Mathematical notation

Mathematical notation
notation (en)
Bayanai
Ƙaramin ɓangare na	notation (en) da mathematical convention (en)
Bangare na	writing system (en) da Lissafi
Amfani	Lissafi
Facet of (en)	mathematical expression (en)
Name (en)	mathematical notation da notation mathématique

Duba Kuma

Lissafin lissafi shine tsarin wakilcin alamomin abubuwan lissafi da ra'ayoyi. Ana amfani da alamar ilimin lissafi a cikin lissafi, kimiyyar jiki, injiniya, da tattalin arziki . Bayanan ilimin lissafi sun haɗa da wakilci mai sauƙi mai sauƙi, kamar lambobi 0, 1 da 2.masu canji kamar x, y da z .masu ƙuntatawa kamar "("da ;"|")alamomin aiki sin ; alamomin aiki kamar " + "; alamomin alaƙa kamar "<"; alamomin ra'ayi kamar lim da <i id="mwFw">dy/dx</i> ; lissafi da hadaddun alamomin zane kamar Bayanin hoto na Penrose da zane -zanen Coxeter -Dynkin .

Ma'ana

Lissafin lissafi shine tsarin rubutu da ake amfani da shi don yin rikodin tunani a cikin lissafi.

• Sanarwar tana amfani da alamomi ko maganganun alama waɗanda aka yi niyya don samun madaidaicin ma’anar kalma.
• A cikin tarihin lissafi, waɗannan alamomin sun nuna lambobi, sifofi, alamu da canji. Sanarwar na iya haɗawa da alamomi don ɓangarorin maganganun al'ada tsakanin masu ilimin lissafi, lokacin kallon lissafi azaman yare.

An ba da labarin kafofin watsa labarai da aka yi amfani da su don yin rubutu a ƙasa, amma kayan yau da kullun sun haɗa da takarda da fensir, allo da alli (ko alamar bushewa), da kafofin watsa labarai na lantarki. Riko da tsare -tsare ga dabarun ilmin lissafi shine ainihin mahimmancin ilimin lissafi. Don ra'ayoyi masu alaƙa, duba muhawara mai ma'ana, dabaru na lissafi, da ka'idar ƙira.

Magana

Maganar lissafi shine jerin alamomin da za a iya kimantawa. Misali, idan alamomin suna wakiltar lambobi, to ana kimanta maganganun gwargwadon tsarin aiki na yau da kullun wanda ke ba da lissafi, idan ya yiwu, na kowane maganganu a cikin rakodin, kowane mai ba da labari da tushen sa ya biyo baya, sannan ninkawa da rarrabuwa, a ƙarshe kowane kari ko ragi, duk an yi daga hagu zuwa dama.

A cikin harshen kwamfuta, waɗannan ƙa'idodin ana aiwatar da su ta hanyar masu tarawa . Don ƙarin bayani kan kimanta magana, duba batutuwan kimiyyar kwamfuta : ƙima mai ɗimuwa, ƙima mara ƙima, ƙimar gajeriyar hanya, da mai aikin tantancewa.

Ma'anar ma'anar kalma daidai

Ilimin lissafi na zamani yana buƙatar zama daidai, saboda ƙididdiga masu rikitarwa ba su ba da izinin hujjoji na yau da kullun ba. Yi tsammani cewa muna da kalamai, denoted da wasu m jerin daga alamomin, game da wasu abubuwa (misali, lambobi, siffofi, alamu). Har sai an nuna cewa maganganun suna da inganci, har yanzu ba a warware ma'anar su ba. Yayin aiwatar da tunani, za mu iya bari alamomin su koma ga waɗancan abubuwan da aka nuna, wataƙila a cikin samfuri. Mahimmancin abubuwan abu yana da gefen heuristic da gefen cirewa. A kowane hali, muna iya son sanin kaddarorin wannan abin, wanda zamu iya jera su cikin mahimmin ma'ana.

Waɗannan kadarorin za a iya bayyana su ta wasu sanannun alamomin da aka yarda da su daga tebur na alamomin lissafi. Wannan bayanin lissafin na iya haɗa da annotations kamar

• "All x", "A'a x", "Akwai wani x" (ko da kamarsa, "Wasu x"), "A sa ", "A yi aiki "
• "Taswira daga ainihin lambobi zuwa lambobi masu rikitarwa "

A cikin mahallin daban -daban, ana iya amfani da alama ɗaya ko alama don wakiltar ra'ayoyi daban -daban (kamar yadda za a iya amfani da alamomi da yawa don wakiltar ra'ayi ɗaya). Sabili da haka, don cikakken fahimtar wani yanki na lissafin lissafi, yana da mahimmanci a fara duba ma'anar bayanan da marubucin ya bayar. Wannan na iya zama matsala, alal misali, idan marubucin ya ɗauka mai karatu ya riga ya saba da bayanin da ake amfani da shi.

Tarihi

 Asalin

Ƙidaya

Anyi imanin cewa lissafin lissafi don wakiltar ƙidaya an fara haɓaka shi aƙalla shekaru ta 50,000 da suka gabata - ra'ayoyin lissafi na farko kamar ƙidaya yatsa suma an wakilta su ta tarin duwatsu, sanduna, kashi, yumɓu, dutse, dutse, itace sassaƙa, da igiyoyi masu ƙulli. Tally stick shine hanyar ƙidaya tun daga Upper Paleolithic . Wataƙila tsoffin sanannun matanin ilimin lissafi sune na tsohuwar Sumerr. A Census Quipu na Andes da Ishango Kashi daga Afirka biyu amfani da Tally lamba Hanyar lissafin kudi don na lamba Concepts.

Haɓaka sifili a matsayin lamba yana ɗaya daga cikin mahimman ci gaba a farkon ilimin lissafi. Babiloniyawa da Masarawa na Girka sun yi amfani da shi a matsayin mai riƙe da wurin, sannan a matsayin mai lamba ta Mayan, Indiyawa da Larabawa (duba tarihin sifiri don ƙarin bayani).

Geometry ya zama mai nazari

Hanyoyin ilmin lissafi na farko a lissafin lissafi ba su ba da kansu da kyau don ƙidaya ba. Lambobi na halitta, alaƙar su da ɓangarori, da kuma gano adadin ci gaba a zahiri ya ɗauki millennia don ɗaukar tsari, har ma ya fi tsayi don ba da damar haɓaka sanarwa.

A zahiri, ba har sai ƙirƙirar ƙirar lissafi ta René Descartes ne geometry ya zama ƙarƙashin batun adadi. An yi amfani da wasu gajerun hanyoyin alamomi don dabarun ilmin lissafi a cikin buga hujjojin geometric. Haka kuma, iko da ikon ka'idar geometry da tsarin hujja sun yi tasiri sosai ga rubuce-rubucen da ba na lissafi ba, kamar su Principia Mathematica ta Isaac Newton misali.

Sanarwar zamani

Karni na 18 da 19 sun ga ƙirƙirar da daidaita daidaiton ilimin lissafi kamar yadda ake amfani da shi a yau. Leonhard Euler shine ke da alhakin yawancin sanarwar da ake amfani da su a halin yanzu: amfani da a, b, c don madaidaiciya da x, y, z don abubuwan da ba a sani ba, e don tushen logarithm na halitta, sigma (Σ) don taƙaitawa, i don sashin hasashe, da bayanin aikin f ( x ). Ya kuma ba da sanarwar amfani da π don Archimedes na dindindin (saboda shawarar William Jones don amfani da π ta wannan hanyar dangane da farkon bayanin William Oughtred ).

Bugu da kari, da yawa filayen lissafi kai da bugu na halittawa domin tsarin rubutu: da bambanci sadarwarka na Leibniz, da manyan infinities na Georg Cantor (a Bugu da kari ga lemniscate (∞) na John Wallis ) da congruence alama ce (≡ ) Gauss, da sauransu.

Bayanan kwamfuta

Harsunan alamar lissafin lissafi kamar TeX, LaTeX kuma, kwanan nan, MathML, suna da ƙarfin isa don bayyana fa'idodin lissafi da yawa.

Software na tabbatar da ka’idar yana zuwa da bayanin kansa na lissafi. aikin OMDoc yana neman samar da buɗaɗɗen wuri don irin waɗannan sanarwa. kuma yaren MMT yana ba da tushe don ma'amala tsakanin sauran alamun.

Bayanan lissafin lissafi ba na Latin ba

Ƙididdigar lissafin larabci na zamani ya dogara ne akan haruffan Larabci kuma ana amfani da shi sosai a cikin ƙasashen Larabawa, musamman a makarantun gaba da sakandare.

(Sanarwar Yammacin Turai tana amfani da adadi na Larabci, amma alamar Larabci kuma tana maye gurbin haruffan Latin da alamomin alaƙa da rubutun Larabci.)

Baya ga rubutun Larabci, lissafi kuma yana amfani da haruffan Girkanci don nuna abubuwa iri -iri na lissafi da masu canji. A wasu lokuta, ana amfani da wasu haruffan Ibrananci (kamar a cikin mahallin kadina marasa iyaka ).

Wasu ƙididdigar lissafin lissafi galibi zane -zane ne, don haka kusan rubuce -rubuce ne masu zaman kansu. Misalai sune ƙirar hoto na Penrose da zane -zanen Coxeter -Dynkin .

Bayanan lissafin Braille da makafi ke amfani da su sun haɗa da Nemeth Braille da GS8 Braille .

Encoding

Lambobi don alamar lissafi a cikin ma'aunin sunayen rubutun ISO 15924 sune Zmth da 995 .

Duba kuma

• Cin zarafin sanarwa
• Begriffsschrift
• Ƙamus na alamomin lissafi
  • Bourbaki alamar lanƙwasa mai haɗari
• Tarihin lissafin lissafi
• ISO 31-11
• ISO 80000-2
• Sanarwar kibiya ta Knuth
• Alamomin Alphanumeric Alamu
• Bayanin a yiwuwa da kididdiga
• Harshen lissafi
• Bayanan kimiyya
• Semasiography
• Teburin alamomin lissafi
• Taron haruffa a cikin dabarun lissafi
• Bayanin Vector
• Ƙididdigar lissafin larabci na zamani

Nassoshi

• Florian Cajori, Tarihin Lissafin Lissafi (1929), kundin 2. ISBN 0-486-67766-4
•   0-471-39340-1. David Bellos, EF Harding, Sophie Wood da Ian Monk ne suka Fassara daga Faransanci. Ifrah ta goyi bayan tafsirinsa ta hanyar faɗar kalmomin jumla daga harsuna a duk faɗin duniya.
• Mazur, Joseph (2014), Alamomin Haskakawa: Taƙaitaccen Tarihin Lissafin Lissafi da Ƙarfinsa na Boye Princeton, New Jersey: Jami'ar Princeton Press. ISBN 978-0-691-15463-3

Hanyoyin waje

• Farkon Amfani da Alamu iri -iri na Lissafi
• Lissafin ilimin lissafi ASCII yadda ake rubuta alamar lissafi a cikin kowane editan rubutu.
• Lissafi a matsayin Harshe a yanke-da-kulli
• Stephen Wolfram : Lissafin Lissafi: Tsohuwa da Gaba . Oktoba 2000. Rubutun babban adireshin da aka gabatar a MathML da Math akan Yanar gizo: MathML International Conference.