A set can totally contain itself. A better question would be: Consider a set, that contains all sets, that do not contain themself. Would that set contain itself?
Yes, just relax the axiom of comprehension, allow U ∈ U and move on with proving things for fun and profit. No one said that you have to pick axioms that seem natural or intuitive.
Fun fact, the word ‘set’ has 430 definitions.
That’s quite a set of definitions
If the set of definitions contains the word set, does the English language implode in a recursive cascade of paradoxes?
A set can totally contain itself. A better question would be: Consider a set, that contains all sets, that do not contain themself. Would that set contain itself?
It would. Source: I just shaved my beard
Yes, just relax the axiom of comprehension, allow U ∈ U and move on with proving things for fun and profit. No one said that you have to pick axioms that seem natural or intuitive.
Define “the” without using the word “the”… Take that logic! Set and match!
A common English definite article