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 in 1851, three years after Bolzano's death, by a friend. 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 coined the term Menge, rendered in English as "set".


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