Talk:Upper and lower bounds

message: Hi. I'm trying to solve for P versus NP problem, and I don't know how subset S and partially ordered set K relate to the various bounds of M. I would appreciate clarification about this, for both myself and others who visit here, to thereby understand and use the concepts on this page. Thank you for reading this. Somethingsea (talk) 02:37, 15 September 2016 (UTC)
thread_title: How does S & K relate to M?

message: If lower bound is going to redirect here then the page should probably be renamed. One does not expect to end up at upper bound if one follows a link to lower bound... Evercat 02:42, 25 Mar 2004 (UTC)
thread_title: Comment

message: this stuff is very complicated. there should be an example so ppl like me can figure out how to solve a problem --Jaysscholar 22:19, 12 October 2005 (UTC)
replies: text: I contest that this article should either initially redirect to Supremum or explicitly mention the distinctions between upper bounds, least upper bounds/supremums, and maximal elements. I doubt that many non-specialists would immediately accept 704 as an upper bound for the set of all negative numbers; they might not realise they need to prefix "upper bound" with "least" in order to find the article they expect. It might solve Jaysscholar's problems, too. Endomorphic 23:43, 13 November 2006 (UTC)
thread_title:  can i get an example? 

message: Some scholars use the expressions "upper-bounded" and "lower-bounded" (a Google search provides several examples). Yet it does not feel like good English. I would appreciate it if somebody can comment on the usage of such expressions and to what degree it is accepted in the professional jargon (it clearly exists there). AmirOnWiki (talk) 14:47, 25 September 2011 (UTC)
thread_title:  Upper-bounded 

message: This subsection is confusing. It is titled "bounds of functions" but it talks about bounds for sets of functions. It also uses a comparison of functions, which may confuse the reader as it has not been defined in the current article
(it is defined in partially ordered set).  If one knows how functions are compared, the case of a set of functions is not different from any other set, so I don't see why this subsection is at all needed.  AmirOnWiki (talk) 15:06, 25 September 2011 (UTC)
thread_title: Bounds of functions

message: In regards to:
   2 and 5 are both lower bounds for the set { 5, 10, 34, 13934 }, but 8 is not.
How can 2 be the lower bound of the given set, when it is NOT part of the set?  
I can see that '8' is not the lower bound, but it seems that something is missing - how can I test the bounds of the given set against a number that is not part of the set? (an example from computer programing is when testing a list or vector to determine if it contains a given element, the method will return a -1 to indicate that the element does not exist, rather than the position in the list - I don't want to confuse the issue, I just saying...). 
If there is some rule that allows '2' to be the lower bounds of the given set, even though '2' is not part of that set, then couldn't it be said (applying the same rule) that '2' is also the lower bound of the other sample set, to wit: {42}?
Lastly, I belive that is it poor grammer to start a sentance with a number (i.e. "2 and 5 are both...")
 — Preceding unsigned comment added by 192.136.15.178 (talk) 16:49, 14 January 2013 (UTC)
replies: text: You are missing that there are really two sets involved: The partially ordered set, and the subset. In the example, the partially ordered set is not explicitly stated, but from the explanation afterwards it is obviously intended to be the set of real numbers with the usual order. The subset is the set {5, 10, 34, 13934}. Now the lower bound needs only to be in the partially ordered set, not in the subset. Now clearly 2 is a real number, that is, an element of the set of real numbers, and therefore it is a lower bound of {5, 10, 34, 13934}.  --132.199.99.50 (talk) 10:18, 14 September 2016 (UTC)
thread_title:  What am I missing here?

message: Can we say this about all preorders, not just posets? ciphergoth (talk) 12:11, 7 December 2015 (UTC)
thread_title:  Preorders? 

message: one can also have an upper bound in a set that's more complicated than the picture  — Preceding unsigned comment added by 2610:130:102:800:18FA:ED36:6C57:8F83 (talk) 12:27, 5 April 2017 (UTC)
thread_title:  misleading 

message: The text says "The upper bound is called sharp if equality holds for at least one value of x." but the referenced source does not support that.  As an example of sharp (or tight) bounds that never achieve equality, see my preprint at math arXiv, in which some of the "tight" bounds only approach equality in a limit.  I'm no mathematician, so not sure what's the best way to state this.  And is there a difference between sharp and tight?  Dicklyon (talk) 03:21, 19 April 2021 (UTC)
thread_title:  Sharp and tight bounds of functions