Math Is Fun Forum

I have read that math is under a crisis due to be heavily based on set theory, and in its turn set theory has unanswered questions. In my opnion, set theory the way I learned is problematic even from the very beginning. Some may not agree with this statement, but I will try to give a start: if possible, can anybody help me with this question : given the two sets A={x} and B={{x}} are they equal?
Well, if we forget for while the rules of set theory and the way of thinking (stablished up to now) and behave like a child and ask: if A = B  then if we do operations on left hand side and/or right hand side, and if in any circunstance we find the same set of symbols, representing LHS and RHS, then A = B.

So following this the LHS = A and RHS = B. Now just ask the contents of the RHS, or what are/is the element(s) of set B, you will find {x}, which is A, then for this analogy A=B (again forgeting rules of set theory for while).

Another question is: could we devolope a set of rules for set theory where this kind of situation is ruled out?

For instance if we think about the expressions A = t and B=(3-2) t^(5-4), in order to find out that A=B we just need to develop the RHS, as before said, and it is enough!

After tiping I realize that according to authors, B is not a set, but a family of set !!

Another question would be: is a family of set a set? That it is to say: can a family of set be considered a set or not?