The cardinality of the complex numbers

This file shows that the complex numbers have cardinality continuum, i.e. #ℂ = 𝔠.

@[simp]

theorem mk_complex : Cardinal.mk ℂ = Cardinal.continuum

The cardinality of the complex numbers, as a type.

theorem mk_univ_complex : Cardinal.mk ↑Set.univ = Cardinal.continuum

The cardinality of the complex numbers, as a set.

theorem not_countable_complex : ¬Set.Countable Set.univ

The complex numbers are not countable.