Talk:Infinity plus one

untitled

The following discussion 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.

---

Some citations would be appreciated. If anyone can find them --FK65 20:47, 18 October 2006 (UTC)

Well:

• Monaghan, John (2001). "Young Peoples' Ideas of Infinity". Educational Studies in Mathematics. 48: 239–257. doi:10.1023/A:1016090925967. {{cite journal}}: |format= requires |url= (help)

I happen to have access to it. Monaghan is actually critical of the idea that young children's concept images of "infinity plus one" correspond to the ordinal number in question, on the basis that they usually think of infinity instead as "a vague generalisation of a large number". Another ultimately skeptical voice is:

• Tall, David (2001). "A child thinking about infinity" (PDF). Journal of Mathematical Behavior. 20 (1): 7–19.

This one is more mathematical and less cognitive:

• Shulman, Polly (1995). "Infinity Plus One, and Other Surreal Numbers". Discover. 16 (12). {{cite journal}}: Unknown parameter |month= ignored (help)

I think we ought to clean up the article before listing any of these as references, though. Melchoir 21:25, 18 October 2006 (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.

Unrelative infinity

The following discussion 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.

---

Isn't Unrelative infinity a repeating number of nines in both directions of the decimal point because 888888...88.99999.. would not be the maxamum number because you can create a larger number which is 999999..99999.99999.....

Also if infinity plus one is equal to infinity then if you subtract infinity on both side of the equation we can see that 1=0 in which we could prove anything. However infinity plus one is equal to x but if you think about it their is no real number for x thus it is a form of an imaginary number. oo+1=oo, then oo-oo+1=oo-oo, 1=0 which cannot happen however oo+1=(a form of an imaginary number), then oo-oo+1=(a form of an imaginary number)-oo, then 1=1 which works.

but then again what do I know?

Ps: dare, what does that have anything to do with mathimatics

Try Ordinal arithmetic. At the bottom of the Addition section, it notes "Unrestricted subtraction cannot be defined for ordinals." Melchoir 02:18, 13 December 2006 (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.

Silly...

The following discussion 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.

---

This is a preeeeetty pretty silly article, is it meant as a joke?? All the Child one: Child two: stuff?? I can't see that any of it serves any useful purpose whatsoever, but I suppose other think differently? 82.69.77.254 (talk) 09:26, 12 October 2008 (UTC)

-perhaps the mathematical stuff is interesting, but I don't know if that's all legit. 82.69.77.254 (talk) 09:27, 12 October 2008 (UTC)

Well, there are certainly cultural aspects to the use of this phrase. However, there should be mention that this is due to the general public's incorrect perception of "infinity", which the article doesn't make clear. Mindmatrix 22:03, 12 October 2008 (UTC)

Aside: apart from movies, TV. and music, the phrase also appears on t-shirts, for Google's extension to unlimited email storage (to "best" Yahoo's similar announcement), and a bunch of articles on .edu sites (most are irrelevant, but a few are OK). There's also this, this, and this, and possibly a few good links in this. There's a mention in this paper (PDF - On unbounded eigenvalues in particle-transport theory), and this one (PDF - Accepting Infinity). There's a brief discussion about incorporating it in non-math university curricula (see this). I'm sure some of this can be used to improve the article. Mindmatrix 22:47, 12 October 2008 (UTC)

Yes, it's silly, and yet still quite notable, in my opinion. It's like saying, "On a scale from one to ten, where one is 'great' and ten is 'lousy', right now I feel like a 27." – PIE ( CLIMAX )  05:26, 3 December 2011 (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.

Broad-concept article?

RL0919 gave a good close of Wikipedia:Articles for deletion/Infinity plus one as no consensus, observing that we generally didn't want to simply delete but could not decide what to do. The main options at the AfD were:

• Certes suggested a broad-concept article. That would most naturally just be an expansion of the article that we have, although Danstronger suggested 'Formalizations of infinity'. I think that formalisation is certainly a thing that such a broad concept article should cover, although since many formalisations have a former life as pre-formal intuitions, I think that should be a part rather than the whole of the article. I suggested 'Mathematics of infinity' as a possible name for a more general article.
• A couple of less ambitious ATDs were suggested, namely redirecting to Ordinal_number#Ordinals_extend_the_natural_numbers or turning into a dab page.

I believe we should start by turning this page into a proper disambiguation page (to fix the immediate issues), then figure out how a (new) broad-concept article about this topic could work, and eventually refer to this new article in the disambiguation page, as a broad-concept treatment of the topic "infinity plus one", among others.

I'm summarising the AfD in this way because I'm curious as to whether there is the energy to tackle creating a broad concept article. If there is, this topic is quite capable of being as successful as the 0.999... article that made it all the way to FA. Until we answer this question, I don't think we can make the right technical choice about what content goes where. — Charles Stewart (talk) 16:29, 17 January 2022 (UTC)

I have a basic understanding of the topic but don't feel competent to write a better article myself. Certes (talk) 16:39, 17 January 2022 (UTC)

I have just had a look at the Transfinite numbers article; it seems to me that that article is already an attempt at a sort of broad-concept article, which then adds a secondary specialised meaning in the second half of a Definition section. There has even been some talk on its talk page of adding surreal numbers to that article too. Felix QW (talk) 13:36, 23 January 2022 (UTC)

As this page has become a disambiguation page, please can knowledgeable editors amend the incoming links to target the most appropriate articles instead? We should also remove the navbox and make any other fixes required by MOS:DAB. Thanks, Certes (talk) 12:48, 19 January 2022 (UTC)

• I'm well versed in some formalizations of infinity (so I could contribute), but I'm not sure how accurate my big picture of infinity is... TucanHolmes (talk) 11:08, 19 January 2022 (UTC)

Here's how I would point to that new broad-concept article in this disambiguation page:

Extended content
In mathematics, infinity plus one is a concept which has a well-defined formal meaning in some number systems, and may refer to: [...] For a general overview of the different formalizations of infinity, see Formalizations of infinity

Maybe we could start with something in Draft space? TucanHolmes (talk) 10:51, 20 January 2022 (UTC)

• I think this is a promising idea. An alternate idea is that this page, now a dab, be expanded to that broad-concept article. I have a suggestion: we start Draft:Infinity plus one, to be that broad-concept article. If it looks best to merge that into this now-dab article, we can do that via a WP:HISTMERGE. Otherwise, we will likely be able to figure out a good target to move the broad-concept article to and we will then be able to follow your suggestion above. — Charles Stewart (talk) 12:37, 20 January 2022 (UTC)

I could also contribute to the broad-concept article, as a logician.

The main issue I have with the dab page as it stands is that the title "Infinity plus one" does not reflect the content; Surely,"infinity plus one" refers to successor cardinal and successor ordinal much rather than to cardinal numbers and ordinal numbers? And probably most readers who are not logically inclined would just take the phrase to mean $\infty +1$, which equals $\infty$ in the usual extension of addition to the extended real line ${\overline {\mathbb {R} }}$. Felix QW (talk) 16:26, 20 January 2022 (UTC)

Or the projectively extended real line, for that matter. Felix QW (talk) 16:42, 20 January 2022 (UTC)

• I'd say the successor cardinal is not the "plus one" operation on infinite cardinals. You can define $\alpha +\beta ={\textrm {card}}(\{0\}\times \alpha \cup \{1\}\times \beta )$; then "plus one" is the identity when restricted to infinite cardinals, just as it is for notions of infinite value derived from projective geometry. While I think this is the most obvious way of extending addition to the cardinals, I don't recall seeing this written up anywhere as cardinal arithmetic, so it might be OR to say so. I raised this fear in the AfD, that it might be hard to develop this article without straying into OR. — Charles Stewart (talk) 20:27, 20 January 2022 (UTC)

• Oh, Tarski studied this in Cardinal algebras, OUP 1949. I think my worries about ORness have receded. — Charles Stewart (talk) 20:50, 20 January 2022 (UTC)

That is a good point. Since "plus one" on the natural numbers refers to both the successor operation and to addition by one, which coincide on the naturals, I think a searcher could feasibly mean either operation on infinite cardinals, where they differ.

We actually have a section on Cardinal arithmetic which discusses this notion of addition, and it could be sourced to most naive set theory books. Felix QW (talk) 11:29, 21 January 2022 (UTC)

If I'd looked at that article before posting my comment, I'd not have been reassured on the OR front: that article calls these operations cardinal arithmetic, but it doesn't give a source for the term. I know that Shelah has a body of work on what he calls cardinal arithmetic, but it's not clear to me that he has much use for those definitions. I'm in the UK for a few weeks and so don't have access to my books: if someone checked if that term is used in association with the definitions in that article I'd be grateful. — Charles Stewart (talk) 14:38, 21 January 2022 (UTC)

See talk:Cardinal number for the reply.