Proofs by Contradiction or Isn’t This an Absurdity?

  • Shlomo Vinner
Part of the Mathematics in Mind book series (MATHMIN)


The nature of this chapter is mathematical again. Usually, at least some students face proofs by contradictions in their high-school courses. For many of them it is a problem. I try to explain the reason for these difficulties. I make an effort to simplify it by presenting some proofs by contradiction. One of them is the claim that \( \sqrt{2} \) is irrational. The second one is the claim that there are infinitely many prime numbers.

I point out difficulties some people may have when asked to assume a counter-reality situation. I chose to demonstrate it by means of a hilarious piece of literature: The Lesson by Ionesco (1951).


  1. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, Netherlands: Springer.Google Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Shlomo Vinner
    • 1
  1. 1.The Hebrew University of JerusalemJerusalemIsrael

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