Soft Question: Struggling at Elementary Set Theory $\rightarrow$ Shouldn't Study Pure Math? Does being bad at elementary set theory, mean someone will be bad at proofs in upper level courses like real analysis, topology, algebra? I can't write Cantor's diagonalization argument as a non-proof by contradiction because I don't understand it well enough. I couldn't prove that the cardinality of Cartesian products of set $M$ and $N$ is $M\times N$ unless I'm spoonfed the answer. I can't understand what a dense subset is. Is analysis, algebra, geometry, not for me? I don't know why we use Cartesian products to prove that the countable union of countable sets is countable. P-adic numbers don't make sense to me. I couldn't tell you why a subsequence is either strictly increasing or decreasing. I don't understand transcendental vs algebraic numbers. Well-ordering principle I can use as a formula but I don't really understand WOP.
 A: At some point, every one learns what it is to struggle. About most concepts, I have nothing intelligent to say, assuming I even recall the definitions. I cannot solve most problems that are out there in mathematics, and I expect that most people in research have similar experience. We need to see examples of how proofs go in order to structure our ideas, and spend a great deal of time to become familiar with concepts.
I know that if I keep at it, stay struggling long enough, think about things long enough and in enough different ways, eventually, I'll get it. And then the thing that I figure out will become an experience which may help me with a different problem.
Eventually you'll get it too. Welcome to mathematics :)
A: Leibniz did just fine with analysis, and even algebra and geometry.  I assure you that not only did he not know a thing about set theory but he actually opposed the actual existence of infinite sets taken for granted in modern set theory. It would have been gibberish to him as it is to you.
