The Paradoxes of the Infinite

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The Paradoxes of the Infinite (German title: Paradoxien des Unendlichen) is a mathematical work by Bernard Bolzano on the theory of sets. It was published by a friend and student, František Přihonský, in 1851, three years after Bolzano's death. The work contained many interesting results in set theory. Bolzano expanded on the theme of Galileo's paradox, giving more examples of correspondences between the elements of an infinite set and proper subsets of infinite sets. In the work he also explained the term Menge, rendered in English as "set", which he had coined and used in several works since the 1830s.


  • Paradoxes of the Infinite; trans. by D.A.Steele; London: Routledge, 1950
  • Bolzano, Bernard (1851), Paradoxien des Unendlichen (PDF), C.H. Reclam (German original)   Faksimile
  • Burton, David (1997), The History of Mathematics: An Introduction (Third ed.), McGraw-Hill, p. 592