Talk:Real projective line

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[edit] Created new article

I have started the article. It is nowhere near complete, but I must take a break now (will continue working on it later today). In the meantime, I will gladly hear any comments, and invite everyone to improve the format. -- Meni Rosenfeld (talk) 10:55, 24 January 2006 (UTC)

On the format, the use of self-links is against basic good practice.

On the content, I'm concerned that this has little of the content I'd expect of a projective line explanation; such as homogeneous coordinates, the transitivity of Möbius transformations, the interpretation as one-dimensional subspaces of a two-dimensional space. Charles Matthews 21:51, 24 January 2006 (UTC)

Agree with Charles. The emphasis of this article should be on projective geometry—of which there is barely a mention—not on arthimetic operations on this structure. I would hardly say that "the most interesting feature of this structure is that it allows division by zero". -- Fropuff 23:09, 24 January 2006 (UTC)

About format, what did you mean by self-links?

About "little of the content...", like I said, this article is nowhere near complete. I will need the help of all of you to finish it...

About what is interesting, that is of course subjective. I have written mostly about things that I find interesting and that I understand. Admittedly, I don't understand very well all the topological and geometrical implications, and I find them less interesting than the arithmetic and analytical ones. Also I wrote more about what is special to this structure, rather than generic things which hold for every 1-point compactification (which can be found in the projective line article). These things should of course be here as well, and I will continue to add things that I know, but I will need your help in those points that I'm not proficient at. For now, I'll rewrite the "most interesting feature" part to be more NPOV.

And also, if anyone is skilled enough to create an image of the circle representing this structure, that would be great. -- Meni Rosenfeld (talk) 08:02, 25 January 2006 (UTC)

BTW did you mean the projectively extended real numbers thing? I did that mostly for emphasis, I will change that if you think it's wrong. -- Meni Rosenfeld (talk) 08:04, 25 January 2006 (UTC)

Yes, that's a self-link because the redirect comes back to the page. Charles Matthews 08:17, 25 January 2006 (UTC)

fixed :) -- Meni Rosenfeld (talk) 08:37, 25 January 2006 (UTC)

[edit] a / 0 = ∞

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)

[edit] Intrval arithmetic

From the article, we have for

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 , 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)

I'm not sure I understand. If then, by the formula above, . 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)

Ah, sorry, I must have missed that. CRGreathouse (t | c) 06:32, 27 September 2006 (UTC)