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Good day to everyone,
I would like to ask this question. I was wondering what is considered to be the hardest area of mathematics, so I searched in forums and outside of answers like Langlands programe and Cohomology there was this answew called Irational number theory, where it was stated that we basically have no idea of how to even solve the basic questions. Which leads me to my question.
Do we have number systems of higher cardinality then Reals? I don´t mean number systems like Complex numbers, Quartions, ... as all of them have the same cardinality as Reals, I mean number systems like the power set of Reals and power set of that power set etc. And do we do some math(outside of set theoretic math), meaning have big open problems like the millenium prize problems in those number systems? Or is it more or less corect to say that almost all of our current math research is done in Computable numbers and mathematics in those "higher infinities" is too hard for our finite brains?
Thank you for your answer.