• rasensprenger@feddit.de
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    1 年前

    About the ambiguity: If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous. It’s correct notation in both cases, used since forever, but you need to explicitly disambiguate if you want to use it.

    I hope this helps you more than the stackexchange post?

    • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱
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      1 年前

      If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous

      The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).

      • rasensprenger@feddit.de
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        1 年前

        You can define your notation that way if youlike to, doesn’t change the fact that commonly f^{-1}(x) is and has been used that way forever.

        If I read this somewhere, without knowing the conventions the author uses, it’s ambiguous

        • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱
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          1 年前

          You can define your notation that way if you like

          Nothing to do with me - it’s in Maths textbooks.

          without knowing the conventions the author uses, it’s ambiguous

          Well they should all be following the rules of Maths, without needing to have that stated.