Labarin game da kome ba

Lokacin da nake yaro, labarin ya burge ni, mai yiwuwa masu karatu da yawa sun sani, game da "miya akan ƙusa." Kakata (ƙarni na XNUMXst na haihuwa) ta gaya mani wannan a cikin sigar "Cossack ya zo ya nemi ruwa, saboda yana da ƙusa kuma zai dafa miya a kai." Mai masaukin baki mai ban sha'awa ta ba shi tukunyar ruwa ... kuma mun san abin da ya faru na gaba: "miya ya kamata ya zama gishiri, daitye, granny, gishiri", sannan ya wanke naman "don inganta dandano" da sauransu. A ƙarshe, ya jefar da ƙusa "dafaffen".

Don haka wannan labarin ya kamata ya kasance game da fanko na sararin samaniya - kuma wannan shine game da saukowa na na'ura na Turai a kan tauraro mai wutsiya 67P / Churyumov-Gerasimenko a ranar 12 ga Nuwamba, 2014. Amma yayin da nake rubutu, na shiga cikin al'ada mai tsawo. Har yanzu ni masanin lissafi ne. Yaya yake da Kamarс Sifili lissafi?

Ta yaya Babu Komai ya wanzu?

Ba za a iya cewa babu wani abu ba. Ya wanzu aƙalla a matsayin falsafanci, lissafi, addini da kuma cikakkiyar fahimtar magana. Sifili lamba ce ta talakawa, sifili digiri a kan ma'aunin zafi da sanyio kuma yanayin zafi ne, kuma ma'aunin sifili a banki abu ne marar daɗi amma abin da ya faru na kowa. Yi la'akari da cewa babu shekara sifili a cikin tarihin tarihi, kuma wannan shi ne saboda an shigar da sifili a cikin lissafi kawai a cikin ƙarshen Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiyar Tsakiya.

Abin ban mamaki, da gaske za mu iya yin ba tare da wannan sifilin ba kuma, don haka, ba tare da lambobi mara kyau ba. A cikin ɗaya daga cikin litattafai akan dabaru, na sami motsa jiki: zana ko faɗi yadda kuke tunanin rashin kifi. Abin mamaki, ko ba haka ba? Kowa zai iya zana kifi, amma ba ɗaya ba?

Yanzu a takaice ilimin lissafi na asali. Bayar da gata na wanzuwa ga saitin da ba kowa wanda aka yiwa alama da da'irar da aka ketare ∅ hanya ce mai mahimmanci mai kama da ƙara sifili zuwa saitin lambobi. Saitin fanko shine kawai saitin da bai ƙunshi kowane abubuwa ba. Irin waɗannan tarin:

Amma babu saitin fanko daban-daban guda biyu. Saitin fanko yana cikin kowane saitin:

Tabbas, ka'idodin ilimin lissafi sun ce saitin A yana ƙunshe a cikin saitin B idan kuma kawai idan jumlar:

ya ƙunshi

A cikin yanayin saitin fanko ∅, shawarar koyaushe karya ce, don haka, bisa ga ka'idodin dabaru, abin da ake nufi gabaɗaya gaskiya ne. Komai ya samo asali ne daga karya ("a nan zan shuka cactus idan kun matsa zuwa aji na gaba ..."). Don haka, da yake saitin da ba kowa a cikin kowannensu yake, to da a ce su biyu ne daban-daban, da kowannensu yana cikin daya. Koyaya, idan saiti biyu sun ƙunshi juna, daidai suke. Shi ya sa: saiti ɗaya ne kawai!

Matsayin wanzuwar saitin fanko bai saba wa kowace dokar lissafi ba, don haka me zai hana a aiwatar da shi? Ka'idar falsafar da ake kiraOccam ta reza» Umarni don ware ra'ayoyin da ba dole ba, amma dai dai tunanin saitin fanko yana da amfani sosai a cikin lissafi. Lura cewa saitin fanko yana da girma na -1 (a debe ɗaya) - abubuwa masu girman sifili maki ne kuma tsarinsu marasa ƙarfi, abubuwa masu girma dabam layi ne, kuma mun yi magana game da abubuwan lissafi masu sarƙaƙƙiya tare da juzu'i a cikin babin kan fractals. .

Yana da ban sha'awa cewa dukan ginin ilimin lissafi: lambobi, lambobi, ayyuka, masu aiki, haɗin kai, bambance-bambance, ƙididdiga ... za a iya samo su daga ra'ayi ɗaya - saiti mara kyau! Ya isa a ɗauka cewa akwai saiti mara kyau, sabbin abubuwan da aka ƙirƙira za a iya haɗa su cikin saiti don samun damar gina duk lissafin. Wannan shine yadda masanin ilimin Jamus Gottlob Frege ya gina lambobi. Sifili aji ne na saiti waɗanda abubuwan da ke cikin haɗin gwiwa tare da abubuwan saitin mara komai. Ɗaya shine nau'i na saiti waɗanda abubuwan da ke cikin haɗin gwiwa tare da abubuwan da ke cikin saitin wanda kawai abin da kawai shi ne saitin fanko. Na biyu rukuni ne na saiti wanda abubuwan da suke zama daya-da-daya tare da abubuwan da ke cikin saitin wanda ya kunshi saitin fanko da saitin wanda kawai abin da ya rage shi ne saitin fanko... da sauransu. A kallo na farko, wannan yana da alama wani abu ne mai rikitarwa, amma a gaskiya ba haka bane.

Blue ya watsa min

mai kamshi mai zafi da kamshin mint...

Wojciech Mlynarski, Yarinyar Girbi

Yana da wuya a yi tunanin

Babu wani abu da ke da wuyar tunani. A cikin labarin Stanisław Lem na "Yadda An Ceci Duniya", mai zane Trurl ya gina na'ura wanda zai yi duk abin da ya fara da wasika. Lokacin da Klapaucius ya ba da umarnin a gina shi Nic, injin ya fara cire abubuwa daban-daban daga duniya - tare da babban burin cire komai. A lokacin da Klapaucius mai firgita ya tsayar da motar, galleys, yews, rataye, hacks, rhymes, bugu, poufs, grinders, skewers, philidrons da sanyi sun bace daga duniya har abada. Kuma lalle ne, sun ɓace har abada ...

Józef Tischner ya rubuta sosai game da komai a cikin Tarihin Falsafa na Dutse. A lokacin hutuna na ƙarshe, na yanke shawarar in fuskanci wannan ba komai ba, wato, na je ƙoƙon peat tsakanin Nowy Targ da Jabłonka a Podhale. Wannan yanki ma ana kiransa Pustachia. Kuna tafiya, ku tafi, amma hanyar ba ta raguwa - ba shakka, akan madaidaicin mu, ma'aunin Poland. Wata rana na hau bas a lardin Saskatchewan na Kanada. A waje akwai filin masara. Na huta tsawon rabin sa'a. Lokacin da na farka, muna tuki ta cikin gonar masara guda ... Amma jira, wannan babu kowa? A wata ma'ana, rashin canji shine kawai fanko.

Mu ne saba da akai gaban daban-daban abubuwa kewaye da mu, kuma daga Wani abu Ba za ku iya gudu ba ko da idanunku a rufe. "Ina tsammanin, saboda haka ni ne," in ji Descartes. Idan na riga na yi tunanin wani abu, to, ina wanzu, ma'ana cewa akwai akalla wani abu a duniya (wato, I). Shin abin da nake tunani ya wanzu? Ana iya tattauna wannan, amma a cikin injiniyoyin ƙididdiga na zamani, an san ka'idar Heisenberg: kowane kallo yana damun yanayin abin da aka gani. Sai mun gani Nic babu shi, kuma idan muka fara kallo, abin ya daina zama Kamar kuma ya zama Wani abu. Yana samun rashin hankali ka'idar ɗan adam: babu amfanin tambayar yaya duniya zata kasance idan bamu wanzu ba. Duniya ita ce kamar yadda muke gani. Watakila sauran halittu za su ga duniya a matsayin angular?

A positron (irin wannan tabbataccen electron) rami ne a sararin samaniya, "babu electron." A cikin aiwatar da halakarwa, wutar lantarki ta shiga cikin wannan rami kuma "babu wani abu da ya faru" - babu rami, babu electron. Zan tsallake ba'a da yawa game da ramuka a cikin cuku na Swiss ("yawan da nake da shi, ƙarancin can ..."). Shahararren mawakin nan John Cage ya riga ya yi amfani da ra'ayinsa har ya tsara (?) wani kida (?) wanda kungiyar makada ke zaune babu motsi na tsawon mintuna 4 da dakika 33 kuma, ba shakka, ba ta yin komai. "Minti hudu da dakika talatin da uku dari biyu da saba'in da uku ne, 273, kuma kasa da digiri 273 ba komai ba ne, wanda duk motsi ya tsaya," in ji mawaki (?).

Tace zuwa sifili, ba kome, nick, nick, kome, sifili!

Jerzy a cikin fim din Andrzej Wajda na tsawon shekaru,

kwanaki suna tafiya"

Yaya game da kowa?

Mutane da yawa (daga manoma masu sauƙi zuwa manyan masana falsafa) sun yi mamakin abin da ke faruwa. A cikin ilimin lissafi, yanayin yana da sauƙi: akwai wani abu da ya dace.

Ta bace cikin ɓangarorin gefe

A cikin cornflowers, ciyawa da bakin zaki ...

To, waɗannan abubuwan suna faruwa

Musamman a lokacin girbi, da lokacin girbi

musamman…

Wojciech Mlynarski, Yarinyar Girbi

Komai yana a sauran iyakar Babu Komai. A ilimin lissafi, mun san haka Komai babu. Ra'ayin da ba daidai ba ne kawai cewa kasancewarsa ba za a yi jayayya ba. Ana iya fahimtar wannan da misalin tsohuwar ɗabi’a: “Idan Allah ne Maɗaukaki, to, ya halicci dutse don ɗauka? Tabbacin lissafin cewa ba za a iya zama saitin duk saitin ya dogara ne akan ka'idar singer-Bershtein, wanda ya ce "lambar mara iyaka" (ilimin lissafi: lambar kadinal) saitin duk membobi na saitin da aka bayar ya fi yawan adadin abubuwan wannan saitin.

Idan saitin yana da abubuwa, to yana da 2ⁿ ƙananan sassa; misali, lokacin da = 3 kuma saitin ya ƙunshi {1, 2, 3} to waɗannan rukunonin sun wanzu:

• saiti guda biyu guda uku: kowannen su ya rasa ɗaya daga cikin lambobi 1, 2, 3,
• saitin fanko daya,
• saitin abubuwa guda uku,
• duka saitin {1,2,3}

- takwas kawai, 2³Kuma masu karatu waɗanda kwanan nan suka kammala karatu a makaranta, zan so in tuna da dabarar da ta dace:

Kowane alamomin Newtonian a cikin wannan dabara yana ƙayyade adadin saitin k-element a cikin saitin -element.

A cikin ilimin lissafi, ƙididdiga na binomial suna bayyana a wasu wurare da yawa, kamar a cikin dabaru masu ban sha'awa don rage yawan haɓakawa:

kuma daga ainihin nau'in su, haɗin kai ya fi ban sha'awa.

Yana da wuya a gane abin da - a game da dabaru da lissafi - shi ne, da abin da Komai ba. Hujjar rashin wanzuwa Daidai da na Winnie the Pooh, wanda cikin ladabi ya tambayi bakon nasa, Tiger, shin Tigers suna son zuma, acorns da sarƙaƙƙiya kwata-kwata? "Tigers suna son komai," in ji wanda Kubus ya kammala cewa idan suna son komai, to, suna son barci a ƙasa, saboda haka, shi, Vinnie, na iya komawa gado.

Wata hujja Rashin daidaituwa na Russell. Akwai wani mai wanzami a garin da yake aske duk mazan da ba su aske kansu ba. Shin yana aske kansa? Dukansu amsoshin sun ci karo da yanayin da aka gabatar cewa sun kashe wadanda, kuma kawai wadanda ba su yi da kansu ba.

Neman tarin duk tarin

A ƙarshe, zan ba da wayo, amma mafi yawan hujjar lissafi cewa babu wani saiti na kowane saiti (kada a ruɗe shi da shi).

Da farko, za mu nuna cewa ga kowane saitin X wanda ba shi da komai, ba zai yuwu a sami wani aiki na musamman na juna wanda ke tsara wannan saitin zuwa saitin rukunin sa na P(X). Don haka bari mu ɗauka cewa akwai wannan aikin. Bari mu nuna shi ta gargajiya f. Menene f daga x? Wannan tarin. xf na x? Wannan ba a sani ba. Ko dai dole ne ko ba haka ba. Amma ga wasu x dole ne har yanzu ya kasance kamar yadda ba ya cikin f na x. To, to, yi la'akari da saitin duk x wanda x ba ya cikin f(x). Nuna shi (wannan saitin) ta A. Ya yi daidai da wani abu a cikin saitin X. Shin yana cikin A? Bari mu ɗauka ya kamata. Amma A saitin ne wanda ya ƙunshi abubuwan x kawai waɗanda ba na f(x) ba ... To, watakila ba na A bane? Amma saitin A ya ƙunshi duk abubuwan da ke cikin wannan dukiya, don haka kuma A. Ƙarshen hujja.

Saboda haka, idan akwai saitin duk saiti, da kansa zai zama wani yanki na kansa, wanda ba zai yiwu ba bisa ga tunanin da ya gabata.

Phew, bana tsammanin yawancin masu karatu sun ga wannan hujja. Maimakon haka, na kawo shi ne don in nuna abin da masana lissafi za su yi a ƙarshen karni na sha tara, lokacin da suka fara nazarin tushen ilimin nasu. Sai ya zama cewa matsalolin sun ta'allaka ne a inda babu wanda ya zaci su. Bugu da ƙari, ga dukan ilimin lissafi, waɗannan dalilai game da tushe ba su da mahimmanci: duk abin da ya faru a cikin cellars - dukan ginin ilmin lissafi yana tsaye a kan dutse mai tsayi.

A halin yanzu, a saman ...

Mun lura da wani halin kirki daga labarun Stanislav Lem. A daya daga cikin tafiye-tafiyensa, Iyon Tichi ya isa duniyar da mazaunanta, bayan dogon juyin halitta, suka kai ga matakin ci gaba. Dukkansu suna da ƙarfi, suna iya yin komai, suna da komai a hannunsu… kuma ba su yin komai. Suka kwanta akan yashi suka zuba a tsakanin yatsunsu. "Idan duk abin da zai yiwu, ba shi da daraja," sun bayyana wa Ijon da ya firgita. Kada wannan ya faru da wayewarmu ta Turai...