Talk:Continuity property

Hmm
I can't say I like this article very much. What is the "contiuity property" a property of? Why is this article separate from the one on the intermediate value theorem. (The latter article is something of a small Augean stable (if the juxtaposition of "small" and "Augean" isn't too oxymoronic) that needs to get cleaned up; it's messy.) Michael Hardy 14:10, 16 Aug 2003 (UTC)

I also don't get this article. I do not think this terminology is standard. (Is it a translation?) It's certainly not a characterization of continuity. And it follows immediately from f(compact) is compact, f(connected) is connected, and characterization of intervals in R.


 * Becasue it's also used for Rolle's theorem? Rich  Farmbrough 22:44 15  March 2006 (UTC).

Article should be deleted
This article does nothing more than combine the extreme value theorem and the intermediate value theorem under a new name. It contained proofs of the latter two assertions (the third assertion's proof was quite unclear if not outright wrong), but I have replaced them with links to existing proofs elsewhere on Wikipedia. It was only cited by the Rolle's Theorem article, but I have updated the link there to point to the extreme value theorem directly, so it is no longer linked to by any other articles on WP. Furthermore, a quick Google search reveals no other sources that use this name or convention. This article seems a clear candidate for removal. Detritus 14:15, 25 July 2007 (UTC)
 * Hi Detritus. I've reverted your changes for now. In particular I've removed the "prod" tag. There are reference works that use term (I've added one to the article). If you would like to submit the article to WP:AFD, so that more editors can review this, please do. Paul August &#9742; 03:17, 20 March 2008 (UTC)
 * Dear Paul,


 * I am disappointed by your reverts to Continuity property, as the proofs you have reverted to are


 * a) unnecessary (duplicated elsewhere; I had linked to them)


 * b) opaque (all of the points proven are proven much more elegantly elsewhere; for example, you may notice if you look carefully that the "proof to claim 2" is a poor proof of the fact that compact subsets of R are bounded)


 * c) Just plain wrong. Cf. the proof of claim 3, whose notation is confusing and wrong. $$

A = \{ x \in \mathbb{R} : f(x) \leq M \} $$ should instead refer to the image of [a,b].


 * Your reverts are thoughtless and rash. I am an undergraduate with one semester of Analysis under my belt; last summer, before taking the course, I ran across the page in question and spent several hours trying to make sense of its abstruse constructions. You have done nothing but set up another undergraduate to waste his or her time with this.


 * Furthermore, regarding your citation of Binmore's "straightforward approach," let me remind you that Wikipedia is not a dictionary. Detritus (talk) 20:15, 22 March 2008 (UTC)