
pratinidhitva (ganeet)

ganitat, pratinidhitva haah eka atishay samanya sambandh aahe joou ganiteey vastoo kinwa sanrachananmadhil samanata (kinwa samanata) vyakt karato. sthoolpane sangayache tarr, ganiteey vastooncha sangrah 'vaay' haah vastooncha 'ex' haah dusra sangrah darshavito asey mhatale jaau shakate, parantu pratinidhitva karananya vastunmadhye 'vaay' asalele gunadharm aanee sambandh kahee pramanat susangat aahet, jeey sambandhit pratinidhitva kelelya vastunmadhye 'xi' madhye astitvat aahet. adhik visheshtah, gunadharm aanee sambandhancha sanch "π" dilyas, "x" yaa kahee sanrachaneche pratinidhitva karnari "π" hii eka rachana "y" aahe jee samarupatekhali "x" chee pratima aahe jee "π" jatan karate. label "pratinidhitva" kadhikadhi swatah samarupatevar dekhil lagoo kele jaate (jase qee gut siddhantatil gut samarupata).
pratinidhitva siddhant.
kadachit yaa samanya kalpaneche sarvat vikasit udaharan mhanje amoort bijganitache upkshetra jyala pratinidhitva siddhant mhanatat, jeey vector spaceschya resheey parivartanandvare bijganitiy sanrachananchya ghatakanche pratinidhitva karnyacha abhyas karate.
itar udaharane.
jaree 'pratinidhitva siddhant' haah shabd varr charcha kelelya bijganitiy arthane changlya prakare sthapit asala, taree sampoorn ganitat 'pratinidhitva' yaa shabdache itar anek upayog aahet.
aalekh siddhant.
aalekh siddhantache sakriy kshetra mhanje aalekh aanee itar sanrachananmadhil samarupateche anveshan.
asha samasyancha eka pramukh varg yaa vastusthitivarun udbhavato qee, dishaheen aalekhatil sanlagnatepramane, sanchanche chhedanbindu
(kinwa, adhik tantotant, gair-visangati) haah eka samamiteey sambandh aahe.
yamule sanchanchya asankhya kutumbansathi chhedanbindu aalekhanchya abhyasala chalana milate.
paul erdos aanee tyachya sahakanyanmule yethe eka moolbhut parinam assa aahe qee pratyek 'aine'-vertex aalekh 'aine' 2/4 peksha jaast nasalelya aakarachya sanchatil upasanchanmadhil chhedanbinduchya drushtine darshavila jaau shakato.
tyachya sanlagnata matricks aanee laplacian matricks mhanoon asha bijganitiy sanrachanandware aalekh darshavinyane varnakrameey aalekh siddhantachya kshetrala janm midato.
aurder siddhant.
pratyek aalekh haah eka chhedanbindu aalekh aahe yaa vareel nirikshanapeksha duheri mhanje pratyek anshatah krambaddha sanch (jyala posset asehi mhanatat) haah samavesh (kinwa niyantran) sambandhadvare krambaddha kelelya sanchanchya sankalanasathi samaroop aahe.
naisargik varganchya vastunsathi samavesh kram mhanoon udbhavananya kahee sthitimadhye booliyan jaali aanee pariman "aine" chya kramancha samavesh hoto.
bhaumitik vastoonchya sangrahatoon (aanee asha prakare darshavile jaau shakate) anek aanshik kram udbhavtat. tyapaiki 'aine'-baul aurder aahet. 1-chenduche aurder heey madhyantar-niyantran aurder aahet aanee 2-chenduche aurder heey tathakathit 'vartul aurder' aahet-vimanatil discommadhil containmentchya drushtine pratinidhitva karnyayogya posets. yaa kshetratil eka vishesh changla parinam mhanje samtol aalekhanche vaishishtyikaran, kaaran jyaa aalekhanche shirobindu-bajuche ghatana sambandh vartul kram aahet.
asha bhaumitik pratinidhyahi aahet jyaa samaveshanavar aadharit naheet. kharokhar, yapaiki eka sarvottam abhyas kelela varg mhanje madhyantar kram, joou vastavik reshevaril antaranchya 'visangat pradhanya' chya sandarbhat aanshik kramache pratinidhitva karatoh sthanakacha pratyek ghatak 'x' heey ['x' 1, 'x' 2] yaa antarane darshavile jaate, mhanje sthanatil konatyahi 'y' aanee 'z' sathee, 'y' heey 'z' chya khalee asel jarr aanee fakt 'y' 2 <'z' 1 asel tarach.
tarkshastra.
tarkshastrat, sambandhit sanrachana mhanoon algebranchi pratinidhitvakshamata bahutekda bijganitiy aanee sambandhit shabdarthshastrachi samanata siddha karnyasathi vaparali jaate. yachya udaharananmadhye sanchachi kshetre mhanoon booliyan algebranche prastar pratinidhitva, sanchanchya algebranna uchch karnyasathi hetting algebranche esakiyache pratinidhitva aanee pratinidhitva karnyayogya sambandh algebrancha aanee pratinidhitva karnyayogya dandgolakar algebrancha abhyas yancha samavesh hoto.
polisemy.
kahee vishisht paristhitinmadhye, ekach karya "f": "x" → "y" ekach velee "x" vareel anek ganiteey sanrachananmadhil samarupata aahe. tyaa pratyek sanrachanecha arth 'vaay' ('vaay' aaplyala sanganyacha prayatna kareet asalelya goshtinpaiki eka) assa antardnyanane vichar keela jaau shakato, yaa ghatanela polysemy mhanatat-bhashashastratun ghetaleli sandnya. polysemychya kahee udaharananmadhye khaleel goshtincha samavesh hotoh