Talk:Distance from Subset of Real Numbers

Might this do better to be split up into more than one page? --prime mover (talk) 23:00, 7 January 2009 (UTC)

I would say no, it basically just sets up a bunch of properties of distance from a subset. However, I just realized that we don't have a Definition:Distance page. Should we just make it as a redirect to Distance on Real Numbers is Metric, or should we have a page to define it? --Cynic (talk) 04:00, 8 January 2009 (UTC)

Not sure. I think a new page to define it, now you mention it. --prime mover (talk) 06:33, 8 January 2009 (UTC)

... and now this is done. --prime mover (talk) 07:23, 8 January 2009 (UTC)

If we give a name to $x$ such that $d(x, S) = 0$ (something like "adjacent to $S$" or "bordering $S$"; it'd be interesting to investigate whether in the general metric space, $d(x, S)=0 \iff x \in S^-$), then these five results can easily be formulated on separate pages with concise titles. It's opposite to our recent efforts and general philosophy to leave this amalgamation in place. --Lord_Farin (talk) 11:52, 9 November 2012 (UTC)

Since it is indeed true that $d \left({x, S}\right) = 0 \iff x \in S^-$ in a general metric space, I doubt that such an $x$ merits a name different from Definition:Adherent Point, since that's exactly the same thing. Thoughts? --abcxyz (talk) 19:02, 9 November 2012 (UTC)

If there is already an established name for such $x$, that's even better, of course. --Lord_Farin (talk) 19:07, 9 November 2012 (UTC)