Lamba

Rukunin lambobi masu rikitarwa

Lamba
Wikimedia disambiguation page (en)

Lamba abu ne na lissafi da ake amfani da shi don ƙidaya, auna, da kuma lakabi. Misalai na asali sune lambobi na halitta 1, 2, 3, 4, da sauransu. Ana iya wakilta lambobi cikin harshe tare da kalmomin lamba . Ƙari a duniya, ana iya wakilta lambobi ɗaya ta hanyar alamomi, da ake kira lambobi ; misali, "5" lamba ce da ke wakiltar lamba biyar. Kamar yadda kawai ƙananan adadin alamomin za a iya haddace su, ƙananan lambobi yawanci ana tsara su a cikin tsarin lambobi, wanda hanya ce mai tsari don wakiltar kowace lamba. Mafi yawan tsarin lambobi shine tsarin lambobi na Hindu-Larabci, wanda ke ba da izinin wakilcin kowane lamba ta amfani da haɗuwa da alamomin ƙididdiga guda goma, da ake kira lambobi. Baya ga amfani da su wajen kirgawa da aunawa, ana amfani da lambobi sau da yawa don lakabi (kamar yadda suke da lambobin tarho ), don yin oda (kamar yadda tare da lambobin serial ), da kuma lambobin (kamar yadda suke da ISBNs). A cikin amfanin gama-gari, lamba ba ta bambanta a fili da lambar da take wakilta ba.

A cikin ilimin lissafi, an tsawaita ra'ayin lamba a cikin ƙarni don haɗawa da sifili (0), lambobi mara kyau, lambobi masu ma'ana kamar rabi ɗaya. $\left({\tfrac {1}{2}}\right)$, lambobi na ainihi kamar tushen murabba'in 2 $\left({\sqrt {2}}\right)$ da π, da lambobi masu rikitarwa waɗanda ke tsawaita ainihin lambobi tare da tushen murabba'i na−1 (da haɗe-haɗe tare da lambobi na ainihi ta ƙara ko rage yawan adadinsa). Ana yin ƙididdigewa tare da lambobi tare da ayyukan lissafi, wanda aka fi sani da ƙari shine ƙari, raguwa, ninkawa, rarrabawa, da ƙari. Nazarin su ko amfani da su ana kiran su lissafi, kalma wanda kuma yana iya komawa zuwa ka'idar lamba, nazarin kaddarorin lambobi.

Bayan amfaninsu na amfani, lambobi suna da mahimmancin al'adu a duk faɗin duniya. Misali, a cikin al'ummar Yamma, ana ɗaukar lamba 13 a matsayin rashin sa'a, kuma "miliyan" na iya nuna "mai yawa" maimakon ainihin adadi. Ko da yake yanzu ana ɗaukarsa azaman pseudoscience, imani da mahimmancin sufi na lambobi, wanda aka sani da numerology, ya mamaye tunanin da da na da. Ƙididdigar ƙididdiga ta yi tasiri sosai ga ci gaban ilimin lissafi na Girkanci, yana ƙarfafa binciken matsalolin da yawa a ka'idar lamba waɗanda har yanzu suna da sha'awa a yau.

lamba

A cikin karni na 19, masu ilmin lissafi sun fara haɓaka ƙididdiga daban-daban waɗanda ke raba wasu kaddarorin lambobi, kuma ana iya ganin su suna faɗaɗa ra'ayi. Daga cikin na farko akwai lambobin hypercomplex, wanda ya ƙunshi nau'i-nau'i daban-daban ko gyare-gyare na tsarin lambobi masu rikitarwa . A cikin ilimin lissafi na zamani, ana ɗaukar tsarin lambobi masu mahimmanci misalai na musamman na ƙarin tsarin algebra gaba ɗaya kamar zobba da filayen, kuma aikace-aikacen kalmar "lambar" lamari ne na al'ada, ba tare da mahimmancin mahimmanci ba.

Tarihi

Lambobi

Ya kamata a bambanta lambobi daga lambobi, alamomin da ake amfani da su don wakiltar lambobi. Masarawa sun ƙirƙiro tsarin ƙididdiga na farko, kuma Girkawa sun bi taswirar ƙidayar su akan haruffan Ionian da Doric. Lambobin Roman, tsarin da ya yi amfani da haɗin haruffa daga haruffan Roman, ya kasance mafi rinjaye a Turai har zuwa yaduwar tsarin lambobi mafi girma na Hindu-Larabci a kusa da ƙarshen karni na 14, kuma tsarin lambobi na Hindu-Larabci ya kasance mafi yawan tsarin wakilci don wakiltar. lambobi a duniya a yau.   Makullin tasirin tsarin shine alamar sifili, wanda tsoffin masana lissafin Indiya suka haɓaka a kusa da 500 AD.

Amfani da lambobi na farko

An gano kasusuwa da sauran kayan tarihi tare da yanke alamomin da mutane da yawa suka yi imani da alama tally ne. Wataƙila an yi amfani da waɗannan alamomin don kirga lokacin da suka wuce, kamar adadin kwanaki, zagayowar wata ko adana bayanai na adadi, kamar na dabbobi.

Tsarin ƙididdigewa ba shi da ra'ayi na ƙimar wuri (kamar yadda yake a cikin ƙayyadaddun ƙayyadaddun ƙayyadaddun ƙayyadaddun ƙayyadaddun ƙididdiga na zamani), wanda ke iyakance wakilcin adadi masu yawa. Duk da haka, ana ɗaukar tsarin ƙididdigewa a matsayin nau'in tsarin ƙididdiga na farko.

Tsarin da aka sani na farko tare da ƙimar wuri shine tushen Mesopotamiya<span typeof="mw:Entity" id="mwhQ"> </span>tsarin 60 ( c. 3400 BC) da kuma sansani na farko 10 tsarin kwanakin zuwa 3100 BC a Misira.

Sifili

  Sanin farko da aka rubuta amfani da kwanakin sifili zuwa AD 628, kuma ya bayyana a cikin Brāhmasphuṭasiddhānta, babban aikin masanin lissafin Indiya Brahmagupta. Ya yi magani 0 a matsayin lamba kuma sun tattauna ayyukan da suka haɗa da shi, gami da rarraba. A wannan lokacin (7th karni) manufar ta kai ga Cambodia a matsayin lambobin Khmer, kuma bayanai sun nuna ra'ayin daga baya ya yadu zuwa kasar Sin da kasashen musulmi.

Lambar 605 a cikin lambobin Khmer, daga rubutu daga 683 AD. Fara amfani da sifili azaman adadi na goma.

Brāhmasphuṭasiddhānta na Brahmagupta shine littafi na farko da ya ambaci sifili a matsayin lamba, don haka Brahmagupta yawanci ana ɗaukarsa a matsayin farkon wanda ya tsara manufar sifili. Ya ba da ka'idojin amfani da sifili tare da lambobi marasa kyau da masu kyau, kamar "sifili da lambar tabbatacce ita ce lamba mai kyau, kuma lambar mara kyau da sifili ita ce mummunan lamba." Brāhmasphuṭasiddhānta shine rubutun farko da aka sani don ɗaukar sifili azaman lamba a kansa, maimakon a matsayin kawai lamba mai riƙewa a wakiltar wata lamba kamar yadda Babila suka yi ko kuma a matsayin alama don ƙarancin yawa kamar yadda Ptolemy ya yi kuma Romawa.

Amfani da 0 a matsayin lamba ya kamata a bambanta daga amfani da shi azaman adadin ma'auni a tsarin ƙimar wuri . An yi amfani da litattafai na dā da yawa 0. Nassosin Babila da na Masar sun yi amfani da shi. Masarawa sun yi amfani da kalmar nfr don nuna sifili ma'auni a cikin lissafin shiga biyu. Rubutun Indiya sun yi amfani da kalmar Sanskrit Shunye ko shunya don komawa ga manufar banza . A cikin rubutun lissafi wannan kalma sau da yawa tana nufin lamba sifili. A cikin irin wannan yanayin, Pāṇini (ƙarni na 5 BC) ya yi amfani da ma'aikacin null (sifili) a cikin Ashtadhyayi, misali na farko na nahawu na algebra don harshen Sanskrit (kuma duba Pingala ).

Akwai sauran amfani da sifili kafin Brahmagupta, kodayake takaddun ba su cika kamar yadda yake a cikin Brāhmasphuṭasiddhānta .

Bayanai sun nuna cewa Girkawan zamanin da ba su da tabbas game da matsayin 0 a matsayin lamba: sun tambayi kansu "ta yaya 'babu' zai zama wani abu?" haifar da ban sha'awa falsafa da kuma, ta hanyar Medieval zamani, addini muhawara game da yanayi da wanzuwar 0 da vacuum. Paradoxes na Zeno na Elea sun dogara da wani sashi akan fassarar rashin tabbas na 0. (Tsohon Helenawa ma sun yi tambaya ko 1 ya kasance lamba.)

Marigayi Olmec na kudancin tsakiyar Mexico sun fara amfani da alamar sifili, harsashi glyph, a cikin Sabuwar Duniya, mai yiwuwa a 4th century BC amma tabbas ta hanyar 40. BC, wanda ya zama wani muhimmin sashi na lambobi na Maya da kalandar Maya. Mayan lissafin da aka yi amfani da tushe 4 da gindi 5 an rubuta azaman tushe 20. George I. Sánchez a cikin 1961 ya ba da rahoton tushe 4 ,baza 5 "yatsa" abacus.  

A shekara ta 130 AD, Ptolemy, wanda Hipparchus da Babila suka rinjaye shi, yana amfani da alamar 0 (ƙaramin da'ira mai tsayi mai tsayi) a cikin tsarin lambobi na jima'i in ba haka ba ta amfani da lambobin haruffa na Helenanci. Domin an yi amfani da shi shi kaɗai, ba a matsayin mai riƙe da wuri kawai ba, wannan sifili na Hellenistic shine farkon rubuce-rubucen amfani da sifilin gaskiya a cikin Tsohuwar Duniya. A cikin rubuce-rubucen Byzantine daga baya na Syntaxis Mathematica ( Almagest ), sifilin Hellenistic ya rikiɗe zuwa harafin Helenanci Omicron (in ba haka ba ma'ana). 70).

lambabo kenan

An yi amfani da wani sifili na gaskiya a cikin tebur tare da lambobin Roman ta 525 (wanda Dionysius Exigus yayi amfani da shi na farko), amma a matsayin kalma, nulla . ma'ana ba komai, ba a matsayin alama ba. Lokacin da aka samar 0 a matsayin saura, nihil , kuma ba ma'anar komai ba, an yi amfani da shi. Wadannan sifilai na tsakiya duk masu kwamfutoci na gaba (masu ƙididdigewa na Easter ) sun yi amfani da su. An yi amfani da keɓantaccen amfani da farkon su, N, a cikin tebur na lambobi na Romawa ta Bede ko abokin aiki kusan 725, alamar sifili na gaskiya.

 

Manazarta

• Tobias Dantzig, Lamba, harshen kimiyya; Wani bincike mai mahimmanci da aka rubuta don wanda ba masanin lissafi ba, New York, Kamfanin Macmillan, 1930. 
• Erich Friedman, Menene na musamman game da wannan lambar? Archived 2018-02-23 at the Wayback Machine Archived
• Steven Galovich, Gabatarwa ga Tsarin Lissafi, Harcourt Brace Javanovich, 1989,  .
• Paul Halmos, Naive Set Theory, Springer, 1974,  .
• Morris Kline, Tunanin Lissafi daga Tsohuwar Zuwa Zamani, Jami'ar Oxford Press, 1990. ISBN 978-0195061352
• Alfred North Whitehead da Bertrand Russell, Principia Mathematica zuwa *56, Jami'ar Cambridge University Press, 1910. 
• Leo Cory, Takaitaccen Tarihin Lambobi, Jami'ar Oxford Press, 2015,  .