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• iglou@programming.dev ⁨1⁩ ⁨day⁩ ago

  Yes, it is. The division of a by b in the set of real numbers and the set of rational numbers (which are, de facto, the default sets used in most professions) is defined as the multiplication of a by the multiplicative inverse of b. Alternative definitions are also based on a multiplication.

  That’s why divisions are called an auxilliary operation.

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  • SmartmanApps@programming.dev ⁨1⁩ ⁨day⁩ ago

    Yes, it is

    No it isn’t.

    The division of a by b in the set of real numbers and the set of rational numbers (which are, de facto, the default sets used in most professions) is defined as the multiplication of a by the multiplicative inverse of b

    No it isn’t. The Quotient is defined as the number obtained when you divide the Dividend by the Divisor. Here it is straight out of Euler…

    Image

    Alternative definitions are also based on a multiplication

    Emphasis on “alternative”, not actual.

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    • iglou@programming.dev ⁨1⁩ ⁨day⁩ ago

      No it isn’t.

      Yes, it is.

      No it isn’t. The Quotient is defined as the number obtained when you divide the Dividend by the Divisor. Here it is straight out of Euler…

      I’m defining the division operation, not the quotient. Yes, the quotient is obtained by dividing… Now define dividing.

      Emphasis on “alternative”, not actual.

      The actual is the one I gave. I did not give the alternative definitions. That’s why I said they are also defined based on a multiplication, implying the non-alternative ones (understand, the avtual one) was the one I gave.

      Feel free to send your entire Euler document rather than screenshotting the one part you thought makes you right.

      Note, by the way, that Euler isn’t the only mathematician who contributed to the modern definitions in algebra and arithmetics.

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      • SmartmanApps@programming.dev ⁨1⁩ ⁨day⁩ ago

        I’m defining the division operation, not the quotient

        Yep, the quotient is the result of Division. It’s right there in the definition in Euler. Dividend / Divisor = Quotient <= no reference to multiplication anywhere

        Yes, the quotient is obtained by dividing… Now define dividing.

        You not able to read the direct quote from Euler defining Division? Doesn’t mention Multiplication at all.

        The actual is the one I gave

        No, you gave an alternative (and also you gave no citation for it anyway - just something you made up by the look of it). The actual definition is in Euler.

        That’s why I said they are also defined based on a multiplication

        Again, emphasis on “alternative”, not actual.

        implying the non-alternative one (understand, the actual one) was the one I gave

        The one you gave bears no resemblance at all to what is in Euler, nor was given with a citation.

        Feel free to send your entire Euler document rather than screenshotting the one part

        The name of the PDF is in the top-left. Not too observant I see

        you thought makes you right

        That’s the one and only actual definition of Division. Not sure what you think is in the rest of the book, but he doesn’t spend the whole time talking about Division, but feel free to go ahead and download the whole thing and read it from cover to cover to be sure! 😂

        Note, by the way, that Euler isn’t the only mathematician who contributed to the modern definitions in algebra and arithmetics.

        And none of the definitions you have given have come from a Mathematician. Saying “most professions”, and the lack of a citation, was a dead giveaway! 😂

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