Talk:Cardinality

Merger proposal Infinite sets

I propose that Infinite set be merged into Cardinality#Infinite sets. I think that the content in the Infinite set article can easily be added to this page, as most of it is already on this page.

DrWikiWikiShuttle (talk) 06:35, 26 June 2016 (UTC)

Oppose: No. I do not think that its content is contained here, and it is important enough to deserve its own article. JRSpriggs (talk) 15:01, 26 June 2016 (UTC)

Oppose - This is a notable article, with a notable context. It should have an article of its own. ♥ Shri Sanam Kumar ♥ 17:55, 18 October 2016 (UTC)

(G)CH and research

Lurking through Jochen Burghardt's talk page, I happened upon a discussion that took place last November or so, where previous text had mentioned ongoing research into CH, which had been labeled with {{cn}}, then someone made the statement less specific and removed the template, then the whole thing got removed. Jochen wrote and edit summary that said restore ((cn)) after sentence that hasn't changed since it was added: I doubt that Cohen.1963 (independence of GCH) leaves much room for research, but I'm not an expert

So here's the thing: independence from ZFC does not close an issue in set theory. All sorts of set-theoretic research is into questions known to be independent of ZFC, and indeed specifically into the continuum hypothesis. It would be easy to supply citations for examples of such research. Finding a reliable secondary source for the specific statement that research continues into the continuum hypothesis would be harder, as this is at a more "meta" level, but I expect it can be done.

If we're going to continue to talk so much about CH in this article, I do think it's reasonable to mention continuing research efforts. It seems to me that it ought to make sense to cite specific research directions and cite those, rather than needing to find a secondary source for the "meta" statement; would others find this acceptable?

On the other hand, I'm not sure that the general article on cardinality needs to deep-dive into this at all. --Trovatore (talk) 20:07, 20 September 2023 (UTC)

@Willondon:, the other participant in the previous discussion. --Trovatore (talk) 20:22, 20 September 2023 (UTC)

Seems you're referring to my post at User talk:Jochen Burghardt#Continuing research on cardinality?. My closing opinion, "I thought (well, assumed, to be honest) that there were surely open questions still. Given that nobody (including 250 page watchers) has addressed the template with an actual citation, I thought it best to delete my essentially original research." That's still my opinion: that my opinion should be dismissed, because it relied on original research by assumption. I have no valid opinion on whether or not research is settled or continues. _signed, Willondon (talk) 21:03, 20 September 2023 (UTC)

Research does continue, and citations can be found. The real question is whether it makes sense to talk about it here (or indeed whether this article should talk so much about the cardinality of the continuum, when the article is about cardinality in general).

But then again, CH is sort of the first question that came up that wasn't immediately resolvable, so it might well make sense. --Trovatore (talk) 21:06, 20 September 2023 (UTC)

Cardinality is size?

I am the only decent antisettheorest you have. Size is precisely defined in original for example ZFC set theory, as well as cardinality and ordinality. The highest level as well as the original set theorists do not consider cardinality or ordinality the same as size. In all finite cases they are the same and it is severely the case that they are mistakenly considered the same. But in infinite cases the same sets can have different size, cardinality, ordinality. So you Wikipedia editors are going further in their error than the original and highest level set theorists. They define 'size' as cardinality (the definition of cardinality) to add to 'size' their lies;

that which applies to the finite by proof does/doesn't apply to the equivalent infinite, the does and separately the doesn't cases defined. 

And not being able to prove something true, by a particular sort of proof, proves it false.

Consider, you in Wikipedia and in the earliest original literature claim your technique in general for comparing infinite thus all set sizes applies to ≤ and ≥ and combining them by a proof =, but not < or > even though the < and > proofs look just as legitimate. This should be articled, we (antisettheorests) should get that. And the diagonal argument is not claimed to nor does prove ≠, but uncountability, thus none of us can prove using your sort of proof = infinite size (though I in particular can using a binary tree proof, don't confuse it or parallel it to your diagonal sort of proofs or your matching proofs), thus the set theorists are claiming disproving proof of = somehow indicates ≠. Consider also this is how they conclude cardinal a + b is not the same as cardinal b + a. By lack of proof of countable. This likewise should be articled. Thus contrary to your edit cardinality is not at all size, but rather historically is quite often considered size contrary to claims of the set theorists, that is how I want it to read. I also want cardinal, ordinal, cardinality, ordinality, way better defined. Victor Kosko (talk) 23:23, 23 March 2025 (UTC)