Welcome guest
You're not logged in.
343 users online, thereof 0 logged in

As you recall from the historical development, Cantor’s naive set definition also allowed constructing a “set of all sets”. With the axiom of separation, such a set cannot exist.

Corollary: There is no set of all sets

There is no such set $X$ which contains the set $\{z\in X\mid z\not\in z\}$ as an element. In other words, a “set of all sets” does not exist.

| | | | | Contributors: bookofproofs | References: [656], [983]

1.Proof: (related to "There is no set of all sets")


This work was contributed under CC BY-SA 3.0 by:

This work is a derivative of:

(none)

Bibliography (further reading)

[983] Ebbinghaus, H.-D.: “Einf├╝hrung in die Mengenlehre”, BI Wisschenschaftsverlag, 1994, 3

[656] Hoffmann, Dirk W.: “Grenzen der Mathematik – Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011

FeedsAcknowledgmentsTerms of UsePrivacy PolicyImprint
© 2018 Powered by BooOfProofs, All rights reserved.