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 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 coined the term
Menge, rendered in English as "set".