>>12478509The cardinality of the reals is 2^aleph_0.
The hyperreals are sequences of reals quotiented out by some ideal. Sequences of reals have cardinality (2^aleph_0)^aleph_0=2^(aleph_0 * aleph_0) = 2^aleph_0, so the cardinality of the hyperreals is at most the cardinality of the reals.
Since the reals inject into the hyperreals, we get the inequality other way around. QED
That said, none of this makes any sense and is basically infinitist schizo nonsense. Don't take it seriously.
