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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeJun 28th 2020

    New page, covering both French and English definitions, as well as limits of relations and spans, and restricted versions.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeJun 29th 2020

    More properties

    diff, v3, current

  1. Added definition of limit of a function for metric spaces, and added link to Wikipedia article on limit of a function


    diff, v8, current

  2. Added definitions of limits of functions between metric spaces for the French language and added a link to the French Wikipedia in the references


    diff, v9, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2023

    Sorry, but this is a weird edit.

    For several reasons it makes no sense to speak of “limits in the English language of Karl Weierstrass”.

    It should just say “limits as defined by Bourbaki”, etc.

    And it seems awkward to verbatim copy-and-paste a lengthy paragraph no less than three times (including its typos such as “could represented” for what must be “could be represented” and ought to be “can be represented”) making it an Easter hunt for the reader to spot which symbols have changed.

    Can somebody help Anonymouse with saying what he wants to say here?

  3. fixed typoes

    typo fixer

    diff, v10, current

  4. removed mention of Weierstrass and Bourbaki

    typo fixer

    diff, v10, current

  5. reordered the material in the “in metric spaces” section

    typo fixer

    diff, v10, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2023
    • (edited Nov 5th 2023)

    The references to Bourbaki and Weierstarss etc. ought to be kept if the intent is to compare different original phrasings of the definition of limit of a function.

    What needs to be removed is the phrasing

    in the sense of the French language, the limit (in the French language) of…


    the limit (in the English language) of…

    which makes no sense.

    I suppose what Anonymouse wants to say is that different explicit formulations of the definition of limit may be more popular in the francophone literature than in the anglophone literature on the subject.

    That might be the case, I don’t know, the claim should be supported by some references. But in either case it is at best worth a side remark.

    For the time being, the phrases about “language” ought to be replaced by explicit references.

    Such as: “Bourbaki defines the limit as follows…”, while “Weierstrass defined the limit as follows…”.

  6. About terminology, the French Wikipedia calls the limits defined by Weierstrass “punctured limits”

    Cette définition moderne, cohérente avec la définition topologique générale (voir infra) et désormais en vigueur en France3, supplante la définition historique de Weierstrass, appelée aussi « limite épointée » ou « limite par valeurs différentes »4, enseignée encore parfois dans les universités françaises et dans d’autres pays5 :

    which translates to:

    This modern definition, consistent with the general topological definition (see below) and now in effect in France3 , supersedes Weierstrass’s historical definition, also known as the “punctured limit” or “limit by different values “4 , which is still sometimes taught in French universities and in other countries5

    The reference at footnote 4 is the text

    C. Deschamps, F. Moulin, A. Warusfel et al., Mathématiques tout-en-un MPSI, Dunod, 2015, 4e éd, p. 506.

    typo fixer

    diff, v11, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2023

    Thanks to “typo fixer” for editing further, I appreciate it.

    Anonymouse has the habit of letting others clean up after him, without bothering to even reply. That’s not how the nLab is meant to work.