Talk:Normed Dual Space of Infinite-Dimensional Normed Vector Space is Infinite-Dimensional

I'm not sure I understand the objection to the theorem statement. We take an infinite dimensional normed vector space, and suppose that $X^\ast$ is finite-dimensional, then derive a (surprisingly non-trivial) contradiction, so $X^\ast$ must have infinite dimension. We always know $X^\ast$ has some non-zero elements (provided $X$ is not just $\set 0$) by Hahn-Banach, though I don't repeat this on each page invoking the definition. I should probably stick Normed Dual Space Separates Points in the "Also See" of that definition page. Caliburn (talk) 15:36, 14 June 2023 (UTC)