkshastrat, aupcharik ganana kinwa aupcharik karya hii eka ganana aahe jee "paddhatshir parantu kathor samarthan nasaleli" aahe. tyat aavashyak atty aahet heey siddha naan karata samanya paryay vaparoon abhivyaktitil chinhanmadhye ferfar karane samavisht aahe. moolatah, tyat abhivyaktichya moolbhut arthacha vichar naan karata abhivyaktichya swarupacha samavesh asato. jevha purava dene katheen kinwa anavashyak asate tevha kahee vidhan kharey aahe yacha sakaratmak purava mhanoon kinwa naveen (purnapane kathor) vyakhya tayar karnyasathi prerana mhanoon haah tark ektar kaam karoo shakato.
tathapi, aupcharik yaa shabdacha haah arth sarvatrikpane swikarla jaat nahee aanee kahijan yala agadi ulat arth manatatah aupcharik ganiteey tarkshastrapramanech eka purnapane kathor yuktivad.
udaharane.
aupcharik gananemule asey parinam houu shakatat jeey eka sandarbhat chukiche aahet, parantu parantu sandarbhat yogya aahet. samikaran
jarr "q" chey nirpeksh moolya 1 peksha qamee asel tarr asey gruheet dharale jaate. yaa nirbandhakade durlaksh karoon, aanee "q" = 2 laa badalalyane
pahilya samikaranachya puravyat "q" = 2 badaloon, eka aupcharik ganana milate jee shevatche samikaran tayar karate. parantu vastavik sankhyanpeksha heey chukiche aahe, kaaran malika ektrit hott nahee. tathapi, itar sandarbhanmadhye (udaa.jee. 2-edic sankhyansah kinwa purnankanchya modulo 2 chya ghatankansah kaam kartana, malika ektrit hote. aupcharik ganana soochit karate qee shevatche samikaran tyaa sandarbhanmadhye vaidh asane aavashyak aahe.
aanakhi eka udaharan "q" =-1. parinami malika 1-1+1-1 + badaloon prapt hote... heey bhinn aahe (vastavik aanee pii-edic sankhyanvar) parantu sesarao yogasarkhya yogachya paryayi paddhatisah tyala moolya niyukt kele jaau shakate. parinami moolya, eka-done, aupcharik gananene midavalelya mulyasarkhech aahe.
aupcharik shakti malika.
aupcharik shakti malika hii eka sankalpana aahe jee vastavik vishleshanatun shakti malikeche swaroop swikarte. aupcharik" haah shabd soochit karato qee malika ektrit karanyachi aavashyakta nahee. ganitamadhye, aanee visheshtah bijganitemadhye, aupcharik malika hii eka anant berries aahe jee abhisaranachya konatyahi kalpanepasoon swatantrapane manali jaate aanee malika (jode, vaja, gunakar, vibhajan, aanshik berries ii.) vareel bijganitiy karyansah hatalali jaau shakate.).
aupcharik shakti malika hii eka vishesh prakarchi aupcharik malika aahe, jee bahupadiche samanyikaran mhanoon pahili jaau shakate, jithe sandnyanchi sankhya amaryad asoo dilee jaate, jyat abhisaran aavashyak nasate. asha prakare, hii malika yapudhe tyachya chalanche karya darshavu shakat nahee, keval gunankancha eka aupcharik kram, power sirijchya ulat, jee abhisaran trijyat chalasathi sankhyatmak moolye gheuun karya paribhashit karate. aupcharik shakti maliket, chalanchya shakti keval gunankansathi sthan-dharak mhanoon vaparlya jaatat, jenekarun sootra _ 3 chaa gunank haah kramatil pachva shabd asel. sanyojanashastrat, karye nirman karanyachi paddhat sankhyatmak anukram aanee bahusanketanche pratinidhitva karnyasathi aupcharik shakti malika vaparte, udaharanarth punaravrutti spashtapane sodavali jaau shakate qee nahee yachee parva naan karata punaravrutti paribhashit anukramasathi sankshipt abhivyaktila parvanagi dete. adhik samanyatah, aupcharik shakti maliket konatyahi maryadit (kinwa mojanyayogya) chalsankhyesah aanee aniyantrit ringmadhye gunankansah malika samavisht asoo shakatat.
aupcharik shakti malikechya rings yaa sampoorn sthanik rings aahet, jyaa bijganitiy bhoomiti aanee parivartaneey bijganitachya purnapane bijganitiy chaukatit ganitachya paddhatinna samarthan detat. teey pii-edic purnankanshi samaan aahet, jyanchi vyakhya pichya shaktinchi aupcharik malika mhanoon kelee jaau shakate.
chinhatil ferfar.
vibhedak samikaran sodavanyasathi
yaa chinhanna samanya bijganitiy chinhe mhanoon manale jaau shakate aanee yaa tappyachya vaidhatebabat konatehi samarthan naan deta, aamhi donhi bajunche parasparsambandh ghetoh
eka sadhee pratijaivikah
hii eka "aupcharik" ganana asalyane, sootra _ 8 dene aanee dusra upay midvane sweekarya aaheh
teey samikaran sodavtat yachee pushti karnyasathi antim upay tapasale jaau shakatat.

