Wikipedia:Articles for deletion/Infinity plus one


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was no consensus. No apparent consensus to delete, but also none for any specific alternative. Fortunately other options don't specifically require an AfD, so discussion about moving, etc, can continue on the article Talk page. RL0919 (talk) 00:05, 16 January 2022 (UTC)

Infinity plus one

 * – ( View AfD View log | edits since nomination)

This is hardly about "infinity plus one", so much as a brief rehash of several existing articles about different kinds of infinity. It would appear that "young people's ideas of infinity", as detailed at, is a noteworthy topic, but the sources seem to focus only on infinity in educational contexts or on specific formalisms of infinity such as the surreal numbers. –LaundryPizza03 ( d c̄ ) 23:29, 30 December 2021 (UTC) Please add new comments below this notice. Thanks,  Sandstein   09:39, 7 January 2022 (UTC)
 * Note: This discussion has been included in the list of Mathematics-related deletion discussions. –LaundryPizza03 ( d  c̄ ) 23:29, 30 December 2021 (UTC)
 * Comment: Would redirecting to Ordinal number (the target of the ω+1 redirect) be a reasonable alternative to deletion here? Maybe it's using "infinity" too narrowly, but just a thought. — MarkH21talk 00:03, 31 December 2021 (UTC)
 * Comment: I won't disagree with deleting it. (Note: I created this article 16 years ago! It had significantly different, and not very encyclopedic, content.) The title is perhaps fairly nonsensical, but I do think this serves some purpose as a jumping off point for different ways to think about addition involving various infinities. The content is probably found elsewhere (e.g. the ω + 1 addition rules are already given in the ordinal addition article), but how would one know to look there? Also it would be good to preserve the references like Tall's "A child thinking about infinity", which I found highly interesting (that could perhaps go into the infinity article itself). &mdash;MattGiuca (talk) 00:42, 31 December 2021 (UTC)
 * Comment. The 200+ hits for this phrase in Google Scholar suggest that this could be an encyclopedic topic and sources like the section "infinity plus one" in Higgins' Number Story might be usable as sources. The fact that this calculation is meaningful and has different results in number systems like the ordinals and the surreals is worth pointing out somewhere and would be lost in any redirect to a specific choice among those meanings. But the article as it stands now is too essay-like and undersourced to retain. —David Eppstein (talk) 01:22, 31 December 2021 (UTC)
 * This could potentially serve as a rather useful disambiguation page for concepts related to infinity plus 1. For example Hilbert's paradox of the Grand Hotel. snood1205 02:38, 31 December 2021 (UTC)
 * Comment Here are the two current references for a potential new article or section about "mental notions of infinity"; I'm not sure what a good title would be. (A third reference, a 1995 Discover article about the surreal numbers, was dropped.) –<b style="color:#77b">Laundry</b><b style="color:#fb0">Pizza</b><b style="color:#b00">03</b> ( d c̄ ) 03:16, 1 January 2022 (UTC)
 * Keep, but turn into disambiguation/outline page. The article in its current form is basically already such a page, so it would just need to be reformatted. "Infinity plus one", as a concept, is used throughout mathematics, philosophy and adjacent disciplines, so it would be nice (and encyclopedically valuable) to have such an overview of the topic. I would be willing to perform the conversion. TucanHolmes (talk) 16:15, 2 January 2022 (UTC)
 * Keep per TucanHolmes. The idea of "infinity plus one" is commonplace and evidently has received scholarly attention; it hasn't been formalized into a single cohesive concept but rather into multiple concepts, and there is undoubtedly scope in an encyclopedic context for a page to direct readers to those relevant concepts (potentially with brief elaboration). It would be a disservice to readers to delete the guidepost. --JBL (talk) 12:06, 5 January 2022 (UTC)
 * <p class="xfd_relist" style="margin:0 0 0 -1em;border-top: 1px solid #AAA; border-bottom: 1px solid #AAA; padding: 0px 2em;"> Relisted to generate a more thorough discussion and clearer consensus.
 * Keep per TucanHolmes. The idea of "infinity plus one" is commonplace and evidently has received scholarly attention; it hasn't been formalized into a single cohesive concept but rather into multiple concepts, and there is undoubtedly scope in an encyclopedic context for a page to direct readers to those relevant concepts (potentially with brief elaboration). It would be a disservice to readers to delete the guidepost. --JBL (talk) 12:06, 5 January 2022 (UTC)
 * <p class="xfd_relist" style="margin:0 0 0 -1em;border-top: 1px solid #AAA; border-bottom: 1px solid #AAA; padding: 0px 2em;"> Relisted to generate a more thorough discussion and clearer consensus.


 * Initial thought was delete, but I do believe as a disambig page this would have merit. Going with keep as disambig page per TucanHolmes. — Preceding unsigned comment added by Caleb Stanford (talk • contribs)
 * Redirect to Ordinal_number. Disambiguation does not make sense because someone who is typing or thinking the informal "infinity plus one" is not looking for the surreal or hyperreal numbers.  They should get sent to an explanation of the simplest context in which "infinity plus one" is formally well-defined and distinct from infinity.  I think this is ω+1. Danstronger (talk) 22:09, 10 January 2022 (UTC)
 * The observation (see the comment by user Charles Stewart on this page) that there is disagreement, even on this talk page, on what "infinity plus one" means/includes/is indicates that we should favour a disambiguation page over a simple redirect. Prematurely narrowing the scope of a concept based on assumptions about the average reader and thereby skewing the picture would be a disservice, even to that average reader, since they wouldn't actually realise that "infinity plus one" is so much more than the ordinals, and that there are different notions of infinity. TucanHolmes  (talk) 16:35, 13 January 2022 (UTC)
 * Comment - The article as it stands makes an important point, namely that observations such as Hilbert's Hotel show us that set-theoretic cardinality doesn't provide a basis for fine intuitions about addition, but von Neumann ordinals and similar do. Beyond that, the discussion risks venturing into OR. Personally, I'd say surreal numbers provide a richer notion of ordinality, based on a richer counterpart to set-theory, while hyperreal numbers are an interesting algebraic artefact we get from nonstandard analysis that isn't grounded in clearly coherent intuition. But I wouldn't add that to the article. I get the sense that keep voters in this AfD agree that a disambig page with a little motivation makes sense, but I don't get the sense that there is agreement among them as to what the article should look like. 17:49, 11 January 2022 (UTC)&mdash; Charles Stewart (talk)
 * Comment – If no subtopic is dominant enough to be the target of a primary redirect then this should be a broad-concept article. The current layout is helpful and should be retained but is wildly non-compliant with WP:DABSTYLE, so it does not qualify as a disambiguation page.  Certes (talk) 16:05, 12 January 2022 (UTC)
 * We have a model for such a broad-concept article in 0.999.... If I felt the energy was there to recreate this success, I would certainly support this. &mdash; Charles Stewart (talk) 15:48, 14 January 2022 (UTC)


 * Comment It's a bit odd that the infinity template has a row called "Formalizations of infinity" but there's no article about that. That seems like the concept that this page is really about.  I suggest renaming this to / creating a "Formalizations of infinity" and "infinity plus one" can redirect there.  There's nothing special about "infinity plus one" in particular that actually has significant RS coverage or warrants its own page. Danstronger (talk) 22:57, 13 January 2022 (UTC)
 * Another point in favour of renaming or reorganisation is that "infinity plus one" is often a proxy/example for "Infinity plus any positive integer n". The main exception is the successor ordinal of (some flavour of) infinity. Certes (talk) 23:33, 13 January 2022 (UTC)
 * I'm in favour of having, eventually, this page be a redirect to a section of an article that gets at what it is we are talking about. It seems to me, though, that "infinity plus one" has a life as a concept before we engage in formalisation, supported by, e.g. the two refs found. If we were allowed to have an OR title, I'd prefer something like 'The fine structure of infinity', something more acceptable might be 'Mathematics of infinity', which could be a main article for that section of Infinity. &mdash; Charles Stewart (talk) 13:57, 15 January 2022 (UTC)


 * Move to "Formalisations of infinity" per Danstronger and then work on the article from there. Felix QW (talk) 11:21, 15 January 2022 (UTC)


 * The above discussion is preserved as an archive of the debate. <b style="color:red">Please do not modify it.</b> Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.