Скачать с ютуб Set Theory Part 0: An informal introduction to sets в хорошем качестве

Set Theory Part 0: An informal introduction to sets

Set Theory is the branch of math that deals with collections of objects called sets. It is commonly used as the foundation of math, as most other areas of math can be phrased entirely in terms of sets. But what exactly is a set? Set Theory playlist:    • Set Theory   Corrections: - Minor point: I say that an arbitrary collection of sets is called a class, but it's a little more subtle than this. The classes of von Neumann–Bernays–Gödel set theory are collections of sets that are "too large" to be contained in a set (for example, the class of all sets). But in Part 2 of this series (the axioms of ZFC), I discuss the possibility of a subcollection of a set which is not itself a set (which potentially could exist as long as its elements are not describable using a predicate), and these would be collections of sets that are not classes. So a class is a type of collection of sets that's more general than sets, but "class" is not necessarily synonymous with "collection of sets". Let me know if you notice any other mistakes!