Journal of Philosophical Logic

, Volume 26, Issue 3, pp 237-239

First online:

Constructing Cantorian counterexamples

  • George BoolosAffiliated withDepartment of Linguistics and Philosophy, Massachusetts Institute of Technology

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Cantor’s diagonal argument provides an indirect proof that there is no one-one function from the power set of a set A into A. This paper provides a somewhat more constructive proof of Cantor’s theorem, showing how, given a function f from the power set of A into A, one can explicitly define a counterexample to the thesis that f is one-one.

Cantor diagonal argument set theory