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	Bolzano (Site not responding. Last check: 2007-10-29)
		Bernard Bolzano senior, the father of the subject of this biography, was born in the north of Italy and had emigrated to Prague.
		Bolzano came top in both competitions, but the university preferred to give him the chair in the philosophy of religion since they were then able to give the mathematics chair to Ladislaw Jandera who had substituted for Vydra during his illness between 1801 and 1804.
		Bolzano's career continued to flourish, despite the fact that charges were bought against him at the Vienna court in 1816, and in 1818 he was elected Dean of the Faculty of Philosophy at Charles University.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Bolzano.html (2386 words)

	10.4. Bolzano, Bernhard (1781-1848)
		Bolzano was appointed to the position at the University of Prague.
		Bolzano, though a priest, was a "free thinker" himself and was not afraid to express his beliefs in Czech nationalism.
		Bolzano had many new mathematical and logical ideas during his lifetime; however, because he was prohibited from publishing by the government, most of his writings existed only in manuscript.
	web01.shu.edu /projects/reals/history/bolzano.html (783 words)

	Bernhard Bolzano Biography / Biography of Bernhard Bolzano World of Mathematics Biography
		Born in Prague, Bohemia in 1781, Bolzano entered the University of Prague at the age of 15 to study philosophy and mathematics.
		In 1804, Bolzano was ordained a Roman Catholic priest, and received his doctorate in mathematics and an appointment to the chair of philosophy and religion at the University of Prague.
		Bolzano's work was largely censored in Austria from then on, but he managed to publish several more important mathematical papers over the next several decades.
	www.bookrags.com /biography-bernhard-bolzano-wom (466 words)

	CATHOLIC ENCYCLOPEDIA: Bernhard Bolzano
		Bolzano spent the remainder of his life in studious retirement, first on the estate of his friend Johann Hoffmann, at Techobuz, near Prague, and later in the house of his brother at Prague.
		Bolzano was always a loyal son of the Catholic Church.
		Bolzano's contributions to the science of mathematics are of the highest order.
	www.newadvent.org /cathen/02643c.htm (348 words)

	MSN Encarta - Search Results - Bolzano Bernhard
		Bolzano (German, Bozen; ancient Bauzanum), city in northern Italy, capital of Bolzano Province in the South Tirol and co-capital (with Trento) of...
		Bernhard, Thomas (1931-1989), Austrian poet, novelist, and playwright.
		Thomas Bernhard was born to Austrian parents in Heerleen in the Netherlands...
	uk.encarta.msn.com /Bolzano_Bernhard.html (97 words)

	Intuition and Rigor
		One of the torch bearers of the formalization attempts in the 19th century was the Czech analyst Bernhard Bolzano (1781-1848.) In his critique of the attempts to prove the Fundamental Theorem of Algebra, he wrote
		The most common kind of proof depends on a truth borrowed from geometry, namely, that every continuous line of simple curvature of which the ordinates are first positive and then negative (or conversely) must necessarily intersect the x-axis somewhere at a point that lies in between those ordinates.
		However, in the footsteps of Bolzano, it would be "an intolerable offense against correct method" to refer to somebody's concept of quantity in a proof claimed to be rigorous.
	www.cut-the-knot.org /fta/bolzano.shtml (645 words)

	Bernhard Bolzano
		Bernhard Placidus Johann Nepomuk Bolzano was born in Prague, Bohemia (now part of the Czech Republic), on October 5, 1781.
		This must have been a crutial year for Bolzano’s career to develop because he was also appointed to the chair of philosophy and religion at the University of Prague.
		Bolzano did establish definitions for basic geometric concepts and was the first person to state the Jordan curve theorem.
	sps.k12.mo.us /phs/jpetersen/projects/mathematicians/bolzano.htm (950 words)

	Título de la página (Site not responding. Last check: 2007-10-29)
		Bolzano's theorem is often used to find out where the roots of equations are located, or in other words, where the function has values of 0, which we will look at in more detail in the problems section.
		This is a simple consequence of Bolzano's theorem known as Darboux's theorem or the intermediate value property.
		Although Bolzano's and the Weierstrass theorems seem obvious they are actually very difficult to prove.
	descartes.cnice.mecd.es /ingles/Bach_HCS_2/Bolzano_Weierstrass_theorems/continuas_ideas_basicas2.htm (991 words)

	References for Bolzano
		L J Cohen, Bolzano's theory of induction, in Impact of Bolzano's epoch on the development of science (Prague, 1982), 443-457.
		L Novy, Bolzano's contribution to science and society, in Impact of Bolzano's epoch on the development of science (Prague, 1982), 9-23.
		S Russ, Influence of Bolzano's methodology on the development of his mathematics, in Impact of Bolzano's epoch on the development of science (Prague, 1982), 335-337.
	www-groups.dcs.st-and.ac.uk /~history/References/Bolzano.html (590 words)

	Bolzano - matematicos (Site not responding. Last check: 2007-10-29)
		Bolzano, Bernard (1781-1848): Bolzano Bolzano's work was a significant influence on that of Husserl, Frege, Lukasiewicz, and Tarski.
		CBC News: Disclosure - The Beast of Bolzano
		Bolzano, Bernhard Bohemian mathematician and theologian who provided a more detailed proof for the binomial theorem in 1816 and suggested the means of
	topindexsite.com /ti/bolzano.html (181 words)

	Bolzano, Bernhard. (Site not responding. Last check: 2007-10-29)
		In 1819, however, Bolzano was suspended from his position because of pressure from the Austrian government, which opposed his pacifism and his expressed concerns with economic justice.
		Although some of his books had to be published outside Austria because of government censorship, he continued to write and to play an important role in the intellectual life of his country.
		Among Bolzano's important works are Rein analytischer Beweis (Pure Analytical Proof, 1817), which contains an effort to free calculus successfully from the concept of the infinitesimal; Wissenschaftslehre (1837; Eng.
	euler.ciens.ucv.ve /English/mathematics/bolzano.html (190 words)

	Bernhard Placidus Johann Nepomuk Bolzano (Site not responding. Last check: 2007-10-29)
		Bernhard Bolzano entered the Philosophy Faculty of the University of Prague in 1796, studying philosophy and mathematics.
		Because of his pacifist beliefs and his concern for economic justice, Bolzano was suspended from his position in 1819.
		It is in a 1817 paper that Bolzano gives a proof of the intermediate value theorem with his new approach, and in this work he defined what is now called a Cauchy sequence.
	www.stetson.edu /~efriedma/periodictable/html/Pb.html (390 words)

	The Nassau Guardian - www.thenassauguardian.com.com
		Mr Wilchcombe told The Guardian on Tuesday, that Ms Seymour is expected to call upon the family of Bernhard Bolzano and Barbara Frelliin von Perfall and present them with a "personal letter" on behalf of The Bahamas government, whenever their funeral services are held sometime this week.
		Bolzano and Ms Von Perfall was found murdered last Sunday July 24 in a hotel room of the Bimini Blue Water Resort in Alice Town.
		Bernhard was reportedly found lying on the floor between the two beds of the hotel room with his hands tied behind his back and gunshot wound to the upper back.
	www.thenassauguardian.com /national_local/307861486687117.php (416 words)

	Bolzano
		One of the first to attack this problem was Bernhard Bolzano, a Czech priest of Italian descent who was Professor in the Philosophy of Religion at the University in Prague, then part of the Austrian empire.
		In his Paradoxes of the Infinite, Bolzano showed for example that there is a 1--1 correspondence between the intervals [1,2] and [1,3], and he suggested that there is no such correspondence between the natural numbers and the reals, anticipating later results by Cantor.
		Both results were needed to prove that every bounded set of numbers has a supremum which in turn is needed to prove the IVT: between any two values of a continuous function f which are of opposite sign, there must always lie at least one root of the equation f(x)=0.
	www.maths.uwa.edu.au /~schultz/3M3/L26Bolzano.html (1642 words)

	Bernhard Bolzano -- Britannica Concise Encyclopedia - The online encyclopedia you can trust! (Site not responding. Last check: 2007-10-29)
		Bolzano graduated from the University of Prague as an ordained priest in 1805 and was immediately appointed professor of philosophy and religion at the university.
		Within a matter of years, however, Bolzano alienated many faculty and church leaders with his teachings of the social waste of militarism and the needlessness of war.
		Upon his refusal to recant his beliefs, Bolzano was dismissed from the university in 1819 and at that point devoted his energies to his writings on social, religious, philosophical, and mathematical matters.
	www.britannica.com /ebc/article-9080527 (941 words)

	Bahamas news - Bahamian news portal: - Tourism Backlash Expected - Headline News (Site not responding. Last check: 2007-10-29)
		The bodies of Bernhard Bolzano, 35 and Barbara Frelln Von Perfall, 32 were found shot to death in their hotel room at the Anchorage Bimini Blue Water Resort.
		They had arrived in Bimini on Thursday and were expected to leave on Saturday, the day that their bodies were found.
		Bolzano's body was face down on the floor between two beds with his hands tied behind his back and gagged.
	www.bahamasb2b.com /news/wmprint.php?ArtID=5639 (575 words)

	Bahamas police investigate killing of Austrian couple - JAMAICAOBSERVER.COM
		The bodies of Bernhard von Bolzano, 34, and his fiancee, Barbara Frelin von Perfall, 32, were found Saturday in their room at the Blue Water Resort and Marina in Alice Town, Bimini, where they had been staying since Thursday, said assistant police commissioner Reginald Ferguson.
		Von Bolzano, who had been shot in the back, was found bound and gagged, face down on the floor.
		Von Bolzano was a business consultant and von Perfall ran a spa, Leuke said in a telephone interview from Vienna.
	www.jamaicaobserver.com /news/html/20050726T190000-0500_84865_OBS_BAHAMAS_POLICE_INVESTIGATE_KILLING_OF_AUSTRIAN_COUPLE.asp (269 words)

	BERNHARD BOLZANO - LoveToKnow Article on BERNHARD BOLZANO (Site not responding. Last check: 2007-10-29)
		In philosophy he followed Reinhard in ethics and the monadology of Leibnitz, though he was also influenced by Kant.
		See Lebensbeschreibung des Dr Bolzano (an autobiography, I8~6); Wisshaupt, Skizzen aus dem L~eben Dr Boizanos (1850); Palagy, Kant und Bolzano (Halle, 1902).
		To properly cite this BERNHARD BOLZANO article in your work, copy the complete reference below:
	www.1911encyclopedia.org /B/BO/BOLZANO_BERNHARD.htm (217 words)

	Bernhard Bolzano -- Encyclopædia Britannica
		Bolzano graduated from the University of Prague as an ordained priest in 1805 and was immediately appointed…
		German journalist and writer Bernhard Kellermann is best known for his novel Der Tunnel (The Tunnel), a sensational utopian work about an attempt to build a transatlantic tunnel.
		The most extraordinary work in the German sphere was produced in the early 18th century in the bishopric of Würzburg, where Balthasar Neumann, trained locally as a military engineer,...
	www.britannica.com /eb/article-9080527 (725 words)

	Cardinality History - Cardinality Information
		Bernhard Bolzano defined cardinality in his book Paradoxes of the Infinite (1851).
		Any set that has the same cardinality as N is said to be countable or denumerable.
		Georg Cantor (1845-1918) built on Bolzano's work and rigorously proved most of the theorems that draw on cardinality.
	www.bookrags.com /sciences/mathematics/cardinality-wom.html (788 words)

	The Nassau Guardian - www.thenassauguardian.com.com
		Assistant Commissioner with responsibility for Crime, Reginald Ferguson, confirmed Thursday that the suspect was found in possession of a 12 gauge Maverick shotgun believed to be the murder weapon, as well as properties belonging to Bernhard Bolzano, 34, and Barbara Frell von Perfall, 32.
		The body of Bernhard was reportedly found lying on the floor between the two beds of the hotel room with his hands tied behind his back and a gunshot wound to the upper back.
		Perfall, was found lying on one of the beds with multiple wounds to the head and face.
	www.thenassauguardian.com /national_local/305523564936678.php (423 words)

	Russell’s Paradox and Possible Solutions
		The origins of set theory can be traced back to a Bohemian priest, Bernhard Bolzano (1781-1848), who was a professor of religion at the University of Prague.
		Bolzano’s paper, Paradoxien des Unendlichen (Paradoxes of the Infinite), is the first to introduce the term set.
		This paper discusses the relationship between the set of natural numbers and their perfect squares, an idea first considered by Galileo, but the paper also considers many other examples of infinite sets.
	www.math.ups.edu /~bryans/Current/Journal_Spring_1999/JEarly_232_S99.html (1301 words)

	WHKMLA : History of the Lands of the Bohemian Crown, 1815-1848
		The Habsburg administration, suspicious even of such a cultural movement, had theology professor at Prague University Bernhard Bolzano dismissed (1820), M. Fesl, professor at the seminary in Litomerice, the founder of a secret society, arrested.
		In 1816 Bolzano had published an essay On the Condition of the Two Nationalities in Bohemia, in which he reflected on the socio-political consequences of this linguistic structure.
		Interestingly, it is these two bilingual groups which contributed most strongly to the Czech cultural and political national awakening - Bolzano is an Italian name, Josef Jungmann has a German name.
	www.zum.de /whkmla/region/germany/bohemiarest.html (487 words)

	The New Schaff-Herzog Encyclopedia of Religious Knowledge, Vol. II: Basilica - Chambers (bolzano_bernhard)
		BOLZANO, bel-tsɑ̄´nō, BERNHARD: German Roman Catholic theologian, and noted mathematician; b.
		He took orders and was made professor of the philosophy of religion in Prague 1805.
		Bibliography: Lebensbeschreibung des Dr. Bolzano, new ed., Vienna, 1875 (an autobiography); Dr.
	www.ccel.org /ccel/schaff/encyc02.bolzano_bernhard.html (225 words)

	MSN Encarta - Bolzano, Bernhard
		Bolzano, Bernhard (1781-1848), Czech mathematician and philosopher, who was also a Roman Catholic priest.
		Born in Prague, Bolzano became a priest in...
		Become a subscriber today and gain access to:
	encarta.msn.com /encyclopedia_761556504/Bolzano_Bernhard.html (76 words)

	MavicaNET - Bolzano, Bernard
		Links: Bolzano's life, Bolzano's works, International Bernard Bolzano Society, Bolzano-Winter Archive Bolzano's Collected Works (Bernard Bolzano-Gesamtausgabe) Bolzano Publication Series (Beiträge zur Bolzano-Forschung) Conferences on Bolzano, Bolzano Web Pages.
		Biography: "Bernard Bolzano was born on 5 October 1781 in Prague as the fourth of 12 children".
		Holdings: Bolzano's Collected Works - Bernard Bolzano-Gesamtausgabe; Bolzano's published works in original copies, reprints and photocopies; The majority of the secondary literature on Bolzano; Selected Works and manuscripts of Eduard Winter; Books, letters and works of Anton Günther, Johann Emanuel Veith (pupils of Bolzano) and Johann Heinrich Löwe (Professor of Philosophy in Salzburg and Prague).
	www.mavicanet.com /lite/ita/7386.html?sortby=8 (287 words)

	Bolzano–Weierstrass theorem - Wikipedia, the free encyclopedia
		A generalization of both theorems to arbitrary topological spaces is: a space is compact if and only if every net has a convergent subnet.
		The Bolzano–Weierstrass theorem is named after mathematicians Bernhard Bolzano and Karl Weierstrass.
		PlanetMath: proof of Bolzano–Weierstrass Theorem (different proof than the one outlined above)
	en.wikipedia.org /wiki/Bolzano-Weierstrass_theorem (270 words)

	Bolzano - Philosophical Dictionary: Bocardo-Boyle
		Bolzano hotels, resorts, inns and BandBs: Visit TripAdvisor, your source for the web's best unbiased reviews, travel articles and guidebook listings about
		Homepage of the Tourist board of the city Bolzano in South Tyrol, Italy.
		Let, for two real a and b, a < b, a function f be continuous on a A complete proof of the Bolzano Theorem appeares elsewhere.
	www.search-ic.com /sic/bolzano.html (190 words)

	Famous Scientists Who Believed in Creation - Lister, Cuvier, Faraday (Site not responding. Last check: 2007-10-29)
		When Bernhard Riemann died, a biographer noted that he had served Christ outside the pulpit as his father had served Christ in the pulpit.
		The first of these Christians was Bernhard Riemann who had developed the mathematics of Riemannian Space, which Einstein found could explain the curvature of space.
		The Roman Catholic Czech theologian Bernhard Bolzano was one of the first to attempt a significant infinity theory.
	www.jcsm.org /Contents/Famous.htm (4765 words)

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