User talk:Dfeuer/Interior Point of Interval/Densely Linearly Ordered Space/Lemma

Is this even worth proving? --Dfeuer (talk) 23:51, 5 February 2013 (UTC)

I reiterate my plea (which I'm approaching making a demand) that you stick to posting up published work, as your ambition clearly outstrips your abilities. The suggestion was made that you start working through Munkres (as you appear to have access to it). --prime mover (talk) 06:13, 6 February 2013 (UTC)

As I have so far made more substantial improvements to your mathematical work than you have to mine, I urge you to quit insulting me. I don't claim to have as much education or experience as you, or any sort of grand mathematical insight, but I am obviously more careful in my proofs. I will try to do some work on Munkres, sure, but cut the crap. As for this particular page, I am quite capable of proving this theorem, but I realized it takes nearly as long to state as to prove, so its value is dubious. --Dfeuer (talk) 06:53, 6 February 2013 (UTC)

Statements of truth are not insults. Yes, you have made lots of footling fussy little fiddles to a lot of the pages on this site, yes, but material of substance? Not much. --prime mover (talk) 07:22, 6 February 2013 (UTC)

PM. You currently exhibit a malignant tendency to reason based on emotional arguments, especially against Dfeuer. This detracts from your credibility and authority. Come on, you are beyond this.

As for "it takes as long to state as to prove", that's immaterial - and it is for any other page as well. Back to the actual content. If I read it correctly, this will be a required step in the proof of the result it is a lemma for. It will thus have to be proved, whether on a separate page or not. Because it is still in user space, you might as well prove it. If it turns out to be more appropriate to enter into the main proof directly, at least the argument's already written. --Lord_Farin (talk) 08:03, 6 February 2013 (UTC)

Lord_Farin, the difficulty here is that it's very difficult to decide what the "main proof" might be. The closest analogy to the reals is that an interval of the form $(a,b)$, $(a,b]$, $[a,b)$, or $[a,b]$ in a close packed lospace which is unbounded above and below. However, it can be generalized immediately to a close packed lospace where $a$ is not a lower bound of the space and $b$ is not an upper bound of the space. It can also be generalized to a lospace that is in some sense I haven't thought about dense around $a$ and $b$. Lots of different options, none of them interesting. It's always true that $(a,b) \subseteq \operatorname{Int}([a,b])$, but this is entirely trivial. My current view is that this entire concept (except for the reals) should be stuck behind the washing machine until someone actually needs a specific form of it for something (or it comes up in a text). --Dfeuer (talk) 16:46, 6 February 2013 (UTC)

Fair enough, then. I see your point. May I suggest leaving the page up for possible future reference rather than deleting it? --Lord_Farin (talk) 18:11, 6 February 2013 (UTC)