Talk:Sequential Right-Continuity is Equivalent to Right-Continuity in the Reals

Just realised this duplicates Limit of Function by Convergent Sequences, oops. Will revise soon. Caliburn (talk) 20:08, 3 January 2022 (UTC)


 * Might be worth slapping a Mergeto template on both pages so we have a record of it in the meantime. --prime mover (talk) 23:48, 3 January 2022 (UTC)


 * Now that I've looked into it, I think it's worth retooling Limit of Function by Convergent Sequences/Corollary to talk about points that are not necessarily boundary points, and having these two results as corollaries. I will have to come back to sorting out real analysis in its own right at some point. Caliburn (talk) 00:44, 4 January 2022 (UTC)


 * Now I've taken a look at both pages, I see they both say different things. One expresses a result in real analysis, the other is for the general metric space. As per usual, we make sure we keep a thread going devoted solely to analysis in the context of real analysis without subsuming any knowledge of metric spaces. Then we implement a second proof of the real-analytical result using the metric space properties of the real number line.


 * But even then, when I look even more closely, they are not actually the same result at all. One demonstrates continuity, the other demonstrates right-continuity, which (while it applies to the real number line) does not apply to the general metric space because it relies upon the fact that the real numbers form a total ordering. --prime mover (talk) 07:05, 4 January 2022 (UTC)