Talk:Projectively extended real line

message: Regarding this edit, I think that the definitions of the artithmetic operations should be given separately for real numbers and ∞. That is, a will always stand for a real number, and ∞ will be explicitly called ∞. I think it will be clearer this way how these definitions extend the operations on real numbers. Any ideas? -- Meni Rosenfeld (talk) 15:27, 25 August 2006 (UTC)
thread_title:  ''a'' / 0 = &infin; 

message: From the article, we have for a,b\in\widehat{\mathbb{R}}
:x \in [a, b] \iff \frac{1}{x} \in \left [\frac{1}{b}, \frac{1}{a}\right ]
But what about [-1, 1]?  In 'ordinary' interval arithmetic this would be either undefined or the negation of (-1, 1) -- it can be infinite, but not strictly smaller than 1 in absolute value.  But the formula above gives [1,-1]=\emptyset, which seems to contadict the article's claim that the result is always an interval.  Or rather, if we accept this as an interval, it no longer follows that the interval contains the results of calculations with points inside the original interval (since 1/0.8 is defined and not in [1, -1]), which would make interval arithmetic useless. CRGreathouse (t | c) 23:24, 25 September 2006 (UTC)
replies: text: I'm not sure I understand. If x \in [-1, 1] then, by the formula above, \frac{1}{x} \in [1, -1] = [1, \infty) \cup \{\infty\} \cup (\infty, -1]. What's the problem? Are you sure you've read the "Definitions for intervals" subsection just before the "Interval arithmetic" section? -- Meni Rosenfeld (talk) 08:47, 26 September 2006 (UTC)
replies: text: Ah, sorry, I must have missed that. CRGreathouse (t | c) 06:32, 27 September 2006 (UTC)
thread_title:  Intrval arithmetic 

message: I would love to understand this article. Especially since I put the image in my signature. Any work that can be done to better explain it is awesome, and if you want to try to break it down for me too, it's much appreciated!-- Patrick {oѺ∞} 06:37, 24 July 2009 (UTC)
thread_title:  In English? 

message: I oppose to this merge. As the subject which is studied is essentially the same, the presentation is not the same. The main difference is that, here, the projective line is not considered independently from the choice of an embedding of the real line into it, while in Projective line, there is no distinguished point ∞. It follows that Real projective line is more elementary than Projective line. However, the different scopes of the two articles must be clarified. This is clear in Projective line, where the other article appear in a  template. I'll be bold and clarify this article by editing the top and moving this article to Projectively extended real line. D.Lazard (talk) 08:15, 11 April 2015 (UTC)
replies: text: I also oppose the merger, essentially for the same reasons D.Lazard has given. This article makes a big deal of the arithmetic structure that is not canonical in the general projective line.  This was essentially behind my comments in the thread above.  I strongly support the move as done by D.Lazard. —Quondum 15:39, 11 April 2015 (UTC)
replies: text: Oppose merger as per . Not withstanding my comments in the above thread, this specialization of the general projective line is the most common way for readers to approach the subject from different fields of mathematics. To have that buried as a section in a more general article seems like a disservice to our readers. I also support D. Lazard's move as it brings some clarity to the subject. Bill Cherowitzo  (talk) 17:43, 11 April 2015 (UTC)
replies: text:   I think we have reached a generally agreeable result: the general reader who understands the specialization under the name "real projective line" is still pointed at this article via the redirect. And yes, I agree that this should not be buried as a section of Projective line. —Quondum 17:50, 11 April 2015 (UTC)
thread_title:  Merger proposal 

message: This article and Real projective line seem to be talking about the same thing. Do you think both articles should be merged? Llightex (talk) 18:18, 3 August 2015 (UTC)
replies: text: No.  The projectively extended real line is the real line with a point added at infinity.  The real projective line is the space of one-dimensional linear subspaces of a two-dimensional real vector space.  These are rather different, and can only be identified when some extra structure is specified.  SławomirBiały 18:24, 3 August 2015 (UTC)
replies: text: Although the previous proposal was to merge with Projective line, most of the length discussion, above, was about the new merge proposal. This may be unclear as, as that time, the article real projective line did not yet exist. Nevertheless, a consensus has been reached for the need of two different articles Projectively extended real line and Real projective line. Thus, I oppose to this merge, for the same reasons as those that are above  developed. IMO this discussion does not need to be continued, unless if new arguments are provided, that could change the consensus. D.Lazard (talk) 20:02, 3 August 2015 (UTC)
thread_title:  Another merger proposal