Limoral faruwal : Wakannde haawniinde

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Limoral faruwal
Limoral faruwal

So mi wiyii ma wonde won ɗo wakannde woni tawa ende loowi defte, heen wootere ina tonngi nguurndam maaɗa fof, tawa woppaani hay piccal gootal. Gila ñalnde njibine-ɗaa haa ñalnde nduttoto-ɗaa, ende loowi sifaa no ciiɓortono-ɗaa kosam muuynatno-ɗaa, ina winndaa e mayre no boje koomtiratno maa, ina he mayre kala konngol, kala durmaango, kala saɓɓitaango, kala ɗojjaango, islaango heɓnoongo rewde e daande maa. Kala conndol meeɗnongol heɓde ma, kala muusalla, kala mbelamma, kala muuya, kala keɓal, kala ɗawre meeɗnoonde walla meeɗoore heɓde ma e nguurndam maa. Ndeen wakannde a yiɗat ko yaawi yiytude nde ngam wiɗaade nde haa njiytaa ndee deftere haawniinde ngam yilmitoraade nde ko nguurno-ɗaa, teeŋti noon ngam diiranoyde kelle cakkitte ɗee, mbele aɗa annda ko araani tawo e nguurndam maa, hay so noon maa a hul hippitde hello waɗtindiingo ngoo !  Maa mi hollu ɗoo wonde ndee wakannde ina woodi, kadi nii eɗe keewi, ɗe ngasataa, keeweendi majje ko kaaɗtari. Ko ɗee bakane ɓuri boom limoreeje goowaaɗe (hono 0, 1, 2, 3, … ekn) heewde !

Ko adii nde eɗen ndallina goodal ɗee bakane kan e keewal mumen moolanaangal ngal, njeewten loowdi ndi wootere kala e majje hattani loowde.

Mbiyen wonde kala deftere loowiinde e wakannde hee winndiraa ko alkule Pulaar capanɗe tati e ɗiɗi ɗee (32), wonndude e toɓɓere, e piccal e yolnde (woni mehum (ŋalde) ndeɗɗotooɗum hakkunde kelme ɗiɗi). Keɓen waɗde jelooɗe 35 ceertuɗe. Kawren e mbaydi binndol ngol nganndu-ɗaa, kala hello (ɗerewol) loowata ko gori 50, kala heen gorol loowata ko jelooɗe 100.

Jooni, so neɗɗo yiɗii winndude jeloode wootere, omo jogii laabi 35 binndirɗi ɗum. So o yiɗii winndude jelooɗe ɗiɗi, o jogoo laabi 35×35 binndirɗi ɗum, hawra 1 225 laawol. Ngam taroowo o ɓura faamde, so tawiino ko jelooɗe tati tan ngoodnoo, mbiyen ɗe {a, b, ɓ}, ina laaɓi so en njiɗii winndude jeloode wootere ko laabi 3 binndirɗi njogi-ɗen, ngati maa wonii en cuɓiima a, walla b, walla ɓ. Kono so en njiɗii winndude jelooɗe ɗiɗi, keɓen laabi 3×3 binndirɗi, hono 9. Ɗiin laabi ngoni, aa, ab, aɓ, ba, bb, bɓ, ɓa, ɓb, ɓɓ. En paamii rewriwal ngal : kala alkulal cuɓangal e binndol gadanol ngol ina hawra e laabi 3 cuɓorɗi alkulal ɗimmal ngal, nde tawnoo ko alkule tati ngoodi, kala heen gootal hawra e cuɓe 3, so rentinaama fota he 9. Hono noon ne, so en kuutoriima haralde men jelooɗe tati yeru mbeeɓtinaangu nguu, eɗen mbaawi yiɗde winndude helmere nde jelooɗe tati, so en ndewii rewriwal ngal keɓen laabi 3x3x3 binndirɗi ɗum, hawra 27 laawol. So en njiɗii waɗde helmere nde jelooɗe 10 keɓen 3x3x3x3x3x3x3x3x3x3 laawol, 59 049 laawol.  Ngam weeɓtinde tonngol hiisaaji ciforiiɗi nii, hiisiwal ina huutoroo tonngi daɓɓi beeɓtinooji : fayannde ko ɗum woodiri. So 3 sowiima hoore mum laabi 10, ɗum tonngiree no weeɓiri 310. Hono noon ne so ɗiɗi sowiima hoore mum laabi 67, ɗum winndatee ko 267. Ko ɓuri yaajde, so limoral p sowiima hoore mum laabi m, ɗum tonngatee ko pm.

Ngarten e haralde jelooɗe meeɗen 35 ɗee, hono loownde alkule pulaar e toɓɓirɗe tati kaalaaɗe ɗee, ngam winndude defte men ɗee. Nde tawnoo kawru-ɗen ko dow kala ɗerewol yo gorol fof loow jelooɗe 100, oon sahaa eɗen njogii laabi 35100 winndude kala gorol. Ɓayde noon kala ɗerewol hawraa waɗata ko gori 50, wadde njogo-ɗen laabi 35100×50=105000 winndude kala ɗerewol (woni kala hello). So en njiɗii winndude deftere nde ɗereeji 500, njogo-ɗen laabi 35100x50x500=352 500 000 binndirɗi ndeen deftere. Ngam weeɓtinande hakkillaaji men no keɓindorii mawneeki ngal limoral,  tesko-ɗen ko kanngal seɓi limoral 103 860 170 ngal, hono 1 dewnuɗo 3 860 170 ndiga ! Ciftoren wonnde keeweendi mitte, hono atomaaji, nder faru hee fof, hono iniweer hee, tolnii ko e 1080, hono 1 dewniiɗo ndigaaji 80. Wadde ɗum feccinaani sooynaade limoral keɓ-ɗen wonande laabi binndirɗi deftere nde 500 ɗerewol dow huutoraade haralde jelooɗe ƴettu-ɗen ndee.

Ɗum ɗoo noon yiɗi wiyde ko  eɗen mbaawi winndude defte 103 860 170 ceertuɗe, ɗe 500 hello, tawa kuutori-ɗen tan ko haralde 35 ɗee.

So en ngoniino ɓalliyankooɓe, mbiyen yo en ndarto ɗoo; ngati ɗum ne fakiti haa heƴataa e ko woodi koo fof, hono faru nguu. Hay so e pamɗitinii deftere heen fof haa fotii e mittere, ko cetta heen tan naatata e faru men, hay ɗum ko maa kala koode, kala lilluɗe, kala ɗaŋe, kala pecoron njaltinee, nde oon cetta waawa naatde!

Kono nde tawnoo hannde mbaɗaten ko hiisiwal, hay keeri faru mbaawaa hanndaade en, nde tawnoo eɗen mbaawi maandaade limoreeje ɓurɗe ɗoon mawnude; so maandaade, hiisoo limoral kaaɗtaral e hoore mum!

Wadde miijo-ɗen wakannde loowoore defte men 103 860 170 ɗee. Heen wootere ina loowi ciimtol nguurndam maa, aan gonɗo e tarde oo. Woɗnde ina loowi ciimtol nguurndam maa tawa ina waɗi saggere e ɗerewol mum 430ɓol ngol, woɗnde ina loowi manooje kuccuɗe e maa haa heddii hello 25aɓo ngoo, ngoon ina waɗi ñiŋooje maa. Woɗnde ina loowi daartol Fuuta, ndeya haaɗi ko e Satigeeɓe, won heen wootere jooɗtirii ko Abdul Bookara fiyi Dodson, heɓti diiwanuuji Fuuta fof, haɗi tuubakiri laamaade. Won woɗnde ina sifoo Fuuta fof, kono wiyi ko bempeƴƴe njuumri ndegata e nehaande maayo Senegaal, won woɗnde waɗaani ɗoon maayo, fawi ɗoon ko jeereende, won keewɗe goɗɗe njanngotaako, heen wootere waɗi tan ko alkulal ŋ ngal … En ngasnataa sifodaade ɗe, ngati fannuuji ɗeen defte ko ɗi keewal kulɓiniingal.

Limoral faruwal

Jooni, ngarten e limoreeje caggal nde cifi-ɗen wakannde men moolanaande ndee. Ƴetten limoral ngalɗoo : 0,123456789101112131415… hono ndiga piccuɗo doggol limoreeje kiɓɓe ɗee kala. E nder piccal hee wadde ina tawee kala limoral kiɓɓal ngal mbaaw-ɗen miijaade nde tawnoo ko doggol majje ɗakkondiraa heen. Ko hono ngal limoral wiyatee limoral faruwal. Limoral faruwal ko loowngal e tonngol mum kala limoral kiɓɓal cuɓangal.

Tesko-ɗen jooni wonde kala hito, kala ayaawo, kala alkulal ina tonngiree limoreeje, ko ɗum woni ko wiyatee limɗinngol, ɗum tammbii kala gollal ordinateer gollotoo. Wadde kala hito wullaango ina hawra e limoral kiɓɓal keeringal, kala mbaydi nataandi ina hawra e limoral kiɓɓal mum, kala binndol ne ko noon. Ndeen noon so limoral gootal loowii limoreeje kiɓɓe fof, wadde ngal loowat kala mbaadiiji, kala ayawuuji, ngal moofta kala hitooji e kala binndi. Wadde ngal loowa kala ko meeɗnooɗo walla ko meeɗoyoowo wuurde wuurnoo walla ko o wuuroyta, gila e ayawuuji mum, haa e hitooji mum, haa e  binndi kaalooji ko wonaa ɗum. Kono haaɗaani ɗoon tan; maa ngal loow kala ko woodi no woodirnoo, kala ko woodoyta no woodiroyta. Kono ngal haaɗaani ɗoon tan, e ngal loowa ɗeen geɗe fof e baylanɗe mumen, ngal loowa wadde kadi ko woodaani, ko meeɗataa woodde. E yeru, engal loowi nguurndam maa fof, kono kadi engal loowi nguurndam maa fof tawa engal wayli heen yettoode maa, walla ñalnde njibine-ɗaa, walla ɗiɗi ɗii fof, e ko wonaa ɗum. Ngal limoral wadde ina loowi wakannde men dow too ndee.

Tawee ɗee limoreeje ina mbiiƴa nder kuuɓal limoreeje laaɓɗe. Tawee ko kañje ɓuri heewde e limoreeje kiɓɓe. Eɗen mbaawi dallinirde ɗum no weeɓiri : ndewen ɗee toɓɓe ɗiɗi :

  1. Ko adii fof kollen wonnde limoreeje ɗe tonngol loowngol A e B (doggi A-B)  ɗe njuuteendi haaɗtari ɓuri heewde e limoreeje kiɓɓe. Daliilu mum ko hujja palal Kantoor. Mbinnden ngalɗoo cawndondiral hakkunde limoreeje kiɓɓe e ɗiin doggi :

0 :  AABABBBAB…

1 :  BBAABAAAA…

2 :  AABAABBBA….

3 :  BAABAABAA….

…..

So tawiino doggi loowɗi A-B ɗii poti e limoreeje kiɓɓe hono {0, 1, 2, …} keeweendi, kala doggol A-B cuɓangol maa tawe ina hawri e limoral kiɓɓal gootal. Hono no  AABABBBAB.. (doggol gadanol ngol) hawriri e 0 nii. Jooni noon eɗen mbaawi fentude doggol A-B tawa kuutori-ɗen ko palal ɓoɗowal dow ɗoo ngal : En ƴettat palal ngal lomtondiren A e B, keɓen BAAA… . Ngolɗoo doggol nanndaani e hay gootol e limtaaɗi ɗii, engol seerti e gadanol ngol tergal 1oɓal ngal, ngol seerti e ɗiɗaɓol ngol tergal ɗiɗmal ngal, e hono noon e hono noon. Wadde woni ɗoon ko doggol ceertungol e limtaaɗi ɗii fof, wadde ngol tawetaake e majji. Oon sahaa noon, keɓen wonde limoreeje tonngiraaɗi doggi loowɗi A e B ɓuri limoreeje kiɓɓe heewde !

2. So ɗum yawtii, ƴetten limoral faruwal ngal kolluno-ɗen dow ngal, hono 0,123456789101112131415161718192021… Ƴetten doggol A-B. So ngol fuɗɗorii ko A, lomtondiren nder limoral faruwal ngal 1 e 2 (woni lime ɗiɗi gadane caggal piccal ngal), so tawii ko B ɗacciren noon. So alkulal ɗimmal doggol ngol ko A, lomtondiren 3 e 4 nder limoral faruwal ngal (hono limal tatiwal e nayaɓal nder faruwal ngal), so ɗum alaa ɗacciren noon… njokken ngaal gollal. Nde tawnoo doggi kuutorto-ɗen ngam waylude faruwal ngal ko keewɗi haa ɓuri keewal kiɓɓe, etee kala mbaylaandi maa addu limoral kesal, wadde keewal kese ɗee maa fot e keewal doggi A-B ɗii, oon sahaa ɗe ɓura kiɓɓe heewde. Jooni noon tesko-ɗen kala heen mbaylaandi addata ko faruwal ! Wadde limoreeje faruwe ɓuri heewde e limoreeje kiɓɓe. En ngasnii daliilu oo.

En njiyii ngalu mawngu suuɗiingu e ganndal limoreeje. Limoral faruwal ina moopti faayidaaji keewɗi pattamlami. Limoral bayngal no pi, lollungal, ceekngal keeri nderiwi hiisiwal ina tuumaa ko faruwal, kono hay gooto waawaani tawo dallinde ɗum. Maa en ngartu e kaawniiɗe jotondirɗe e nde kollir-ɗen ɗoo ndee e binndanɗe garooje.

Kelmeendi

Limoral faruwal                 nombre univers

Limoral kiɓɓal    nombre entier

Fayannde            puissance

Faru       univers

Ɗaŋre    planete

Rewriwal             logique Muhammadu Faalil Sih

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