The paradoxes of the theory of sets. 4th edition, stereotypical. Yashchenko I.V.

With the development of the theory of sets on which all modern mathematics are based, paradoxes arose. For example, the paradox of the branded, formulated as follows: “Does the brandy shakes himself if he shakes those and only those who do not shave himself?.”

The brochure tells how the theory of sets is treated with similar situations, as well as other paradoxes, including the selection axiomes arising when considering. In particular, you will learn how to make two from one orange.

In Appendix 3, tasks are given, an independent solution of which will help the reader to more fully understand the brochure material.

The text of the brochure is processed Records of lectures read by the author on April 8, 2000 on small Mehmat for schoolchildren of grades 9-11 (entry by E. N. Osmova) and in July 2001 as part of the Modern Mathematics School for schoolchildren and students 1-2 courses (entry of Yu. L. Pritykin).

The brochure is designed for a wide range of readers interested in mathematics: high school students, primary school students, teachers.