Puzzles/Set theory puzzles/Russell's Paradox/Hint

< Puzzles < Set theory puzzles < Russell's Paradox

Puzzles | Set theory Puzzles | A strange set (Russel's paradox) | hint

In set theory you can specify a set by naming the elements of a set (say $a$ ) and giving constraints on them (say $cond(a)$ ): $\{a | cond(a) \}$ .

Now try to construct the set of all sets that do not contain themselves in the above notation. If it were to exist, all sets should be unambigously elements of that set or not. Otherwise a contradiction would result. Which set would be most worthwhile to consider?

This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.