Bernard Bolzano

Bernard Bolzano
Henkilötiedot
Syntynyt5. lokakuuta 1781
Praha, Böömin kuningaskunta
Kuollut18. joulukuuta 1848 (67 vuotta)
Praha, Böömin kuningaskunta
Koulutus ja ura
Tutkinnot Kaarlen yliopisto
Väitöstyön ohjaaja František Josef Gerstner
Tutkimusalue Matemaattinen analyysi, logiikka, tieteenfilosofia, epistemologia, matematiikka, filosofia, estetiikka ja kirkko

Bernard Placidus Johann Nepomuk Bolzano (5. lokakuuta 1781 – 18. joulukuuta 1848)[1] oli tšekkiläinen saksankielinen matemaatikko, teologi, filosofi ja loogikko. Hän syntyi Prahassa. Bolzano tunnetaan nykyisin ennen kaikkea Bolzanon lauseesta, joka on jatkuvien funktioiden väliarvolauseen erikoistapaus, sekä Bolzanon–Weierstrassin lauseesta.[2]

Bolzano aloitti opintonsa Prahan Kaarlen yliopistossa vuonna 1796, pääaineinaan filosofia, fysiikka ja matematiikka. Syksyllä 1800 hän alkoi opiskella myös teologiaa. Vuonna 1804 hän väitteli geometriasta, ja kaksi päivää väitöstilaisuuden jälkeen hänet vihittiin papiksi.[3]

Bolzanon työ logiikan parissa on vaikuttanut myöhempien matemaatikkojen saavutukseen, kuten esimerkiksi Georg Cantor ja Richard Dedekind.[4]

Teoksia

  • Betrachtungen über einige Gegenstände der Elementargeometrie
  • Versuch einer objectiven Begründung der Lehre von den drei Dimensionen des Raumes
  • Die drey Probleme der Rectification, der Complanation und der Cubirung
  • Über Haltung, Richtung, Krümmung und Schnörkelung bei Linien
  • Paradoxien des Unendlichen ("Äärettömän paradoksit")

Lähteet

  1. ↑ Bernard Placidus Johann Nepomuk Bolzano
  2. ↑ Thompson, Jan & Martinsson, Thomas: Matematiikan käsikirja, s. 46–47. Helsinki: Tammi, 1994. ISBN 951-31-0471-0
  3. ↑ J J O'Connor and E F Robertson: Bernard Placidus Johann Nepomuk Bolzano MacTutor. Viitattu 7.12.2014.
  4. ↑ Bernard Bolzano The Society of Catholic Scientists. Viitattu 5.10.2023. (englanti)

Aiheesta muualla

  • Corazzon, Raul: Bernard Bolzano and the Theory of Science Theory and History of Ontology (englanniksi)
  • Morscher, Edgar: Bernard Bolzano The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab. Stanford University. (englanniksi)
  • Sebestik, Jan: Bolzano's Logic The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab. Stanford University. (englanniksi)
  • Boyer, Carl B. & Merzbach, Uta C.: Tieteiden kuningatar – Matematiikan historia, osa II, s. 721–722. Suomentanut Kimmo Pietiläinen. Helsinki: Art House, 1994. ISBN 951-884-158-6

Read other articles:

Menara Shanghai

Menara Shanghai上海中心大厦Shànghǎi Zhōngxīn DàshàMenara Shanghai pada tahun 2015.Informasi umumStatusSelesai dibangunLokasiLujiazui, Pudong, Shanghai, TiongkokMulai dibangun29 November 2008[1]Perkiraan rampungTutup atap: 3 Agustus 2013[2][3] Overall completion: 2014[4]BiayaUS$2,2 miliar[4]TinggiArsitektural632 m (2.073 ft)[5]Lantai atas5.567 m (18.264 ft)[5]Data teknisJumlah lantai121[5]Luas lanta...

 

Pansy Parkinson

Pansy Parkinson Goyle, Malfoy, Crabbe, dan Pansy Parkinson di Harry Potter and the Prisoner of Azkaban PemeranGenevieve Gaunt (film ketiga)Scarlett Byrne (film keenam dan ketujuh)InformasiJenis kelaminPerempuan Pansy Parkinson adalah salah satu tokoh fiksi dalam seri Harry Potter karya J. K. Rowling. Ia adalah anggota asrama Slytherin, satu angkatan dengan Harry di Hogwarts. Pansy digambarkan sebagai seorang dengan muka keras, seperti anak anjing, dan sering terlihat bersama-sama dengan Draco...

 

Al-Jamawat, Madinah

Al-JamawatLingkunganNegara Arab SaudiProvinsiProvinsi MadinahKotaMadinahZona waktuUTC+3 (EAT) • Musim panas (DST)UTC+3 (EAT) Al-Jamawat adalah sebuah lingkungan di kota suci Madinah di Provinsi Madinah, tepatnya di sebelah barat Arab Saudi.[1] Referensi ^ National Geospatial-Intelligence Agency. GeoNames database entry. (search Diarsipkan 2017-03-18 di Wayback Machine.) Accessed 12 May 2011. lbsLingkungan sekitar Masjid Nabawi, Madinah, Arab Saudi • Al-Jumu'ah • -...

برايان هولمان

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (أبريل 2019) برايان هولمان معلومات شخصية الميلاد 25 يناير 1965 (58 سنة)  دنفر  مواطنة الولايات المتحدة  الحياة العملية المهنة لاعب كرة قاعدة  الرياضة كرة القاعدة ...

 

Довгоногові

?ДовгоноговіЧас існування: ранній міоцен - сучасність Pedetes sp. Біологічна класифікація Домен: Ядерні (Eukaryota) Царство: Тварини (Animalia) Тип: Хордові (Chordata) Підтип: Хребетні (Vertebrata) Клас: Ссавці (Mammalia) Підклас: Звірі (Theria) Надряд: Гризуни (Rodentia) Ряд: Мишоподібні (Muriformes) Підряд: Шипохв

 

Belle Vue Quarry

Site of Special Scientific Interest in Dorset Looking down into the quarry Belle Vue Quarry (grid reference SZ014782) is a 3.2 hectare biological Site of Special Scientific Interest in Dorset, notified in 1977. It is used as a roosting site by Greater Horseshoe bats. Sources English Nature citation sheet for the site (accessed 29 August 2006) External links English Nature website (SSSI information) vteSites of Special Scientific Interest in Dorset Abbotsbury Blind Lane Abbotsbury Castle Alder...

Sultan (2008 film)

2008 Indian filmSultanDirected bySreeprakashWritten byVinod GuruvayoorJayan SivapuramProduced byGopi ManasseriStarringVinu MohanVaradaCinematographyP. SukumarEdited byRanjan AbrahamMusic byM. JayachandranRelease date 5 December 2008 (2008-12-05) CountryIndiaLanguageMalayalam Sultan is a 2008 Indian Malayalam-language film directed by Sreeprakash, starring Vinu Mohan and Varada in the lead roles.[1][2] Plot Sivan is a medical college student better known in the c...

 

Tumulus culture

Prehistoric European culture characterized by burial mounds Tumulus cultureGeographical rangeCentral EuropePeriodMiddle Bronze AgeDatesc. 1600–1200 BCPreceded byUnetice culture, Ottomány culture, Rhône culture, Mad'arovce culture, Encrusted Pottery cultureFollowed byUrnfield culture, Lusatian culture The Tumulus culture (German:Hügelgräberkultur) was the dominant material culture in Central Europe during the Middle Bronze Age (c. 1600 to 1300 BC). It was the descendant of the...

 

Heathrow Terminal 5 Transit

Automated people mover at London Heathrow Airport Heathrow Terminal 5 TransitA Bombardier Innovia APM 200 at Terminal 5OverviewLocaleLondon Heathrow Airport,Transit typeAutomated guideway transit/People moverNumber of lines1Number of stations3Annual ridership13 million per yearWebsiteHeathrow Terminal 5 guideOperationBegan operation2008Operator(s)Heathrow Airport HoldingsCharacterUndergroundRolling stock10 × Bombardier Innovia APM 200Number of vehicles8 in normal operationTechnicalSystem len...

Belém (São Paulo Metro)

São Paulo Metro station BelémGeneral informationCoordinates23°32′36″S 46°35′22″W / 23.543216°S 46.58952°W / -23.543216; -46.58952Owned by Government of the State of São PauloOperated by Companhia do Metropolitano de São PauloPlatformsIsland platformConnections SPTrans Bus LinesConstructionStructure typeAt-gradeAccessibleYesOther informationStation codeBELHistoryOpenedSeptember 5, 1981Passengers38,000/business day[1] Services Preceding station S...

 

Inconsequential Tales

This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Inconsequential Tales – news · newspapers · books · scholar · JSTOR (January 2009) (Learn how and when to remove this template message) First edition cover art by Jason C. Eckhardt Inconsequential Tales is a collection of horror stories by Ramsey Campbell, published by Hippocamp...

 

Puteri Indonesia Sumatera Utara

Puteri Indonesia Sumatera UtaraLogo Puteri IndonesiaSingkatanPuteri Indonesia SumutDinamai berdasarkanPuteri Indonesia regionalTanggal pendirian1992; 30 tahun lalu (1992)Didirikan diJakarta, DKI Jakarta, IndonesiaTipeKontes kecantikan regionalKantor pusatKota Medan, IndonesiaLokasi IndonesiaJumlah anggota Puteri IndonesiaBahasa resmi Bahasa IndonesiaBahasa InggrisPresiden dan CEO Puteri IndonesiaMooryati SoedibyoKetua Puteri IndonesiaPutri KuswisnuwardhaniOrganisasi indukPuteri Indo...

Abdulmanap Nurmagomedov

Soviet-Russian wrestling coach (1962–2020) In this name that follows Eastern Slavic naming conventions, the patronymic is Magomedovich and the family name is Nurmagomedov. Abdulmanap NurmagomedovАбдулманап НурмагомедовNurmagomedov in 2016BornAbdulmanap Magomedovich Nurmagomedov(1962-12-10)10 December 1962Sildi, Dagestan ASSR, Russian SFSR, Soviet Union(now Sildi, Dagestan, Russia)Died3 July 2020(2020-07-03) (aged 57)Moscow, RussiaNationalitySoviet (1962–1991...

 

Волгин, Игорь Леонидович

В Википедии есть статьи о других людях с фамилией Волгин. Игорь Леонидович Волгин Дата рождения 6 марта 1942(1942-03-06) (81 год) Место рождения Молотов, РСФСР, СССР Страна  СССР Россия Научная сфера история России, история литературы Место работы факультет журналистики МГУ, ...

 

Kompi Kavaleri 4

artikel ini perlu dirapikan agar memenuhi standar Wikipedia. Tidak ada alasan yang diberikan. Silakan kembangkan artikel ini semampu Anda. Merapikan artikel dapat dilakukan dengan wikifikasi atau membagi artikel ke paragraf-paragraf. Jika sudah dirapikan, silakan hapus templat ini. (Pelajari cara dan kapan saatnya untuk menghapus pesan templat ini) Kompi Kavaleri 4/Tarantula Hitam CaktiLambang Kikav 4/THCAktif24 Oktober 2005NegaraIndonesiaCabangKavaleriTipe unitSatuan Bantuan TempurPeranPasuk...

Main Event (college basketball)

Main Event (college basketball)FormerlyMGM Grand Main Event (2014)Men Who Speak Up Main Event (2015-2016)MGM Resorts Main Event (2017-2019)Men's Vegas Bubble (2020)Roman Main Event (2021)SportCollege BasketballFounded2014Owner(s)bdG SportsNo. of teams4CountryUnited StatesVenue(s)Heavyweight BracketT-Mobile Arena (2017-present)MGM Grand Garden Arena (2014-2016)Middleweight BracketEd W. Clark High School (2019)Cox Pavilion (2018)T-Mobile Arena (2017)MGM Grand Garden Arena (2014-2016)Most recent...

 

Amado Aguirre Santiago

Amado Aguirre Santiago Aguirre Santiago en 1920 (Archivo General de la Nación) Gobernador del Distrito Sur del Territorio de Baja California 1 de noviembre de 1927-9 de agosto de 1929Presidente Emilio Portes Gil (1927-1928)Plutarco Elías Calles (1927-1928)Predecesor Carlos M. EzquerroSucesor Agustín Olachea Gobernador del Territorio de Quintana Roo 1925-1925Presidente Plutarco Elías CallesPredecesor Enrique Barocio BarriosSucesor Enrique Barocio Barrios Director del Heroico Colegio Milita...

 

Grodziskie

Style of beer from Poland GrodziskiePiwo z Grodziska, a modern Polish recreation of Grodziskie, brewed in Grodzisk Wielkopolski, served in a tall conical glass designed for this style of beerCountry of originPolandYeast typeTop-fermentingAlcohol by volume2.5% – 5% Grodziskie (Polish pronunciation: [ɡrɔˈd͡ʑiskʲɛ]; other names: Grätzer, Grodzisz[1]) is a historical beer style from Poland made from oak-smoked wheat malt with a clear, light golden color, high carbonation...

Acquisition of Activision Blizzard by Microsoft

Business acquisition held from 2022 to 2023 Acquisition of Activision Blizzard by MicrosoftInitiatorMicrosoftTargetActivision BlizzardTypeFull acquisitionCostUS$68.7 billionInitiatedJanuary 18, 2022 (2022-01-18)CompletedOctober 13, 2023 (2023-10-13)StatusClosed On January 18, 2022, Microsoft announced its intent to acquire Activision Blizzard for $68.7 billion. The deal was finalized on October 13, 2023. Under the terms of the agreement, Microsoft broug...

 

York Region Paramedic Services

York Region Paramedic ServicesEstablished2000Headquarters80 Bales Drive East, East Gwillimbury, Ontario (York Region)JurisdictionRegional Municipality of YorkEmployees480 full-timeBLS or ALSBoth ALS and BLSAmbulances48 and 27 other support vehiclesChiefChris SpearenMedical directorCentral East Prehospital Care ProgramResponses75,000+WebsiteWebsiteYork Region Paramedic Services York Region Paramedic Services provides legislated land ambulance services and paramedic care for the local municipal...

 

Strategi Solo vs Squad di Free Fire: Cara Menang Mudah!