• cecilkorik@lemmy.ca
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    1 month ago

    Parenthesis, exponents, multiplication, division, addition, subtraction.

    should actually be

    Parenthesis, exponents, (multiplication and division), (addition and subtraction).

    Addition and subtraction are given the same priority, and are done in the same step, from left to right.

    It’s not a great system of notation, it could be made far clearer (and parenthesis allow you to make it as clear as you like), but it’s essentially the universal standard now and it’s what we’re stuck with.

    • iglou@programming.dev
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      1 month ago

      No, it should simply be “Parenthesis, exponents, multiplication, addition.”

      A division is defined as a multiplication, and a substraction is defined as an addition.

      I am so confused everytime I see people arguing about this, as this is basic real number arithmetics that every kid in my country learns at 12 yo, when moving on from the simplified version you learn in elementary school.

        • iglou@programming.dev
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          5 days 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.

          • 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…

            Alternative definitions are also based on a multiplication

            Emphasis on “alternative”, not actual.

            • iglou@programming.dev
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              5 days 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 one (understand, the actual 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.

              • 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! 😂

      • 13igTyme@lemmy.world
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        1 month ago

        You want PEMA with knowledge of what is defined, when people can’t even understand PEMDAS. You wish for too much.

        • Cethin@lemmy.zip
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          1 month ago

          I hate most math eduction because it’s all about memorizing formulas and rules, and then memorizing exceptions. The user above’s system is easier to learn, because there’s no exceptions or weirdness. You just learn the rule that division is multiplication and subtraction is addition. They’re just written in a different notation. It’s simpler, not more difficult. It just requires being educated on it. Yes, it’s harder if you weren’t obviously, as is everything you weren’t educated on.

          • Mistic@lemmy.world
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            1 month ago

            That’s because (strictly speaking) they aren’t teaching math. They’re teaching “tricks” to solve equations easier, which can lead to more confusion.

            Like the PEMDAS thing that’s being discussed here. There’s no such thing as “order of operations” in math, but it’s easier to teach by assuming that there is.

            Edit: To the people downvoting: I want to hear your opinions. Do you think I’m wrong? If so, why?

            • they aren’t teaching math.

              Yes we are. Adults forgetting it is another matter altogether.

              There’s no such thing as “order of operations” in math

              Yes there is! 😂

              Do you think I’m wrong?

              No, I know you’re wrong.

              If so, why?

              If you don’t solve binary operators before unary operators you get wrong answers. 2+3x4=14, not 20. 3x4=3+3+3+3 by definition

              • Mistic@lemmy.world
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                1 day ago

                Yes we are

                Yes and no. You teach how to solve equations, but not the fundamentals (and if you do then kudos to you, as it’s not a trivial accomplishment). Fundamentals, most of the time, are taught in universities. It’s so much easier that way, but doesn’t mean it’s right. People call it math, which is fair enough, but it’s not really math in a sense that you don’t understand the underlying principles.

                Yes there is!

                Nope.

                There’s only commutation, association, distribution, and identity. It doesn’t matter in which order you apply any of those properties, the result will stay correct.

                2×2×(2-1)/2 = 2×(4-2)/2 = 1×(4-2) = 4-2 = 2

                As you can see, I didn’t follow any particular order and still got the correct result. Because no basic principle was broken.

                Or I could also go

                2×2×(2-1)/2 = 4×(2-1)/2 = 4×(1-0.5) = 4×0.5 = 2

                Same result. Completely different order, yet still correct.

                My response to the rest goes back to the aforementioned.

                • You teach how to solve equations, but not the fundamentals

                  Nope. We teach the fundamentals. Adults not remembering them doesn’t mean they weren’t taught. Just pick up a Maths textbook. It’s all in there. Always has been.

                  Fundamentals, most of the time, are taught in universities

                  No they’re not. They only teach order of operations from a remedial point of view. Most of them forget about The Distributive Law. I’ve seen multiple Professors be told by their students that they were wrong.

                  it’s not really math in a sense that you don’t understand the underlying principles

                  The Constructivist learners have no trouble at all understanding it.

                  Nope.

                  Yep!

                  There’s only commutation, association, distribution, and identity.

                  And many proofs of other rules, which you’ve decided to omit mentioning.

                  It doesn’t matter in which order you apply any of those properties, the result will stay correct

                  But the order you apply the operations does matter, hence the proven rules to be followed.

                  2×2×(2-2)/2

                  Notably you picked an example that has no addition, subtraction, or distribution in it. That’s called cherry-picking.

                  Completely different order, yet still correct

                  Yep, because you cherry-picked a simple example where it doesn’t matter. It’s never going to matter when you only pick operations which have the same precedence.

                  My response to the rest goes back to the aforementioned

                  …cherry-picking.

                  • Mistic@lemmy.world
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                    1 day ago

                    We teach the fundamentals

                    Sure. They are, however, not the focus. At least that’s not how I’ve been taught in school. You’re not teaching kids how to prove the quadratic formula, do you? No, you teach them how to use it instead. The goal here is different.

                    They only teach order of operations.

                    Again, with the order of operations. It’s not a thing. I’ve given you two examples that don’t follow any.

                    The constructivist learners…

                    That’s kinda random, but sure?

                    And many proofs of other rules…

                    They all derive from each other. Even those fundamental properties are. For example, commutation is used to prove identity.

                    But the order you apply operators does matter

                    2+2-2 = 4-2 = 2+0 = 0

                    2 operators, no order followed.

                    If we take your example

                    2+3×4 then it’s not an order of operation that plays the role here. You have no property that would allow for (2+3)×4 to be equal 2+3×4

                    Look, 2+3×4 = 1+3×(2+2)+1 = 1+(6+6)+1 = 7+7 = 14

                    Is that not correct?

                    Notably you picked…

                    It literally has subtraction and distribution. I thought you taught math, no?

                    2-2 is 2 being, hear me out, subtracted from 2

                    Same with 2×(2-2), I can distribute the value so it becomes 4-4

                    No addition? Who cares, subtraction literally works the same, but in opposite direction. Same properties apply. Would you feel better if I wrote (2-2) as (1+1-2)? I think not.

                    Also, can you explain how is that cherry-picking? You only need one equation that is solvable out of order to prove order of operation not existing. One is conclusive enough. If I give you two or more, it doesn’t add anything meaningful.

        • iglou@programming.dev
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          1 month ago

          I’m just confused as to how that is not common knowledge. The country I speak of is France, and we’re not exactly known for our excellent maths education.