Talk:Piecewise property

Origin

A disambigation was requested at Talk:Piecewise_function#Requested_move_20_July_2024. I split the part here that did not apply to the new title. 142.113.140.146 (talk) 00:55, 25 August 2024 (UTC)

Requested move 26 August 2024

Piecewise property → Piecewise – The "piecewise" isn’t a property in the way, say, the continuity is a property of a function. The same point has been made by other editors at Talk:Piecewise_function#Requested_move_20_July_2024. Taku (talk) 08:08, 26 August 2024 (UTC)

• Support: "piecewise" is an adverb that describes how a property relates to a function, such as "piecewise differentiability". IntGrah (talk) 09:27, 26 August 2024 (UTC)
• Oppose. Article titles should be WP:NOUNs. In any case, "piecewise" is a property of a definition of the function, whereas e.g. piecewise continuous is a property of the function itself. Tercer (talk) 09:50, 26 August 2024 (UTC)
• Support Alt Piecewise (disambiguation) to fix the {{redir}} hatnote WP:INTDAB. Not just Piecewise because a piecewise function is the topic most discussed in math resources and "whatever readers might type in the search box". The parentheses alleviate the NOUN and internal-only property comments my previous RM made and others reiterated here 142.113.140.146 (talk) 10:28, 26 August 2024 (UTC)
• Oppose: there is very little new content here, it'd be easier to merge it into a section of the main article, e.g., Piecewise-defined function#Generalizations (or "Extensions" or "Related concepts"). fgnievinski (talk) 13:38, 27 August 2024 (UTC)
• Support per nom. This isn't an article, so it doesn't need to strictly adhere to the WP:NOUN principle. It's simply there to disambiguate between different usages of piecewise on the project.  — Amakuru (talk) 10:25, 3 September 2024 (UTC)

Definition

(refactored from Talk:Piecewise_property#Requested_move_26_August_2024)

Is piecewise [continuous differentiable] [really] a property of the function itself? The absolute value piecewise-defined function is. But counterexample: $\left|\sin(x)\right|$ with domain restriction $\left[0,4\right]$ is non-differentiable at $\pi$ and is defined using 1 subfunction. Redefine it with 2 identical subfunctions and it becomes piecewise differentiable. These are contradictory properties as "the function itself" is the same under equality of $(x,y)$ pairs. 142.113.140.146 (talk) 10:51, 26 August 2024 (UTC) 174.89.12.36 (talk) 23:44, 11 September 2024 (UTC)

It is always piecewise differentiable, doesn't matter how you define it. Tercer (talk) 14:09, 26 August 2024 (UTC)

So you're saying it's iff it admits a definition that is. The article should say that. I added it. 142.113.140.146 (talk) 18:20, 26 August 2024 (UTC) 174.89.12.36 (talk) 23:44, 11 September 2024 (UTC)

I don't really see where that College Board source you cited asserts a different meaning of piecewise differentiability. SilverLocust 💬 22:57, 4 September 2024 (UTC)

@SilverLocust: The College Board source's Theorem 2 requires the definition to be examined for $p(x)$ and $q(x)$. This is not a different meaning but the article's original definition. The next 2 sources contain the generalization in this thread. The Nikolsky source does not require a definition (see no {), and supports the new claim doesn't matter how you define it. 174.89.12.36 (talk) 23:54, 11 September 2024 (UTC)

It doesn't even mention piecewise differentiability anywhere, just differentiability of a piecewise-defined function at a point. SilverLocust 💬 00:26, 12 September 2024 (UTC)

Idk how to fix this, so I put up a {{bsn}}. I prefer Tercer's generalization, but the rest of the article uses the version that looks at the subfunctions. 174.89.12.36 (talk) 01:44, 12 September 2024 (UTC)