Bigger infinity than real number infinity

Question

Is there a bigger infinity than the infinity of cardinality of the real numbers $R$ ? i.e. is there a set to which real numbers can't be mapped one-one to ?

Answer 1

Yes there is. P(R) = {every subset of R}. There is a theorem that states that for every set g |p(g)|>|g|.
That means that for R: |p(R)|=2^א < א=|R| That also means that the real numbers cannot be mapped one-one to every subset of the real numbers R