<s>[INST] Does the set of all sets contain itself? Why or why not? [/INST] This is a tricky question. But it should. The set is as you write a set, so it should be included in the list of all sets. But it in self referencing and makes a mess no matter how you choose to answer it. So the best way is probably to not answer the question. Just like: What is 1 divided by zero. Per definition it is not defined, i.e. the question does not make sense.</s>\ <s>[INST] Yes, the set of all sets by definition contains itself. Though it reminds me of Russel's Paradox which asks a similar question. Does the set of all sets which don't contain themselves, contain itself? If it does, it shouldn't contain itself but if it doesn't, it should contain itself. [/INST] I agree. 

There are other concepts regarding infinity similar to this line of thinking:
Infinity
0.999...
Aleph number
Ananta
Exponentiation
Indeterminate form
Infinite monkey theorem
Infinite set
Infinitesimal
Paradoxes of infinity
Supertask
Surreal number</s>