Talk:Primitive recursive function: Difference between revisions

Revision as of 22:57, 28 February 2024

Latest revision as of 03:36, 9 March 2024

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{{WikiProject banner shell|class=B|vital=yes|1=

{{WikiProject Mathematics|priority=Mid|field=foundations}}

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:Moreover, these sections are not sourced. This could be a reason for removing them as [[WP:OR]].

:So, I have reverted your tag removals. Please do not remove them again without addressing the issues of these sections. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 10:08, 28 February 2024 (UTC)

:: According to [[Second-order_arithmetic]] there is more than one PA. Which might be contextually relevant, since the principia used higher order logic, as noted by Gödel 2.1 Definitions https://hirzels.com/martin/papers/canon00-goedel.pdf

:: [[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 12:33, 28 February 2024 (UTC)

:: Nobody uses the terminology "multivariate" in recursion theory. The term n-ary means a function with n-arguments. The Cantor [[Pairing_function]] can be used to encode two or more arguments in one argument, and its also possible to reverse the process. The function is itself primitive recursive, so are its projections.

:: [[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 23:02, 28 February 2024 (UTC)

About the used references in the article. Instead of Rose as reference for Elimination of Parameters, its seems you could also use Moschovakis 1994, ch. 5.

Or as SEP has put it, they show the other way around from h, to h2 and then to h1, but then have the following remark:

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:You do not adress the main issue of these sections. Wikipedia is not for summarizing some specific articles, relying on these articles to know author's definitions of the technical terms. The aim of an encyclopedy is to present the most important results in a language that is compatible with the most common terminology, and is accessible to (in the case of this article) a undergraduate student in mathematics. It must also be clear why a result is important enough to belong to the article (per [[WP:UNDUE]]). Neither the sections under discussion nor your above comments satisfy these requisites. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 14:12, 28 February 2024 (UTC)

::To reduce complexity of the article I would split off Gödel, and I would also split off LOOP/WHILE. Devote separate articles to the two, would make the primitive recursive article more readable and less cluttered with applications of the notion primrecprimitive recursive in Gödels theorem and computational devices such as LOOP, that show primitive recursive behaviour.

::[[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 22:41, 28 February 2024 (UTC)

I have deleted the first disputed section,

The wording of the two banners is wrong, given Lazard explanation. The wording

and move the second disputed section to here:

of the banner says there is a "what for" missing by means of an uneducated "I guess" of the layman that put down the banner. It is obviously factual not true for the present text that a "what for" is missing, only a layman that doesn't understand the first paragraph and the last two pagagraphs can claim such a nonsense.

[[Gödel's β function]]

There I would also like to add a reference to this:

PRIMITIVE RECURSIVE FUNCTIONS by<br>

Zéev Rosenfeld - March 1959<br>

Department of Mathematics McGill University Montreal.

But I don't know how to edit and add a reference.

The Lazard explanation tells a different story. It talks about a) addressing people in a common language b) setting priorities for inclusion/exclusion. So the banner should have a different phrasing, to not form the laughing stock of Wikipedia.

[[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 22:51, 28 February 2024 (UTC)