I know that there is no set of all sets in ZFC. Is there a way to manipulate the axioms and define a set of all finite sets? I am asking because if you think about it, the cardinality looks a lot like a function. You give me a finite set and I can tell you a number, which is its cardinality. Input-Output. However, in order for this to be a function, it needs to have a domain. So, can this domain be defined? Or do we have to say that there cannot be a function that given a set can return its cardinality?
2026-04-22 01:29:48.1776821388
Does the set of all finite sets exist according to ZFC?
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