ganita tatvasaastraaniki parichayam

ganita tatvasaastraaniki parichayam anedi maark colvan rachinchina ganita tatvasaastrampai 2012 paatyapustakam. idhi samakaaleena tatvasaastramlooni ganita vaastavikata-vyatiraeka-vaastavikata charcha mariyu ganita abhyasam yokka taatvika praamukhyata vanti samasyalapai drushti saarinchindi mariyu ekkuvagaa chaaritraka charchalanu daatavestundi. idhi ganita shaastram yokka samakaaleena tatvasaastramlo vividha rakaalaina ganita vaastavikata, quain-putnam anivaarya vaadana, ganita kalpana, ganita vivarana, "ganita shaastram yokka asamanjasamaina prabhavam", paraconsistent ganitam mariyu ganita shaastram yokka purogati loe ganita sanketam yokka paathratho sahaa aneka amsaalanu kaligi undhi. eee pustakam andubaatulo mariyu baga vrayabadinatluga prasamsimchabadimdi mariyu daani samakaaleena drushtini ekkuvagaa sanukoolamgaa pratibimbimchimdi, ayinappatikee kontamandi vidya sameekshakulu idhi tarkavaadam, laanchanavaadam mariyu antar drushti meeda chaaritraka charchalanu marinta vivaramgaa cover chesi undaalani bhaavinchaaru. prasamsalu andukunna pustakamloni itara amsaalu ganita vivarana, ganita saastravettalu mariyu itara tatvavettalu kaani vaariki daani vignapti, mariyu daani charcha prasnalu mariyu tadupari pathanaalu, ayithe daani upakhyanam mariyu swalpa nidivi marinta mishrama spandananu pondaayi.
sameeksha.
"ganita tatvasaastraaniki parichayam" anedi ganita vaastavikata samasyapai drushti saarinche ganita tatvasaastrampai oka paatyapustakamgaa undhi, antey.ii. ganita vastuvulu unnaya ledhaa anae prasna, mariyu ganita vivarana. colvan eee pustakam patla thana uddesaanni "iravayyava sataabdam modati ardhabhaagaaniki minchina paatyapustakamgaa mariyu samakaaleena ganita tatvavettala drushtini aakarshinche samasyalanu [anveshistundi]" anie abhivarninchaadu. phalitamgaa, eee pustakam itara saaruupya paatyapustakaala kante ganita tatvasaastramlo chaaritraka charchalapai takkuva drushti pedutundi mariyu ganita abhyasa tatvasaastramtoe sahaa samakaaleena samasyalapai ekkuva drushti pedutundi.
saaraamsam.
eee pustakamlo enimidi adhyayalu mariyu prati adhyayam charcha prasnalu mariyu tadupari pathanaala jaabitaato mugise upasamhaaram unnaayi. 20va sataabdam praarambhamlo ganita shaastra tatvasaastramlo aadhipatyam chelaayinchina "pedda siddhaantaalu" anie collivan piliche vaatini modati adhyayam kluptamgaa vivaristundihi tarkavaadam, laanchanavaadam mariyu antar drushti. appudu adhi paal benasseraph thana patraalalo levanettina taatvika samasyalaku maarutundi "ganita satyam antey emiti?"(1965) mariyu" "yea sankhyalu undalevu" "(1971)".
2va adhyayam ganita parimitulu mariyu sambandhita parimita ganita siddhaantaalaku sambandhinchinadi. idhi lovenheim-scome siddhaantam mariyu contor siddhaantamtoe daani sambandhaanni charchistundi, indulo contor siddhaantam yokka rujuvu mariyu rendu siddhaantaalu enduku viruddhamgaa laevu anae vivarana unnaayi. idhi godel yokka asampuurnata siddhaantaalu mariyu continume hypothesis yokka swatantratapai godel mariyu kohen yokka panini kooda charchistundi. ganita vaastavikata mariyu vaastavikata vyatiraekata madhya charchanu prerepinchadaaniki eee phalitaalu upayoginchabadataayi.
hilarii putnam taruvaata, colvan 3va adhyaayamlo ganita satyaala gurinchi vaastavikata mariyu ganita vastuvula gurinchi vaastavikata madhya thedaanu paerkonnaadu. athanu "idhi vastunishtha satyam nundi vastuvulaku chaalaa vegavantamaina maargamgaa anipistundi" anie vaadinchaadu, anduvalla ganita vastuvula gurinchi vaastavikatapai tadupari charchapai drushti pedutundi. eee adhyayam vividha rakaala vaastavikata madhya thedaanu chooputundi, veetilo puurti-rakta platonism, nirmaanavaadam mariyu penelope maadi vanti rachayitala bhouthikavaada vaastavikata, mariyu prakrutivaadam mariyu quin-putnam anivaarya vaadananu cover chestundi. maddy, hartree feeled mariyu elliot sobar nundi anivaarya vaadanapai abhyantaraalu kooda pradarsinchabaddaayi.
4va adhyayam ganita vyatiraeka vaastavikata (namavachakam), mukhyamgaa ganita kaalpanikatapai drushti pedutundi. idhi hartree feeled yokka kaalpanikata mariyu athani naamineekarana kaaryakramaaniki parichayaanni istundi, dheenini collivan naamineekaranaku kathinamaina maargam anie pilustaadu. colvan naamavaachakatvaaniki sulabhamaina margalu anie pilavabade vaatini kooda kaligi untundi; atuvanti abhiprayalu "sulabham" endukante avi mana uttama shaastreeya siddhaantaala nundi ganita entiteelanu tolaginchadaaniki prayatninchavu, endukante feeled yokka nominalization project dheenini tolaginchadaaniki prayatnistundi. veetilo jody ajauni yokka kaalpanikata mariyu stephen yablo pratipaadinchina ganita bhasha yokka roopaka vivarana unnaayi. eee adhyaayamlo, collivan yablo abhipraayaalanu vyatiraekistuu, shaastreeya vivaranalalo ganitam kanipistundani, vivaranalalo roopaka bhashanu upayoginchina chota, adhi akshararahita vivaranaku sankshiptalipigaa upayoginchabadutundani, lekapothe daanini aksharala ardham chesukovali anie paerkonnaadu.
eee charcha taruvaata, 5va adhyayam ganita vivaranaku mariyu vaastavikata-vyatiraeka-vaastavikata charchalo "vivaranaatmaka malupu" kii sambandhinchinadi, dheenilo ganita shaastram yokka vivaranaatmaka shakti paramgaa anivaarya vaadananu punarnirminchaaru. idhi vivarana yokka vividha siddhaantaalanu parigananaloki teesukovadamto praarambhamavutundi, phalitamgaa collivan ekikarana khaataa kosam vaadistaadu. oke saiddhaantika chatram kinda bahula vibhina drugvishayaalanu teesukuraavadam dwara vivaranalu panichestaayane abhiprayam idhi. aaa taruvaata athanu ganita shaastram lopala vivaranalu, ganita vaastavaala ganita vivaranalu, ganita shaastram velupala vivaranalu, ganita shaastram kaani, anubhavika vaastavaala ganita vivaranala madhya thedaanu gurtistaadu. euclid siddhaantam, roll siddhaantam mariyu modati "n" sahaja sankhyala mottaaniki suutram yokka rujuvulanu vivaranaatmakamainavi kaani rujuvulaku udaaharanalugaa paerkontuu, vivaranaatmakamaina mariyu laeni ganita rujuvula madhya vyatyaasaanni vivarinchadaaniki athanu vivarana yokka ekikarana khaataanu upayogistaadu. appudu athanu ganita shaastram kevalam vivaranaatmaka sadhanam kante ekkuva anie vaadistuu, anubhavika vaastavaalaku nijamaina vivaranalanu andistuu, ganita shaastram velupala vivaranaatmaka vivaranalaku veltaadu. athanu aavartana sicadas yokka jeevita chakraala yokka ganita vivaranala udaaharanalanu, theneteega-theneteega enduku shatkona nirmaanaanni kaligi undhi, soura vyavastha antataa grahasakalaala pampinhee mariyu thana vaadanaku maddatugaa lorentz sankocham.
6va adhyayam ganita shaastram yokka vartaneeyata mariyu vignaana saastramlo vartimpajesinappudu daani "asamanjasamaina prabhavam" gurinchi undhi. ganitasastram yokka asamanjasamaina prabhavanni vivarinchadaaniki, james clerk maxwell maxwell-ampere niyamanni neutonian gurutvakarshana siddhaantaaniki saruupyamgaa elaa roopondinchaado collivan raasaaru, conny adhi puurtigaa kotta anchanaalanu utpatti chesi, nirdhaarinchabadindi. ganita anuvartanam yokka mapping khaataanu andinchadam dwara eee asamanjasamaina prabhavanni vivarinchadaaniki athanu prayatnistaadu. eee kathanam prakaram, ganita namuunaalu nirdishta vivaraala nundi vyavastha yokka marinta nirmaanaatmaka lakshanaalaku dhooramgaa sangrahinchadam dwara bhouthika vyavasthala pataluga panicheestaayi. eee vidhamgaa, ganita shaastram yokka nairoopya nirmaanaalanu saaruupyata sambandhaala dwara bhouthika vyavasthalanu suuchimchadaaniki upayoginchavacchu. eee mapping khaataanu vivarinchadaaniki collivan janabha paryaavarana saastramlo ganita namuunaala cases studdini andistundi.
7va adhyayam paraconsistent ganitam mariyu tarkam chuttoo unna samasyalanu anveshistundi. collivan ganita siddhaantam upayogakaramgaa unnappatikee asthiramgaa undavacchani vaadinchaaru, amayaka samiti siddhaantam mariyu prarambha ananta calculusnu ganita siddhaantaalaku udaaharanalugaa suuchimchaaru, ivi taruvaata asthiramgaa niroopinchabaddaayi conny ganita saastravettalache phalavantamaina pani cheyabaddaayi. ganita saastravettalu upayoginche tarkam eee vaastavaanni parigananaloki teesukoovadaaniki shaastreeya tarkam kante oka rakamaina vairudhya-sahanam ledhaa paraconsistent tarkam ayi undaali anie kooda ayana pratipaadinchaaru. savarinchina satya pattikalu mariyu moodava satya viluva "i" nuu upayoginchadam dwara paeludu suutraaniki daariteeyani atuvanti paraconsistent logiccu udaaharanagaa athanu paradox (elpi) tarkaanni andistaadu, dheenini "nijam mariyu tappu" anie suuchimchaalani athanu suuchistaadu.
8va adhyayam ganita sanketam yokka taatvika praamukhyatapai undhi. ganita purogati konnisaarlu sangnaamaanamlo maarpulaku kaaranamani colvan vaadinchaaru. eee aalochanaku maddatugaa eee adhyaayamlo aneka udaaharanalu unnaayi. udaaharanaku, roman sankhyala nundi arabic sankhyalaku maaradam ganita purogatini prerepinchi undavacchani collivan chepparu, endukante roman sankhyala maadirigaa kakunda arabic sankhyalu punaraavrutaanni kaligi untaayi. andinchina maroka udaaharana vruttaanni vargapariche asaadhyata rujuvulo ganita sanketam yokka auchityam, idhi oke prakriyanu vividha margallo soochinchadam ganitamlo spashtamaina sambandhaalanu bahirgatam cheyagaladane aalochananu vivarinchadaaniki upayoginchabadutundi. polyheadron anae padam yokka abhivruddhi chendutunna nirvachanam yokka udaaharananu upayoginchi ganitamlo nirvachanam yokka praamukhyatanu kooda eee adhyayam pariseelistundi.
upasamhaaram "edaari dveepa siddhaantaalu" anae sheershikato undhi mariyu ganitasastra tatvavettalandaru telusukovalani collivan vishwasinche 20 mukhyamaina siddhaantaalu mariyu 5 bahiranga samasyala jaabitaanu kaligi undhi. aasaktikaramaina sankhyala" rendu paejeela jabita kooda undhi. eee siddhaantaalu, samasyalu mariyu sankhyala yokka taatvika praamukhyata mariyu prabhaavampai chinna charchalu kooda prati amsam tarvaata chaerchabadataayi.
swaagatam.
eee pustakam yokka samakaaleena drushti prasamsalu andukundi. metassians" loe pustakaanni sameekshinchina noah friedman-biglin, eee pustakamloni eee lakshanam "vilakshanamainadi" anie bhaavinchi, ganita vivarana yokka kavarejeeni prasamsimchaaru, dheenini ayana "ippudu ganita shaastram yokka aneka mandhi vruttiparamaina tatvavettala aasaktini aakarshistunna amsam" anie pilicharu. dhi bulletin off symbolic logic" loe pustakaanni sameekshinchina richard pettigroo, eee pustakam 5va adhyaayamlo "nijamgaa praarambhamavutundi" anie bhaavinchaaru, ikkada idhi "chaalaa praamaanikamaina, prasamsaneeyamgaa spashtamgaa unte, baga dharinchina padaarthaala pradarsana" nundi "saapekshamgaa takkuva saahityam unna kotta amsaala yokka uttejakaramaina anveshana" kii maarutundi."puurtigaa erpadina vaadanalaku badulugaa eee amsaalanu anveshinchetappudu eee pustakam udaaharanalanu upayoginchadam anedi pustakam yokka oka lakshanam, idhi" [vidyaarthulanu] vaari swantha taatvika parikalpanalu mariyu vaadanalanu marinta saampradaaya paatyapustakaala kante marinta sulabhamgaa roopondinchadaaniki prerepistundi "anie ayana annaru."eee pustakamlo kontha bhaagamlo vivaralu mariyu drudhatvam lekapoyina, eee amsaaniki sambandhinchina bhavishyat vidyaarthulu viluvainavaaravvaalani neenu korukuntunnanu, colvan ganita shaastra tatvasaastramlo prastuta kaalaaniki vidyaarthulanu prerepinche modati paatyapustakaanni raasaaru" anie ayana muginchaaru."" "bodhana tatvasaastram" "loe oka sameekshalo, carle wagner matladutu," "konasagutunna eee charchala utsahanni teliyajeyadamlo mariyu eee samasyalapai vaari swantha abhipraayaalanu pempondinchukovadaaniki paatakulanu prothsahinchadamlo kolvanku nijamaina pratibha undhi". ayana 5va adhyayanni "eee pustakamloni itara ekareeti adbhutamaina adhyaayaala nundi kooda [nilabadi]" anie abhivarninchaaru mariyu "mukhyamgaa aasaktikaramgaa" unnanduku ganitaaniki minchina vivaranala kavarejeeni pratyaekamgaa prasamsimchaaru. zeane-pier marquis eee pustakaanni "ganita sameekshalalo" "ganita tatvasaastram yokka arudaina vaataavaranamloo challani sheethaakaalam tarvaata vecchani gaali" gaa abhivarninchaaru."[f] ledhaa chaalaa kaalam kritam, eee rangam laanchanapraayata, tarkavaadam mariyu antar drushti yugamlo stambhinchipoyindani, marinta samakaaleena vishayalanu pradarsinchaalanae daani lakshyaaniki sambandhinchi, eee pustakam" "adbhutamaina vijayam" "saadhinchindani ayana vaadinchaaru". pustakam yokka samakaaleena drushti, alaage vaastava ganita shaastram yokka upayogam kooda maark hunasek chetha pustakam yokka aasaktikaramaina amsaalugaa gurtinchabaddaayi, athanu eee pustakaanni mathematical association off america kosam sameekshinchaadu.
eee pustakam andubaatulo undagaladani mariyu baga vraayabadindani kooda vistrutamgaa varninchabadindi. david irvin "philosophia mathematical" loe oka sameekshalo, alegzander georg mariyu daniel wellman yokka "ganita tatvaalu", stevert shapiro yokka "ganitam gurinchi aalochinchadam" mariyu maikhel patter yokka "sett theory und itts philosophy" latho paatu, 2000 nundi vidudalaina ganita tatvasaastrampai uttama paatyapustakaallo eee pustakam okati anie chepparu. eee pustakam yokka "samasya yokka gundeku dookadam yokka naipunhyam" antey "[enn] eppuduu adhikamgaa untundi" anie ayana annaru mariyu "bodhinchadam aanandamgaa undhi mariyu ganita tatvasaastramlo amsaalaku modati bahirgatam chesina vidyaarthulu daanini andubaatulo mariyu uttejaparichevigaa kanugonnarani [athanu] nivedinchagaladani nirdhaarinchaaru."australian journal off philosophylo" "jaak webber eee pustakam gurinchi matladutu, collivan thana sonta parisoedhananu atyanta andubaatulo unde paatyapustakamgaa kudinchaadu"."" "sameekshalo tatvasaastram" "loe oka sameekshalo, saam baaran eee pustakaanni" "andamgaa vraayabadindi" "anie pilicharu mariyu idhi" "tatvasaastramlo paatyapustakamlo undavalasina mukhya lakshanaalanu [udaaharanagaa] istundih idhi spashtamgaa, utsaahamgaa mariyu chadavadaaniki aahladakaramgaa untundi"."hunasek eee pustakaanni" "utsaahabharitamaina mariyu vinodabharitamainadi" "gaa abhivarninchaadu, alaage" "[ganita tatvasaastram] paie aneka itara pustakaala nundi kontavaraku vaerugaa unche ejendaatho kuudina oka chaatii, aasaktikaramaina pustakam". christian soto eee pustakaanni "critica rivista hispanoamericana dii philosophia" loe sameekshinchaaru, eee pustakaanni "[ganita tatvasaastram] looni konni atyanta aasaktikaramaina chikkulaku khachitamaina mariyu andubaatulo unde peethika" anie paerkonnaaru. noah friedman-biglin, "metassians" loe, pustakam yokka rachana sailini "andubaatulo" undani prasamsimchaaru mariyu eee pustakaanni "raddiigaa unna praantaaniki chakkati sahakaram" gaa abhivarninchaaruh idhi ganita tatvasaastrampai prastuta saahityamlooni konni amsaalaku spashtamgaa vraasina, saanketikata laeni parichayaanni andistundi."eee pustakam" "chaalaa baga vrayabadi, chadavadaaniki aanandamgaa undhi" "mariyu adhyayalu" "chinnavi, spashtamainavi mariyu baga nirmanatmakamga unnaayi" "anie marquis chepparu".
eee pustakam yokka prekshakulu mariyu vishwavidyaalaya course paatamgaa anukuulata bahula sameekshalalo cover cheyabaddaayi. ganita phalitaalanu pustakamlo andubaatulo unchadam, "ganita vaastavikatapai charchapai parichaya saamagrini atyaadhunika parisoedhanatoe sajavuga nesina" vidhaanamtho jatacheyadam under graduate ledhaa post graduate korsulaku taginadani baaran abhiprayapaddaru. eee pustakam "aascharyakaramgaa vistruta shreni amsaalanu kaligi undhi" anie, idhi vividha drushti saarinchina korsulanu roopondinchadamlo daani prayojanaanni penchindani taanu bhavinchanani kooda ayana annaru. friedman-biglin "vidyaarthulu ganita tatvasaastraanni adhyayanam cheyadam praarambhinchadaaniki eee pustakaanni oka adbhutamaina pradaesamgaa kanugontaaru, mariyu idhi under graduatelaku aasaktikaramaina korsuku sulabhamgaa aadharam kaagaladu" anie bhaavinchaaru."pustakam yokka" "sambhaashana shaili mariyu churukaina vegam" "dheenini" "utsaahabharitamaina under graduate course kosam spashtamgaa roopondinchabadindani webber bhaavinchaadu". ayithe, eee pustakam chinnadani, ardha semister ledhaa vesavi korsuku ledhaa charchalaku prarambha binduvugaa marinta anukuulamgaa undani ayana bhaavinchaaru. eee pustakam gurinchi thana pradhana aandolana daani takkuva podavu anie hunasek cheppadu, idhi puurti-semister korsuku maddatu ivvagalada anie aascharyapovadaaniki daariteesindi. edemaina, idhi "[course] vachanamgaa upayoginchadam kakunda gananeeyamaina viluvanu kaligi undani" bhaavinchi, "oka ganita shaastravetta dheenini (neenu chesinatlugaa) noppilekunda mariyu vinodaatmakamgaa, aasaktikaramaina aalochanala gurinchi neerchukunee maargamgaa chadavadam aanandinchavacchu" anie annaru. mottamgaa, eee pustakaanni taanu aasvaadinchaanani, sifaarasu chesanani ayana chepparu. wagner matladutu, "eee pustakam, bahusha pradhanamgaa tatvasastra vidyaarthula kosam vrayabadinappatiki, ganita vidyaarthulu mariyu upaadhyaayulu kooda chaalaa labhadayakamga chadavavacchu. nijaaniki, eee sameekshakudu dheenini under graduate mathematics majerla kosam capstone courselo mariyu secondary school mathematics upaadhyaayula kosam graduate seminarlo upayoginchaalani bhaavistaadu."soto adevidhamgaa ganita saastravettalu mariyu saastravettalato paatu tatvavettala kosam eee pustakaanni sifaarasu chesaaru, idhi" "vaari praantaalanu kaligi unna charchalaku telivaina maargadarsini" "andinchindani annaru".
kontamandi sameekshakulu pustakamloni konni amsaala gurinchi charchinchaaru. irvin "pustakamlo balaheenata unte, tarkavaadam, laanchanapraayavaadam mariyu antar drushti meeda saampradaaya charchalu ara dozenu kante takkuva pageelalo untaayi, paatakulu eee gandaragolam deniki sambandhinchinado anie aascharyapotaaru."rendava edition eppudaina vidudala cheyabadithe, adhi eee amsaala meeda vistarinchaalani ayana annaru. eee pustakamlo russell yokka vairudhyaaniki rujuvu vanti marinni aadharalu unte taanu ishtapadataanani kooda ayana chepparu. adevidhamgaa baaran "pedda siddhaantaala" sankshipta coverage kontamandiki asantruptikaramgaa anipinchavacchani paerkonnaadu, ayithe pustakaalu vaastavikata samasyapai drushti saarinchinanduna idhi sarainadani vaadinchaadu, dheenini baaran "modati adhyaayamlo charted chesina pedda siddhaantaalaku ekkuvagaa orthogonal" anie pilustaaru."eee vyakhyalaku viruddhamgaa, wagner 1va adhyaayamlooni" "pedda siddhaantaala" "gurinchi colvan kavarejeeni sampeedana vivarana yokka naipunhyam kaligina bhaagam anie pilicharu". vargam siddhaantam, riverse mathematics, automated reasoning mariyu computer aided proofs coverage lekapovadam gurinchi pettigroo vyakhyaaninchaadu, conny "yea paatyapustakamuu anni amsaalanu cover cheyadu, mariyu ivi marinta sahajamgaa marinta adhunaatana korsuku chendinavani bhaavinchavachchu."ganita satyam yokka swabhaavam mariyu ganita punaadulapai pani vanti amsaalu eee pustakamlo levani friedman-biglin bhaavinchaaru. pustakaanni takkuva saanketikamgaa unchaalane korika kaaranamgaa colvan eee amsaalanu minahaayinchaadani, ayithe "daani prabhavanni tagginchadaaniki chaalaa dhooram velutunnaanani" bhaavinchaadani ayana vaadinchaaru. edemaina, konni praantaalalo ganita vivaralu lekapovadam gurinchi aandolanalu "ekkuva baruvunu kaligi undavu" anie ayana bhaavinchaaru, endukante "colvan pustakamloni pradhana vaadana chaalaa laanchanaalanu cherchadam dwara aspashtamgaa undavacchu". marquis eee amsampai ilaa annadu, "eee vishayam gurinchi ledhaa aaa vishayam gurinchi, eee suuchana ledhaa aaa vishayam gurinchi evarainaa godavapadavacchu, conny eee vimarsalu paayintnu kolpotayani neenu bhaavistunnaanu. eee rangaaniki parichayamgaa, pratipaadita amsaala empika puurtigaa samarthinchabadutundi."
chinna upasamhaaram gurinchi pettigroo matladutu, adhi takkuva siddhaantaalanu mariyu ekkuva rujuvulu mariyu anuvartanaalanu kaligi unte taanu ishtapadataanani cheppadu. edemaina, "balamaina ganita nepathyam lekunda ganita tatvasaastramloki pravesinche vidyaarthiki idhi khachitamgaa viluvaina vanaru" anie ayana annaru."hunasek matladutu, upasamharanni cherchadam dwara taanu" "ayomayaniki gurayyanani" "cheppadu, indulo" "nirdishta taatvika praamukhyata laeni amsaalu unnayani" "athanu cheppadu". wagner prasamsimchina upasamharanni prasamsistuu, daanini "adbhutamainadi" anie pilichi, daani siddhaantaala pradarsanalo konni maarpulanu suuchimchaadu. tadupari pathanaalanu "tadupari adhyayanaaniki adbhutamaina maargadarsakaalu" gaa webber prasamsimchaaru. charcha prasnalu mariyu tadupari pathanaalanu cherchadaanni kooda marquis prasamsimchaaru, dheenini "adbhutamaina chorava" anie paerkonnaaru.

