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

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: no consensus. Clarity did not develop. (closed by non-admin page mover) -- Maddy from Celeste (WAVEDASH) 14:15, 3 October 2024 (UTC)

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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) — Relisting. Steel1943 (talk) 21:20, 17 September 2024 (UTC) — Relisting. BD2412 T 01:01, 25 September 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)
• Oppose – the current noun phrase title makes good enough sense, better than just the adverb. Dicklyon (talk) 04:49, 16 September 2024 (UTC)

Relisting comment: Relist one more time to see if clarity develops BD2412 T 01:01, 25 September 2024 (UTC)

• Move to List of piecewise properties or Types of piecewise functions or List of piecewise function types or merge into Piecewise function. The content of this article is not really a disambiguation page. It's more of an article or a list. It's not an explanation of various different meanings for the phrase "Piecewise function" or "Piecewise". —⁠ ⁠BarrelProof (talk) 19:49, 25 September 2024 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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)