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du Bois-Raymond and Cantor's diagonal argument

An edit saying du Bois-Raymond invented the argument earlier was reverted, correctly I believe. However there probably should be something here about the attribution and why it is wrong and there is the chance that Cantor was inspired by d Bois-Raymond's proof as he had an interest in infinity and infinitesimals. See note 1 page 187 in Simmons, Keith (1993). Universality and the Liar: An Essay on Truth and the Diagonal Argument. CUP. p. 187.. Dmcq (talk) 18:02, 9 January 2018 (UTC)[reply]

The line removed was
Historically, the diagonal argument first appeared in the work of Paul du Bois-Reymond in 1875.[1]
  1. ^ Du Bois-Reymond, Paul (1875), "Über asymptotische Werte, infinitäre Approximationen und infinitäre Auflösungen von Gleichungen", Mathematische Annalen, 8 (3): 363–414, doi:10.1007/bf01443187
    2. Dmcq (talk) 18:09, 9 January 2018 (UTC)[reply]

    I will restore the reference to du Bois-Reymond together with a book on his work by G. H. Hardy, where the diagonal argument is explained.nikita (talk) 17:37, 25 July 2020 (UTC)[reply]

    What's the problem with this disproof?

    Hi, I'm not a mathematician, but I've always thought this theorem was false, and I thought somebody might have an intelligent opinion. Here is an explanation of why:

    1. Define an enumeration A of all expressions in language (e.g. by enumerating sequences of letters and symbols).

    2. Define an enumeration B of all infinite sequences of binary digits, as those items in A which define infinite sequences of binary digits. This will be the enumeration used for Cantor's Theorem.

    3. Cantor's additional sequence must be within A, because it is written in language. For example, A must contain "The additional sequence that will be defined in terms of B for Cantor's Theorem."

    4. If this additional sequence defines an infinite sequence of binary digits, then it will be an element of B with an index n. However, because of the nature of its definition, its nth digit would be its own complement.

    5. Therefore, the additional sequence does not define an infinite sequence of binary digits. The sequence Cantor proposes to generate does not exist in this case.

    Furthermore, there are multiple ways of writing a description of a sequence in language, implying a 1-to-1 mapping of describable sequences to natural numbers, but not of natural numbers to describable sequences. There are more natural numbers than describable sequences.

    I mentioned this to my high school calculus teacher in class around 2001, and this point is where the argument stalled. Xloem (talk) 21:03, 10 October 2018 (UTC)[reply]

    Hi Xloem. Per the talk page guidelines, the article talk pages are for discussing improvements to the article. If you have general questions about the subject matter, you can ask at the math reference desk. Also, this talk page has an arguments subpage. --Trovatore (talk) 21:11, 10 October 2018 (UTC)[reply]
    Pinging OP: Xloem. --CiaPan (talk) 07:29, 11 October 2018 (UTC)[reply]
    A quickie though, any more should go to the arguments page, in step one you are at best describing the computable numbers. And the argument can be used to show one can't list out the computable numbers even though they are countable.This is the Halting problem. Dmcq (talk) 10:58, 11 October 2018 (UTC)[reply]

    Cantor's diagonal argument, float to integer 1-to-1 correspondence, proving the Continuum Hypothesis

    Moved to talk:Cantor's diagonal argument/Arguments#Cantor's diagonal argument, float to integer 1-to-1 correspondence, proving the Continuum Hypothesis. --Trovatore (talk) 19:53, 1 December 2018 (UTC)[reply]

    Automatic archiving

    Apparently, there's some confusion with automatic archiving of this talk page. As far as I can see, there are the following archive pages:

    Only the first archive page in that list is referenced by the archive index. Can someone more knowledgable than me please fix this? In the mean time I have managed to only make the mess worse by moving Talk:Cantor's diagonal argument/Archives/ 2 to Talk:Cantor's diagonal argument/Archives/Archive 2. Sorry about that. – Tea2min (talk) 08:28, 2 December 2018 (UTC)[reply]

    Hello, Tea2min! Archive pages' history shows they are created and managed by User:ClueBot III. As the bot's userpage informs, it is operated by User:Cobi. So maybe Cobi could explain naming discrepancy, and help in fixing it? --CiaPan (talk) 15:47, 6 April 2019 (UTC)[reply]
    Hi, Tea2min, Cobi is not very active recently, as can be seen from the contributions list – just six edits this year on five distinct days, most recently on 21 March 2019. So I think we should not expect a prompt reply. --CiaPan (talk) 07:38, 20 May 2019 (UTC)[reply]

    no reals

    moved to talk:Cantor's diagonal argument/Arguments#no reals --Trovatore (talk) 19:04, 6 April 2019 (UTC)[reply]

    The proof is (EDIT: NOT) incomplete

    Moved to arguments page. --Trovatore (talk) 06:34, 16 July 2021 (UTC)[reply]

    Set of all sets

    Moved to arguments page. --Trovatore (talk) 06:30, 16 July 2021 (UTC)[reply]

    diagonal counterexample

    Moved to arguments page. --Trovatore (talk) 06:30, 16 July 2021 (UTC)[reply]

    In his 1891 article...

    "In his 1891 article, Cantor considered the set T of all infinite sequences of binary digits (i.e. each digit is zero or one):"

    No, he didn't. In his 1891 article, Cantor considered a bicoloring by m and w. It is standard in wikipedia for modified proofs to be indicated as such and it is amateurish not to do so when the article itself is referred to by date and linked to in the footnotes. The proof should either conform to the reference or (if we're so endeared to the modification that we prefer it to the original) be indicated as an updated or simplified restatement thereof. — Preceding unsigned comment added by 2603:7000:8E03:3E7E:6979:D94F:B78E:B1DA (talk) 18:56, 15 November 2021 (UTC)[reply]

    Cantor's proof is unrelated to binary sequences. Binary sequences are related to Cantor's proof. — Preceding unsigned comment added by 2603:7000:8E01:2B47:F8AA:FA7F:B5CA:53D8 (talk) 19:59, 19 April 2022 (UTC)[reply]

    diagonal = contradiction

    Cantor’s diagonal argument leads to a contradiction. Assume one wishes to list all the real numbers. Cantor’s diagonal real D cannot exist until the list is completed. But the list is not completed if there exists a real that isn’t on it. Therefore the existence to D entails that both the list is completed and the list in not completed. 71.184.87.187 (talk) 19:17, 21 May 2022 (UTC)[reply]

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