Talk:Smoothness

Infinitely differentiable

Infinitely differentiable redirects here but this page doesn't explain what infinitely differentiable means.

Fixed Abitslow (talk) 15:36, 17 January 2015 (UTC)[reply]

This exact thing, the infinitely differentiable redirect, brought me here as well, and I was equally confused. I was brought here by the Taylor Series page, and near the bottom of that page (Comparison with Fourier series) there is a really good example that helped me understand and that I am going to edit in here. I just wanted to let the talk page know, there is likely more to say on this topic. I am talking about the Weierstrass function, which instead of being smooth and continuous because it has a derivative, is uniformly smooth while having no derivative at any point in its domain. The fact that this function even exists is what allowed me recognise the need for the general taylor series (which has infinite derivatives) to require an 'infinitely differentiable function". As this helped me with why I was directed to this page to begin with, and it directly relates to the topic being discussed, see my edit, I think it makes the most sense to add the information -kindlin (talk) 9:13pm (PST) September 25, 2020.

I have fixed the problem by adding "infinitely differentiable" at the right places. About extending the page ("more to say on the topic"), be care that "smooth" is ambiguous (as stated in the lead). It means "infinitely differentiable" in some contexts, but means also "sufficiently differentiable" in other contexts. I have never heard the term "uniformly smooth" used as a synonymous of "uniformly continuous" (as you did above). In any case, considerations on uniform continuity do not belong to this article. D.Lazard (talk) 10:16, 26 September 2020 (UTC)[reply]

0-forms

The Wikipedia article Exterior derivative claims a smooth function is another name for a 0-form. This seems to me to be true, but I'm no mathematician. If it is correct, that fact should be mentioned here, as well as a link to Differential forms added. It also suggests that the section on Multivariate differentiability should link to it (as well as differential structure, which it now does). Could someone add the verbage and links, if appropriate? Note that the article titled differential structure contains NO mention of differential forms! I don't understand why, but that's another subject. Thx. Abitslow (talk) 15:50, 17 January 2015 (UTC)[reply]

EB1911

The was an article called Geometric continuity which is now a redirect to this article.

Geometric continuity Revision as of 21:11, 1 February 2006 introduced EB1911 without an article name, however there is an EB1911 article called "Geometrical Continuity" volume 11 p. 674–675 Revision as of 03:28, 22 October 2009 merged Geometric continuity into Smooth function which in turn with Refision as of 06:33, 11 September 2014 was was merged into Smoothness (this article).

So I have added the EB1911 article "Geometric Continuity" to the EB1911 template and move the template out of general references and up to be an in-line citation to the two paragraphs in the section "Geometric Continuity". -- PBS (talk) 20:35, 9 October 2018 (UTC)[reply]

I cannot see how the definition of parametric continuity here would be correct, especially not with the camera example. This only applies if the parameter is equal to the arc length. See https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/curves/continuity.html for an example how the definition of continuity depends on the parametrisation of a certain curve. — Preceding unsigned comment added by 2A02:8109:D3F:F49A:9C9C:79CE:9FC4:94FB (talk) 08:00, 14 July 2019 (UTC)[reply]

"Continuously differentiable function" listed at Redirects for discussion

A discussion is taking place to address the redirect Continuously differentiable function. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 October 17#Continuously differentiable function until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 𝟙𝟤𝟯𝟺𝐪𝑤𝒆𝓇𝟷𝟮𝟥𝟜𝓺𝔴𝕖𝖗𝟰 (𝗍𝗮𝘭𝙠) 21:21, 17 October 2020 (UTC)[reply]

Should this article also mention Lipschitz smoothness?

Voggum (talk) 19:17, 19 December 2021 (UTC)[reply]

It is a real shame

that this article does not make clear that "smooth" is a technical term that usually means "infinitely differentiable".

Instead, the unfortunate introductory section makes it appear that "smooth" can mean almost anything.