Commit 2023-08-22 03:35 8f782305
View on Github →feat: compute rank of ℂ and ℝ as ℚ-modules (#6672)
This adds a trivial cardinality argument that shows that when V is a free K-module where K is infinite and satisfies the strong rank condiiton, then the rank of V coincides with its cardinality. This is then used to establish that Module.rank ℚ ℝ = continuum = Module.rank ℚ ℂ, and therefore that ℝ and ℂ are isomorphic as vector spaces over ℚ.
As requested on Zulip