# Proofs by Contradiction or Isn’t This an Absurdity?

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## Abstract

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).

## References

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

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