Me ya sa ba za mu raba da sifili ba?
Abubuwa
Masu karatu na iya mamakin me yasa na sadaukar da labarin gaba daya ga irin wannan matsalar banal? Dalili kuwa shi ne yawan adadin ɗalibai (!) da suke gudanar da aikin da sunan. Kuma ba ɗalibai kaɗai ba. Wani lokaci na kama da malamai. Menene daliban irin wadannan malamai za su iya yi a fannin lissafi? Abin da ya sa na rubuta wannan rubutu a nan take shi ne tattaunawa da wani malami wanda rabonsa da sifili ba shi da matsala...
Tare da sifili, a, sai dai ga wahalar komai kwata-kwata, saboda ba ma buƙatar gaske mu yi amfani da shi a rayuwar yau da kullun. Ba ma zuwa siyayya don kwai sifili. "Akwai mutum ɗaya a cikin ɗakin" sauti ko ta yaya na halitta, kuma "mutane sifili" sauti na wucin gadi. Masana harshe sun ce sifili yana wajen tsarin harshe.
Za mu iya yin ba tare da sifili ba a cikin asusun banki kuma: kawai amfani - kamar a kan ma'aunin zafi da sanyio - ja da shuɗi don kyawawan dabi'u da mara kyau (lura cewa ga zafin jiki yana da dabi'a don amfani da ja don lambobin tabbatacce, kuma ga asusun banki shi shine sauran hanyar, saboda zare kudi ya kamata ya jawo gargadi, don haka ana bada shawarar ja sosai).
Ta haɗa sifili azaman lambar halitta, muna taɓa matsalar bambancewa Lambobin kadinal od gida. A cikin 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ....
ikon lambar daidai yake da adadin wurin da yake tsaye. In ba haka ba, ya riga ya kasance a cikin jerin 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ....
Adadin saitin singleton ya zo na biyu, adadin saitin da abubuwa biyu ya zo na uku, da sauransu. Dole ne mu bayyana dalilin da ya sa, alal misali, ba mu ƙidaya wuraren ƴan wasa a cikin gasa daga karce. Sannan wanda ya zo na daya zai sami lambar azurfa (zinariya ya tafi ga wanda ya ci sifili), da sauransu. An yi amfani da irin wannan hanya a wasan kwallon kafa—Ban sani ba ko masu karatu sun san cewa "league one" yana nufin. "bin mafi kyau." ", kuma ana kiran gasar sifili don zama "babban gasar".
Wani lokaci muna jin jayayya cewa muna buƙatar farawa daga karce, saboda ya dace da mutanen IT. Ci gaba da waɗannan la'akari, ya kamata a canza ma'anar kilomita - ya kamata ya zama 1024 m, saboda wannan shine adadin bytes a cikin kilobyte (Zan koma ga barkwanci da aka sani ga masana kimiyyar kwamfuta: "Mene ne bambanci tsakanin sabobin da kuma sabon abu). dalibin kimiyyar na'ura mai kwakwalwa kuma dalibin shekara na biyar na wannan jami'a? cewa kilobyte kilobytes 1000, na karshe - cewa kilomita yana da mita 1024)!
Wani ra'ayi, wanda ya kamata a ɗauka da gaske, shine: koyaushe muna aunawa daga karce! Ya isa a kalli kowane ma'auni a kan mai mulki, a kan ma'auni na gida, ko da a kan agogo. Tunda muna aunawa daga sifili, kuma ana iya fahimtar kirgawa azaman ma'auni tare da raka'a maras girma, to yakamata mu ƙidaya daga sifili.
Abu ne mai sauki, amma...
Bari mu bar dalili na gama-gari kuma mu koma rarraba ta sifili. Al'amarin yana da sauƙi kuma zai zama mai sauƙi idan ba don ... to menene? Mu yi tunani mu gwada. Nawa zai iya zama - wanda aka raba da sifili? Bari mu ga: 1/0 = x. Haɓaka ɓangarorin biyu da ma'aunin gefen hagu.
Muna samun 1 = 0. Wani abu ba daidai ba ne! Me ya faru? Ah zato! Zaton cewa akwai jigon haɗin kai da sifili yana haifar da sabani. Idan kuma ba za a iya raba mutum da sifili ba, to wata lamba na iya. Idan mai karatu ka kade kafadu kana mamakin dalilin da yasa marubucin (wato ni) ya rubuta game da irin wadannan lafuzzan, to... Na yi matukar farin ciki!
Ƙididdigar 0/0 = 0 za a iya kare shi bisa ga taurin kai, amma ya saba wa ka'idar cewa sakamakon rarraba lamba da kanta daidai yake da ɗaya. Lallai, amma mabanbanta sune alamomin kamar 0/0, °/° da makamantansu a cikin lissafi. Ba suna nufin kowace lamba ba, amma alamu ne na alama don takamaiman jeri na wasu nau'ikan.
A cikin littafin injiniyan lantarki, na sami kwatance mai ban sha'awa: rarraba ta sifili yana da haɗari kamar wutar lantarki mai ƙarfi. Wannan al'ada ce: Dokar Ohm ta bayyana cewa rabon ƙarfin lantarki zuwa juriya daidai yake da na yanzu: V = U / R. Idan juriya ta kasance sifili, a ka'ida marar iyaka na halin yanzu zai gudana ta cikin madugu, yana ƙone duk mai yiwuwa conductors.
Na taba rubuta waka game da illar raba kan sifili a kowace rana ta mako. Na tuna cewa ranar da ta fi ban mamaki ita ce ranar Alhamis, amma abin tausayi ne ga duk aikina a wannan yanki.
Lokacin da ka raba wani abu da sifili
Da sanyin safiyar Litinin
Makon abin da ya faru kawai
Kun riga kun gaza sosai.
Lokacin da la'asar Talata
Kun sanya sifili a cikin adadin
Zan gaya muku to, kun yi kuskure
Mugun mathematician!
Lokacin da ta hanyar sifili, ta hanyar karkatarwa,
Wanna raba ranar Laraba
Za ku shiga cikin matsala mai yawa
Kun sami ciyawa da ruwa a kan ku!
Wani Bartek yana tare da mu.
Ya yi hannun riga da ka'idoji.
A ranar Alhamis, ana iya raba shi da sifili.
Ba ya tsakaninmu kuma!
Idan wani bakon sha'awa ya kama ku
Raba da sifili ranar Juma'a
Zan yi gaskiya, zan yi gaskiya:
Mummunan farawa zuwa karshen mako.
Lokacin zero, wani wuri ranar Asabar
Mai rarraba zai zama naku (ba mai ƙarfi ba)
Ku durkusa a ƙarƙashin shingen coci.
Wannan ita ce tashinku.
Kuna son sifili a ƙarƙashin dash,
Yi hutu ranar Lahadi
Kawo alli, baƙar allo.
Rubuta: ba a raba shi da sifili!
Sifili yana hade da fanko da komai. Lalle ne, ya zo ilimin lissafi a matsayin adadi wanda, idan aka ƙara zuwa kowane, ba ya canza shi: x + 0 = x. Amma yanzu sifili yana bayyana a cikin wasu dabi'u da yawa, musamman kamar farawa sikelin. Idan a waje da taga babu ingantaccen zafin jiki ko sanyi, to ... wannan sifili ne, wanda baya nufin cewa babu zafin jiki kwata-kwata. Wani abin tunawa da sifili ba wanda aka daɗe ana rushewa ba kuma babu shi. Akasin haka, wani abu ne kamar Wawel, Hasumiyar Eiffel da Statue of Liberty.
To, mahimmancin sifili a cikin tsarin matsayi ba za a iya ƙima da shi ba. Ka san mai karatu, sifili nawa Bill Gates yake da shi a asusun ajiyarsa na banki? Ban sani ba, amma ina son rabi. A bayyane yake, Napoleon Bonaparte ya lura cewa mutane suna kama da sifili: suna samun ma'ana ta matsayi. A cikin fim ɗin Andrzej Wajda As the Years, As the Days Go by, ƙwararren mai zane Jerzy ya fashe: "Bafiliste ba kome ba ne, nihil, ba kome, kome ba, nihil, sifili." Amma sifili na iya zama mai kyau: "sifili karkata daga al'ada" yana nufin cewa duk abin da ke tafiya da kyau, kuma ci gaba da shi!
Mu koma ilimin lissafi. Za'a iya ƙara sifili, cirewa da ninka ba tare da wani hukunci ba. Manya ya ce wa Anya: "Na sami kilogiram na sifili." "Kuma wannan yana da ban sha'awa, saboda na rasa nauyi iri ɗaya," in ji Anya. Don haka bari mu ci sifili shida na ice cream sau shida, ba zai cutar da mu ba.
Ba za mu iya raba da sifili ba, amma za mu iya raba da sifili. Za a iya ba da farantin sifili na dumplings cikin sauƙi ga waɗanda ke jiran abinci. Nawa kowanne zai samu?
Sifili ba shi da inganci ko mara kyau. Wannan kuma lambar mara kyauи mara kyau. Yana gamsar da rashin daidaituwa x≥0 da x≤0. Sabanin "wani abu tabbatacce" ba "wani abu mara kyau bane", amma "wani abu mara kyau ko daidai da sifili". Masana ilimin lissafi, sabanin ka'idojin harshe, koyaushe za su ce wani abu "daidai da sifili" ba "sifili ba." Don tabbatar da wannan al'ada, muna da: idan muka karanta dabarar x = 0 "x zero", sannan x = 1 mun karanta "x daidai yake da ɗaya", wanda za'a iya haɗiye, amma "x = 1534267" fa? Hakanan ba za ku iya sanya ƙimar lamba ga halin 0 ba0ko tada sifili zuwa mummunan iko. A daya hannun, za ka iya tushen sifilin a so...kuma sakamakon zai kasance ko da yaushe zero.
Ƙaddamar da aikin y = ax, tabbataccen tushe na a, ba zai zama sifili ba. Yana biye da cewa babu sifili logarithm. Lalle ne, logarithm na a zuwa tushe b shine ma'anar da dole ne a ɗaga tushe don samun logarithm na a. Don a = 0, babu irin wannan alamar, kuma sifili ba zai iya zama tushen logarithm ba. Duk da haka, sifili a cikin "masu ƙima" na alamar Newton wani abu ne daban. Muna ɗauka cewa waɗannan ƙa'idodin ba sa haifar da sabani.
shaidar karya
Rarraba da sifili batu ne na gama-gari don hujjojin ƙarya, kuma yana faruwa har ga ƙwararrun ƙwararrun mathematics. Bari in ba ku misalai biyu na fi so. Na farko algebraic ne. Zan "tabbatar" cewa duk lambobi daidai suke. A ce akwai lambobi biyu da ba daidai ba. Don haka, ɗayansu ya fi ɗaya girma, bari a > b. Bari mu ɗauka cewa c shine bambancin su
c \uXNUMXd a - b. Don haka muna da a - b = c, daga ina a = b + c.
Muna ninka sassan biyu na karshen ta a - b:
a2 ab = ab + ac – b2 – bc.
Ina fassara ak zuwa gefen hagu, ba shakka na tuna game da canza alamar:
a2 ab - ac = ab - b2 - bc.
Na ware abubuwan gama gari:
A (a-b-c) \uXNUMXd b (a-b-c),
Ina raba kuma ina da abin da nake so:
a = b.
Kuma a zahiri har ma baƙo, saboda na ɗauka cewa a> b, kuma na sami cewa a = b. Idan a cikin misalin da ke sama "maguɗi" yana da sauƙin ganewa, to, a cikin hujjar geometric da ke ƙasa ba ta da sauƙi. Zan tabbatar da cewa ... trapezoid ba ya wanzu. Adadin da ake kira trapezoid ba ya wanzu.
Amma ɗauka da farko cewa akwai irin wannan abu kamar trapezoid (ABCD a cikin adadi a ƙasa). Yana da bangarori guda biyu masu kamanceceniya da juna ("tushe"). Bari mu shimfiɗa waɗannan ginshiƙai, kamar yadda aka nuna a hoton, domin mu sami kwatance. Diagonal dinsa yana raba sauran diagonal na trapezoid zuwa ɓangarorin da tsayin su ke nuna x, y, z, kamar a cikin hoto 1. Daga kamanni na triangles masu dacewa, muna samun ma'auni:
inda muka ayyana:
Oraz
inda muka ayyana:
Rage ɓangarori na daidaiton da aka yiwa alama da alamar alama:
Gajarta bangarorin biyu ta x -z, muna samun - a/b = 1, wanda ke nufin cewa a + b = 0. Amma lambobi a, b sune tsayin tushe na trapezoid. Idan jimlar su sifili ne, to su ma sifili ne. Wannan yana nufin cewa adadi kamar trapezoid ba zai iya wanzuwa ba! Kuma tun da rectangles, rhombuses da murabba'ai suma trapezoids ne, to, mai karatu, babu rhombuses, rectangles da murabba'i ko dai ...
Kamar haka
Raba bayanai shine mafi ban sha'awa da ƙalubale na ayyuka huɗu na asali. A nan, a karon farko, mun haɗu da wani al'amari da ya zama ruwan dare a cikin girma: "kimanta amsar, sa'an nan kuma duba idan kun yi daidai." Daniel K. Dennett ya bayyana wannan da kyau sosai ("Yadda ake yin Kuskure?", a cikin Yaya Yayi - Jagoran Kimiyya ga Universe, CiS, Warsaw, 1997):
Wannan hanyar “zato” ba ta tsoma baki a rayuwarmu ta manya-watakila domin mun koyi shi da wuri kuma hasashe ba shi da wahala. A akida, al'amari iri ɗaya yana faruwa, misali, a cikin shigar da lissafi (cikakke). A wuri guda, muna “ƙima” dabarar sannan mu bincika ko hasashenmu daidai ne. Dalibai koyaushe suna tambaya: “Ta yaya muka san tsarin? Ta yaya za a fitar da ita?" Lokacin da dalibai suka yi mani wannan tambayar, nakan juya tambayarsu ta zama abin dariya: "Na san wannan saboda ni ƙwararre ce, saboda ana biya ni sani." Dalibai a makaranta za a iya amsa su a cikin salo iri ɗaya, kawai mafi mahimmanci.
Motsa jiki. Lura cewa mun fara ƙarawa da rubuta rubũta tare da mafi ƙanƙanta raka'a, da kuma rarraba tare da mafi girma.
Haɗin ra'ayoyi biyu
Malaman lissafi koyaushe suna nuna cewa abin da muke kira rabuwar manya shine haɗin kai na ra'ayoyi guda biyu daban-daban: Gidaje i rabuwa.
Na farko (Gidaje) yana faruwa a cikin ayyuka inda archetype shine:
Raba-raba Waɗannan ayyuka ne kamar:
? (Muna riƙe da ainihin salon wannan matsala, wanda aka ɗauko daga littafin littafin Julian Zgozalewicz da aka buga a Krakow a cikin 1892 - zloty shine Rhenish zloty, kuɗin da ke gudana a cikin Daular Austro-Hungary har zuwa farkon karni na XNUMX).
Yanzu la'akari da matsaloli biyu tare da mafi tsufan littafin lissafi a cikin Yaren mutanen Poland, baba Tomasz Clos (1538). Rabe-rabe ne ko juyin mulki? Warware shi kamar yadda yaran makaranta a ƙarni na XNUMX ya kamata:
( Fassara daga Yaren mutanen Poland zuwa Yaren mutanen Poland: Akwai kwata da tukwane hudu a cikin ganga. Tukwane kwata hudu ne. Wani ya sayi ganga 20 na ruwan inabi a kan 50 zł don ciniki. Takaddun haraji da haraji (excise?) zai zama 8 zł. Nawa ne zuwa sayar da kwata don samun 8 zł?)
Wasanni, physics, concomruence
Wani lokaci a wasanni dole ne ku raba wani abu ta sifili (raɗin manufa). To, ko ta yaya alkalai suna magance shi. Koyaya, a cikin abstraction algebra suna kan ajanda. wadanda ba sifili yawawanda murabba'in shi ne sifili. Ana iya ma bayyana shi a sauƙaƙe.
Yi la'akari da aikin F wanda ke haɗa aya (y, 0) tare da batu a cikin jirgin (x, y). Menene F2, wato kisa biyu na F? Ayyukan sifili - kowane batu yana da hoto (0,0).
A ƙarshe, waɗanda ba sifili yawa waɗanda murabba'in 0 ne kusan gurasa yau da kullun ga masana kimiyyar lissafi, da lambobi na nau'in a + bε, inda ε ≠ 0, amma ε2 = 0, masu lissafi suna kira lambobi biyu. Suna faruwa ne a cikin nazarin lissafi da kuma a cikin nau'ikan lissafi daban-daban.
Bayan haka, akwai wani abu a cikin lissafi wanda ke da rabo ta sifili a cikin akalla sunan. Ya fito daga haɗuwa. Bari Z ya nuna saitin lamba. Rarraba saitin Z da p yana nufin mu daidaita kowace lamba (integer) da wasu, wato, zuwa waɗanda ta inda ake raba bambancinsu. Don haka, idan muna da nau'ikan lambobi biyar daidai da lambobi 0, 1, 2, 3, 4 - abubuwan da za a yi saura idan aka raba su da 5. An rubuta dabarar kamar haka:
mod lokacin da bambancin ya kasance mai yawa.
Domin = 2, muna da lambobi biyu ne kawai: 0 da 1. Rarraba ƙididdiga zuwa nau'ikan nau'i biyu daidai yake da raba su cikin ma'ana da ban mamaki. Bari mu maye gurbinsa yanzu. Bambancin koyaushe yana rarraba ta 1 (kowane lamba ana iya raba shi da 1). Shin yana yiwuwa a ɗauka =0? Bari mu gwada: yaushe ne bambancin lambobi biyu ke zama mahara na sifili? Sai lokacin da waɗannan lambobi biyu suka yi daidai. Don haka rarraba saitin lamba ta sifili yana da ma'ana, amma ba abin sha'awa ba ne: babu abin da ke faruwa. Duk da haka, ya kamata a jaddada cewa wannan ba rabon lambobi ba ne a ma'anar da aka sani daga makarantar firamare.
Irin waɗannan ayyuka an haramta su kawai, da kuma dogon lissafi.
Shinkafa 2. Gano lambobi ta amfani da kwatanta
(itace 5 da itace 2)
