In the historical development of set theory, it was mentioned that Russel demonstrated, the following classical definition is not sufficient since it leads to paradoxical constructs. If you are a beginning student of the set theory, the classical definition of Cantor is a good starting point, because it is highly intuitive.
A set is a combination of well-distinguishable, mathematical objects. Let \(X\) be a set.
1 Nowadays, we use the Zermelo-Fraenkel axioms (ZFA) to define sets.
| | | | | created: 2014-03-22 15:09:49 | modified: 2019-09-07 08:12:09 | by: bookofproofs | references: , 
 Hoffmann, Dirk W.: “Grenzen der Mathematik – Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011
 Kohar, Richard: “Basic Discrete Mathematics, Logic, Set Theory & Probability”, World Scientific, 2016