Talk:Real coordinate space

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Untitled

See talk: Euclidean space/Archive 1 for background.

Redirects

I would re-direct to here redirects real n-space, R-n, R^n, standard topology, and usual topology. Some new, such as Rⁿ, R^3, R^4, ℝn, ℝⁿ, ℝ^n, ℝ², ℝ³, and ℝ⁴, will possibly be created too. Objections? Incnis Mrsi (talk) 10:38, 16 April 2013 (UTC)[reply]

Needs more even coverage of applications

In my current version certain applications are explained rather detailed (geometry, linear programming), some are explained but briefly (topology, differential geometry, mathematical analysis), and some are not even mentioned (differential equations, probability theory). Could anybody help to compile a list of all notable applications of $R n$ ? Incnis Mrsi (talk) 08:09, 21 April 2013 (UTC)[reply]

Reliable sources

Currently there are two sources: Kelley and Munkres. Both use the term "Euclidean space" for this concept. I cannot find any mention of any version of the phrase "real coordinate space". (Further, I have never heard this phrase in my career as a mathematician. But then I am not a reliable source.) It would be nice to support the article with reliable sources. Mgnbar (talk) 21:30, 5 September 2019 (UTC)[reply]

Grid lines on first picture problematic?

I'm not sure I understand the value of having so many grid lines on the [first picture](https://en.wikipedia.org/wiki/Real_coordinate_space#/media/File:Real_2-space_as_square_grid.png). Even under magnification, the one-tenth multiple lines are not super clear, and I don't think many readers are likely to need to place specific points in real 2-space in an encyclopedic context. Maybe more importantly, having only rational numbers marked on the grid could easily be read as suggesting that there's something special about rational numbers in real 2-space, or even that irrational numbers can't be visually represented in it.

I suggest changing this picture so it only has integer lines; it seems much less likely that anyone would read the grid as only capable of representing points with integer coordinates. Plotting some example points with irrational, even transcendental, values could also more clearly show the representative possibilities of the grid.

AdamPronouncedAdam (talk) 01:30, 3 April 2022 (UTC)[reply]

I agree that the picture is problematic. It suggests wrongly that the article is about grids. I will change it. D.Lazard (talk) 08:07, 3 April 2022 (UTC)[reply]

I have changed the image, and, by the way, rewritten the lead. D.Lazard (talk) 09:17, 3 April 2022 (UTC)[reply]

Thank you! The picture is clearer and I think the third paragraph gives a much better sense of the article's importance.

AdamPronouncedAdam (talk) 02:24, 4 April 2022 (UTC)[reply]