You still fail to define what a "class" is simply because you didn't and don't understand it still.
https://math.stackexchange.com/a/173002 here read up. Also read on Russell's Paradox. I'm not objectively wrong you're just uneducated and your ego is too large. The irony is I was saying the exact same thing you were in my very first comment, except with more precision.
And I still would want you to think about what exactly "output" is.