• starman2112@sh.itjust.works
      2·
      1 year ago

      If you really wanna see a bloodbath, watch this:

      You know that a couple has two children. You go to the couple’s house and one of their children, a young boy, opens the door. What is the probability that the couple’s other child is a girl?

        • starman2112@sh.itjust.works
          2·
          1 year ago

          Oops, I changed it to a more unintuitive one right after you replied! In my original comment, I said “you flip two coins, and you only know that at least one of them landed on heads. What is the probability that both landed on heads?”

          And… No! Conditional probability strikes again! When you flipped those coins, the four possible outcomes were TT, TH, HT, HH

          When you found out that at least one coin landed on heads, all you did was rule out TT. Now the possibilities are HT, TH, and HH. There’s actually only a 1/3 chance that both are heads! If I had specified that one particular coin landed on heads, then it would be 50%

          • Hacksaw@lemmy.ca
            5·
            1 year ago

            No. It’s still 50-50. Observing doesn’t change probabilities (except maybe in quantum lol). This isn’t like the Monty Hall where you make a choice.

            The problem is that you stopped your probably tree too early. There is the chance that the first kid is a boy, the chance the second kid is a boy, AND the chance that the first kid answered the door. Here is the full tree, the gender of the first kid, the gender of the second and which child opened the door, last we see if your observation (boy at the door) excludes that scenario.

            1 2 D E

            B B 1 N

            B G 1 N

            G B 1 Y

            G G 1 Y

            B B 2 N

            B G 2 Y

            G B 2 N

            G G 2 Y

            You can see that of the scenarios that are not excluded there are two where the other child is a boy and two there the other child is a girl. 50-50. Observing doesn’t affect probabilities of events because your have to include the odds that you observe what you observed.

            • Zagorath@aussie.zone
              0·
              1 year ago

              I was about to reply to you with a comment that started with “oh shit you’re right!” But as I wrote it I started rethinking and I’m not sure now.

              Because I actually don’t think it matters whether we’re BB1 or BB2. They’re both only one generation of the four possible initial states. Which child opens the door is determined after the determination of which child is which gender. Basically, given that they have two boys, we’re guaranteed to see a boy, so you shouldn’t count it twice.

              Still, I’m now no where near as confident in my answer as I was a moment ago. I might actually go and write the code to perform the experiment as I outlined in an earlier comment (let me know if you think that methodology is flawed/biased, and how you think it should be changed) to see what happens.

              • Hacksaw@lemmy.ca
                0·
                1 year ago

                That’s a great idea let me know how it turns out. If you randomly pick the genders and randomly pick who opens the door, I think it will be 50-50. With these kinds of things they can get pretty tricky. Just because an explanation seems to make sense doesn’t mean it’s right so I’m curious!

                • Zagorath@aussie.zoneEnglish
                  1·
                  1 year ago

                  I put it together. Here’s the code I wrote in Python.

                  import random

genders = ['boy', 'girl']

def run():
    other_child_girls = 0
    for i in range(10000):
        other_child = get_other_child()
        if other_child == 'girl':
            other_child_girls += 1
    print(other_child_girls)

def get_other_child():
    children = random.choices(genders, k=2)
    first_child_index = random.randint(0, 1)
    first_child = children[first_child_index]
    if first_child == 'boy':
        other_child_index = (first_child_index + 1) % 2
        return children[other_child_index]
    # Recursively repeat this call until the child at the door is a boy
    # (i.e., discard any cases where the child at the door is a girl)
    return get_other_child()

if __name__ == '__main__':
    run()

                  And it turns out you were right. I ran it a few times and got answers ranging from 4942 to 5087, i.e., clustered around 50%.

          • Floey@lemm.ee
            1·
            9 months ago

            This is a ridiculous argument when taken to the extreme. Say you have three bags. Bag A contains 100 blue marbles. Bag B contains 99 blue marbles and 1 red marble. Bag C contains 100 red marbles. You reach into a random bag and draw a red marble. You’ve only eliminated bag A. Would you say it is a 50-50 whether you are left with a bag now containing 99 blue marbles or 99 red marbles? No, the fact that you drew a red marble tells you something about the composition of the bag you drew from. The odds that you drew out of bag B is 1/101, the total number of red marbles in bag B divided by the total number of red marbles across all bags. The odds that you are dealing with bag C is 100x that.

            Now let’s say you have 4 bags. BB, BR, BR, and RR. You draw an R. There is a 50% chance you are dealing with bag 2 or 3 because together they contain 2 out of 4 R. There is also a 50% chance you are dealing with bag 4. So it is equally likely that you draw either color of marble if you take the remaining marble out of the bag you randomly selected despite there being twice as many BR bags as RR bags.

      • Zagorath@aussie.zone
        0·
        1 year ago

        This is basically Monty Hall right? The other child is a girl with 2/3 probability, because the first one being a boy eliminates the case where both children are girls, leaving three total cases, in two of which the other child is a girl (BG, GB, BB).

  • Pavidus@lemmy.world
    3·
    1 year ago

    There’s quite a few calculators that get this wrong. In college, I found out that Casio calculators do things the right way, are affordable, and readily available. I stuck with it through the rest of my classes.

  • mindbleach@sh.itjust.works
    3·
    1 year ago

    Different compilers have robbed me of all trust in order-of-operations. If there’s any possibility of ambiguity - it’s going in parentheses. If something’s fucky and I can’t tell where, well, better parenthesize my equations, just in case.

    • linuxdweeb@lemm.ee
      1·
      1 year ago

      This is best practice since there is no standard order of operations across languages. It’s an easy place for bugs to sneak in, and it takes a non-insignificant amount of time to debug.

      • mindbleach@sh.itjust.works
        3·
        9 months ago

        That’s the same ambiguity, numbnuts. Your added parentheses do nothing. If you wanted to express the value 8 over the value 2*(1+3), you should write 8/(2*(1+3)). That is how you eliminate other valid interpretations.

        As illustration of why there are competing valid interpretations: what human being is going to read “8/2 * (1+3)” as anything but 4*4? Those spaces create semantic separation. But obviously most calculators don’t have a spacebar, any more than they have to ability to draw a big horizontal line and place 2(1+3) underneath it. Ambiguous syntax for expressing mathematics is not some foundation-shaking contradiction. It’s a consequence of limitations in how we express even the most concrete ideas.

        “The rules of math” you keep spamming about are not mathematical proofs - they’re arbitrary decisions made by individuals and organizations. In many cases the opposite choice would be equally sensible. Unlike the innate equivalence of multiplication and division, where dividing by two and multiplying by half are interchangeable. Same with addition and subtraction.

        Do you want to argue that 8 - (2) + (1+3) should be 2?

        • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
          1·
          9 months ago

          Your added parentheses do nothing

          So you’re saying Brackets aren’t first in order of operations? What do you think brackets are for?

          If you wanted to express the value 8 over the value 2*(1+3), you should write 8/(2*(1+3))

          or, more correctly 8/2(1+3), as per the rules of Maths (we never write unnecessary brackets).

          That is how you eliminate other valid interpretations

          There aren’t any other valid interpretations. #MathsIsNeverAmbiguous

          what human being is going to read “8/2 * (1+3)” as anything but 4*4

          Yes, that’s right, but 8/2x(1+3) isn’t the same as 8/2(1+3). That’s the mistake that a lot of people make - disobeying The Distributive Law.

          Those spaces

          …have no meaning in Maths. The thing that separates the Terms, in your example, is the multiply. i.e. an operator.

          most calculators don’t have a spacebar

          …because it’s literally meaningless in Maths.

          any more than they have to ability to draw a big horizontal line and place 2(1+3) underneath it

          Some of them can actually.

          “The rules of math” you keep spamming about are not mathematical proofs

          You should’ve read further on then. Here’s the proof.

          they’re arbitrary decisions made by individuals

          No, they’re a natural consequence of the way we have defined operators. e.g. 2x3=2+2+2, therefore we have to do multiplication before addition.

          In many cases the opposite choice would be equally sensible

          2+2x3=2+6=8 the correct answer, but if I do addition first…

          2+2x3=4x3=12, which is the wrong answer. How is getting the wrong answer “equally sensible” as getting the right answer?

          Do you want to argue that 8 - (2) + (1+3) should be 2?

          No, why would I do that? 8-(2+1+3) does equal 2 though.

          • mindbleach@sh.itjust.works
            2·
            9 months ago

            You are a smug idiot.

            8/2(1+3) is exactly the sort of thing programs love to misinterpret. I don’t give a shit what “rules of math” you insist are super duper universal, or what “we” do. They are not reliable. Clear parentheses are. Insisting you’re correct is not relevant. You stumbled into a pragmatic issue with grand philosophical assurances that aren’t even sound.

            Yes, that’s right, but 8/2x(1+3) isn’t the same as 8/2(1+3).

            … no, that’s fucking stupid.

            Some of them can actually.

            Hence the word “most.” Your cocksure months-late manic episode across this thread is the most “akshually” thing I have ever witnessed.

            Here’s the proof.

            You dense bastard! That’s a category error! You can’t prove that 2(3) means something different from 2*3. It’s only convention! It’s a thing we made up, unlike actual mathematical proofs, which are laws of the universe. If everyone disagreed with that then it would stop being true. That’s not a sentence you can say about anything that has a proof, instead of some evidence.

            You keep talking about “rules of math” when what you mean is rules of this particular notation. Reverse Polish Notation doesn’t have this issue, at all. Distribution is not even possible in RPN. So however important you think it might be… it’s not universal.

            [Those spaces] have no meaning in Maths.

            THAT’S THE POINT, NUMBNUTS. It’s semantic separation that human beings will read in for context. Which they need, because some grammars have ambiguities, which can only be resolved by convention. Like how -6 is a number, and you can add or multiply -6, but 1 + -6 looks kinda weird, -6(3) is fine, and (3) -6 is asking for trouble.

            The convention overwhelmingly used in computation is that parentheses are resolved first. Nothing is distributed over them - they are evaluated, and then used. In exactly the same way that multiplication can be treated as repeated addition, operations on parentheticals are treated as operations on equations reduced to scalars. It doesn’t fucking mean anything, to say 8/2*(1+3) is different from 8/2(1+3), because in the notation used by coders, they both become 8/2*4.

            You might as well barge in pick a fight with N=N+1.

            • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
              1·
              9 months ago

              You are a smug idiot

              That’s your colloquialism for Maths teachers. Ok, got it.

              8/2(1+3) is exactly the sort of thing programs love to misinterpret.

              Programs, written by programmers, who have forgotten the rules of Maths.

              that’s fucking stupid

              So you’re saying the rules of Maths are stupid. Got it.

              You can’t prove that 2(3) means something different from 2*3. It’s only convention!

              No, it’s a rule of Maths - it’s literally the opposite operation to factorising.

              It’s a thing we made up

              Nothing in Maths is made up. It’s based on our observations of how things work.

              mathematical proofs, which are laws of the universe

              Now you’re getting it.

              this particular notation

              …which is Maths.

              Reverse Polish Notation doesn’t have this issue, at all

              Neither does infix notation. All notations have to obey the rules of Maths, since the rules of Maths are universal.

              Distribution is not even possible in RPN

              Second hit in my Google results…

              (3) -6 is asking for trouble

              It’s -3 - where’s the trouble?

              say 8/2*(1+3) is different from 8/2(1+3), because in the notation used by coders, they both become 8/2*4

              Welcome to why almost every single e-calculator is wrong (as opposed to handheld calculators) - MathGPT gets it right.

              • mindbleach@sh.itjust.works
                2·
                9 months ago

                Nothing in Maths is made up. It’s based on our observations of how things work.

                The notation and syntax of how we express that, is made-up. There’s multiple options. There’s disagreements. Fuck me sideways, you are a teacher, and you can’t figure out how being off-topic works?

                Evidently not, as you flip between ‘this particular notation is the notation!’ to ‘of course other notations exist’ and suffer zero cognitive dissonance. By capital-M “Maths,” do you mean the notation on paper, or the underlying laws-of-reality stuff? It depends! It’s ambiguous and requires context, or maybe you’re just factually wrong at least one of those times, and either way, that means it’s plainly not THE SAME KIND OF THING as the laws-of-reality stuff.

                It’s a category error. You can prove that the word prove isn’t spelled proove, for some reason, but the heavens would not bend the other direction if that changed. We could swap square braces and parenthesis and nothing would be different. We could use the glyph “&” instead of “7.” These details are mutable and completely fucking arbitrary. But then & - 6 = 1, and you could never proove otherwise.

                Second hit in my Google results…

                Shows B being subtracted from A before that value is multiplied by C. It’s not distribution. It’s evaluating the parenthetical.

                It’s -3 - where’s the trouble?

                The fact it’s 3 and -6, not 3 - 6. Which is why I explicitly mentioned that -6 was a number, and used two other examples with -6. I wasn’t just making conversation. Jesus fucking Christ, a state trusts you with the education of children.

                According to the textbook you’re now screenshotting at people, A(B) and (B)A are both correct - yes? They’re both valid? And spaces have no impact on an equation? And writing equations like -6 + 1 are fine, instead of (-6) + 1, since you don’t want needless parentheses?

                • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
                  1·
                  9 months ago

                  ‘this particular notation is the notation!’ to ‘of course other notations exist’

                  The notation for division in some countries is the obelus, in other countries it’s a colon. Whatever country you’re in, the notation for that country is the notation for division (be it an obelus or a colon).

                  Maths,” do you mean the notation on paper, or the underlying laws-of-reality stuff

                  Both! Whatever notation your country uses, all the rules for Maths and use of that Maths notation are defined.

                  It’s ambiguous

                  No, it’s not.

                  It’s not distribution. It’s evaluating the parenthetical

                  And Distribution applies to brackets/parentheses where they have a coefficient. In other words, same same.

                  it’s 3 and -6, not 3 - 6

                  You didn’t put a comma between 3 and -6, so no, it’s not 3 and -6, it’s 3-6. That’s what you wrote, that’s what it is.

                  a state trusts you with the education of children

                  Related - have you noticed how children never get this wrong? It’s only adults who’ve forgotten the rules of Maths who get it wrong.

                  According to the textbook you’re now screenshotting at people, A(B) and (B)A are both correct - yes? They’re both valid? And spaces have no impact on an equation? And writing equations like -6 + 1 are fine, instead of (-6) + 1, since you don’t want needless parentheses?

                  Yes (though the latter is unconventional), yes (though the latter is unconventional), yes, yes (though unconventional - 1-6 is the conventional way to write that), yes, yes.

    • Crozekiel@lemmy.zip
      0·
      1 year ago

      This is the way. It’s an intentionally ambiguously written problem to cause this issue depending on how and where you learned order of operations to cause a fight.

        • Crozekiel@lemmy.zipEnglish
          2·
          9 months ago

          Please see this section of Wikipedia on the order of operations.

          The “math” itself might not be ambiguous, but how we write it down absolutely can be. This is why you don’t see actual mathematicians arguing over which one of these calculators is correct - it is not either calculator being wrong, it is a poorly constructed equation.

          As for order of operations, they are “meant to be” the same everywhere, but they are taught differently. US - PEMDAS vs UK - BODMAS (notice division and multiplication swapped places). Now, they will say they are both given equal priority, but you can’t actually do all of the multiplication and division at one time. Some are taught to simply work left to right, while others are taught to do multiplication first; but we are all taught to use parentheses correctly to eliminate ambiguity.

          • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
            1·
            9 months ago

            Please see this section of Wikipedia on the order of operations

            That section is about multiplication, and there isn’t any multiplication in this expression.

            The “math” itself might not be ambiguous, but how we write it down absolutely can be

            Not in this case it isn’t. It has been written in a way which obeys all the rules of Maths.

            This is why you don’t see actual mathematicians arguing over which one of these calculators is correct

            But I do! I see University lecturers - who have forgotten their high school Maths rules (which is where this topic is taught) - arguing about it.

            it is not either calculator being wrong

            Yes, it is. The app written by the programmer is ignoring The Distributive Law (most likely because the programmer has forgotten it and not bothered to check his Maths is correct first).

            US - PEMDAS vs UK - BODMAS

            Those aren’t the rules. They are mnemonics to help you remember the rules

            notice division and multiplication swapped places

            Yes, that’s right, because they have equal precedence and it literally doesn’t matter which way around you do them.

            you can’t actually do all of the multiplication and division at one time

            Yes, you can!

            Some are taught to simply work left to right

            Yes, that’s because that’s the easy way to obey the actual rule of Left associativity.

            we are all taught to use parentheses correctly to eliminate ambiguity

            Correct! So 2(2+2) unambiguously has to be done before the division.

            • Crozekiel@lemmy.zipEnglish
              1·
              9 months ago

              Just out of curiosity, what is the first 2 doing in “2(2+2)”…? What are you doing with it? Possibly multiplying it with something else?

              there isn’t any multiplication in this expression.

              Interesting.

              I really hope you aren’t actually a math teacher, because I feel bad for your students being taught so poorly by someone that barely has a middle school understanding of math. And for the record, I doubt anyone is going to accept links to your blog as proof that you are correct.

              • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
                1·
                9 months ago

                Just out of curiosity, what is the first 2 doing in “2(2+2)”…? What are you doing with it? Possibly multiplying it with something else?

                Distributing it, as per The Distributive Law. Even Khan Academy makes sure to not call it “multiplication”, because that refers literally to multiplication signs., which, as I said, there aren’t any in this expression - only brackets and division (and addition within the brackets).

                I feel bad for your students

                My students are doing well thanks.

                I doubt anyone is going to accept links to your blog as proof that you are correct

                You mean the blog that has Maths text book references, historical Maths documents, and proofs? You know proofs are always true, right? But thanks for the ad hominem anyway, instead of any actual proof or evidence to support your own claims.

  • Queue@lemmy.blahaj.zoneEnglish
    2·
    9 months ago

    For anyone like me who has math as their worst subject: PEMDAS.

    PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

    So we gotta do it in the proper order. And remember, if the number is written like 2(3) then its multiplication, as if it was written 2 x 3 or 2 * 3.

    So we read 8/2(2+2) and need to do the following;

    • Read the Parentheses of (2 + 2) and follow the order of operations within them, which gets us 4.
    • Then we do 2(4) which is the same as 2 x 4 which is 8
    • 8 / 8 is 1.

    The answer is 1. The old calculator is correct, the phone app which has ads backed into it for a thing that all computers were invented to do is inaccurate.

    • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
      1·
      9 months ago

      Turns out I’m wrong, but I haven’t been told how or why. I’m willing to learn if people actually tell me

      Well, I don’t know what you said originally, so I don’t know what it is you were told was wrong - 1 or 16? 😂 The correct answer is 1.

      Anyhow, I have an order of operations thread which covers literally everything there is to know about it (including covering all the common mistakes and false claims made by some). It includes textbook references, historical Maths documents, worked examples, proofs, memes, the works! I’m a high school Maths teacher/tutor - I’ve taught this topic many times.

    • Coreidan@lemmy.worldEnglish
      0·
      1 year ago

      PEMDAS evaluated from left to right. If you followed that you’d get 16. 1 is ignoring left to right.

    • nutcase2690@lemmy.dbzer0.com
      0·
      1 year ago

      The problem with this is that the division symbol is not an accurate representation of the intended meaning. Division is usually written in fractions which has an implied set of parenthesis, and is the same priority as multiplication. This is because dividing by a number is the same as multiplying by the inverse, same as subtracting is adding the negative of a number.

      8/2(2+2) could be rewritten as 8×1/2×(2+2) or (8×(2+2))/2 which both resolve into 16.

      • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
        1·
        9 months ago

        Division is usually written in fractions

        Division and fractions aren’t the same thing.

        fractions which has an implied set of parenthesis

        Fractions are explicitly Terms. Terms are separated by operators (such as division) and joined by grouping symbols (such as a fraction bar), so 1÷2 is 2 terms, but ½ is 1 term.

        8/2(2+2) could be rewritten as 8×1/2×(2+2)

        No, it can’t. 2(2+2) is 1 term, in the denominator. When you added the multiply you broke it into 2 terms, and sent the (2+2) into the numerator, thus leading to a different answer. 8/2(2+2)=1.

      • Zagorath@aussie.zone
        1·
        1 year ago

        You left out the way it can be rewritten which most mathematicians would actually use, which is 8/(2(2+2)), which resolves to 1.

    • amtwon@lemmy.worldEnglish
      0·
      1 year ago

      not to be That Guy, but the phone is actually correct… multiplication and division have the same precedence, so 8 / 2 * 4 should give the same result as 8 * 4 / 2, ie 16

    • a_fine_hound@lemmy.world
      0·
      1 year ago

      Well that’s just wrong… Multiplication and division have equal priorities so they are done from left to right. So: 8 / 2 * (2 + 2)=8 / 2 * 4=4 * 4=16

        • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
          2·
          9 months ago

          Correct! 2(2+2) is a single term - subject to The Distributive Law - and 2x(2+2) is 2 terms. Those who added a multiply sign there have effectively flipped the (2+2) from being in the denominator to being in the numerator, hence the wrong answer.

          But it’s not called “implicit multiplication” - it’s Terms and/or The Distributive Law which applies (and they’re 2 separate rules, so you cannot lump them together as a single rule).

      • nutcase2690@lemmy.dbzer0.com
        0·
        1 year ago

        Not quite, pemdas can go either from the left or right (as long as you are consistent) and division is the same priority as multiplication because dividing by something is equal to multiplying by the inverse of that thing… same as subtraction being just addition but you flip the sign.

        8×1/2=8/2 1-1=1+(-1)

        The result is 16 if you rewrite the problem with this in mind: 8÷2(2+2)=8×(1/2)×(2+2)

        • Omega_Jimes@lemmy.ca
          0·
          1 year ago

          I’ve never had anyone tell me operations with the same priority can be done either way, it’s always been left to right.

          • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
            2·
            9 months ago

            I’ve never had anyone tell me operations with the same priority can be done either way, it’s always been left to right

            It’s left to right within each operator. You can do multiplication first and division next, or the other way around, as long as you do each operator left to right. Having said that, you also can do the whole group of equal precedence operators left to right - because you’re still preserving left to right for each of the two operators - so you can do multiplication and division left to right at the same time, because they have equal precedence.

            Having said that, it’s an actual rule for division, but optional for the rest. The actual rule is you have to preserve left-associativity - i.e. a number is associated with the sign to the left of it - and going left to right is an easy way to do that.

          • nutcase2690@lemmy.dbzer0.com
            0·
            1 year ago

            I’ve always heard it that way too but I think it is for consistency with students, imo Logically, if you are looking at division = multiplying by inverse and subtraction = adding the negative, you should be able to do it both ways. Addition and multiplication are both associative, so we can do 1+2+3 = (1+2)+3 = 1+(2+3) and get the same answer.

            • ReveredOxygen@sh.itjust.worksEnglish
              0·
              1 year ago

              But subtraction and division are not associative. Any time you work on paper, 2 - 2 - 2 would equal -2. That is, (2-2)-2=0-2=-2. If you evaluate right to left, you get 2-2-2=2-(2-2)=2-0=2

              • nutcase2690@lemmy.dbzer0.com
                1·
                1 year ago

                Correct, subtraction and division are not associative. However, what is subtraction if not adding the opposite of a number? Or division if not multiplying the inverse? And addition and multiplication are associative.

                2-2-2 can be written as 2 + (-2) + (-2) which would equal -2 no matter if you solve left to right, or right to left.

                In your example with the formula from right to left, distributing the negative sign reveals that the base equation was changed, so it makes sense that you saw a different answer.

                2 - (2 - 2) = 2 + ((-2) + 2) = 2

    • hallettj@beehaw.orgEnglish
      0·
      1 year ago

      The problem is that the way PEMDAS is usually taught multiplication and division are supposed to have equal precedence. The acronym makes it look like multiplication comes before division, but you’re supposed to read MD and as one step. (The same goes for addition and subtraction so AS is also supposed to be one step.) It this example the division is left of the multiplication so because they have equal precedence (according to PEMDAS) the division applies first.

      IMO it’s bad acronym design. It would be easier if multiplication did come before division because that is how everyone intuitively reads the acronym.

      Maybe it should be PE(M/D)(A/S). But that version is tricky to pronounce. Or maybe there shouldn’t be an acronym at all.

    • CaptDust@sh.itjust.works
      0·
      1 year ago

      Uh… no the 1 is wrong? Division and multiplication have the same precedence, so the correct order is to evaluate from left to right, resulting in 16.

  • I Cast Fist@programming.devEnglish
    1·
    1 year ago

    The problem is that there’s no “external” parentheses to really tell us which is right: (8 / 2) * 4 or 8 / (2 * 4)

    The amount of comments here shows how much debate this “simple” thing generates

  • linuxdweeb@lemm.ee
    1·
    1 year ago

    Please Excuse My Dear Aunt Sally, she downloaded a shitty ad-infested calculator from the Google Play store.

  • subignition@kbin.social
    1·
    1 year ago

    […] the question is ambiguous. There is no right or wrong if there are different conflicting rules. The only ones who claim that there is one rule are the ones which are wrong!

    https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

    As youngsters, math students are drilled in a particular
    convention for the “order of operations,” which dictates the order thus:
    parentheses, exponents, multiplication and division (to be treated
    on equal footing, with ties broken by working from left to right), and
    addition and subtraction (likewise of equal priority, with ties similarly
    broken). Strict adherence to this elementary PEMDAS convention, I argued,
    leads to only one answer: 16.

    Nonetheless, many readers (including my editor), equally adherent to what
    they regarded as the standard order of operations, strenuously insisted
    the right answer was 1. What was going on? After reading through the
    many comments on the article, I realized most of these respondents were
    using a different (and more sophisticated) convention than the elementary
    PEMDAS convention I had described in the article.

    In this more sophisticated convention, which is often used in
    algebra, implicit multiplication is given higher priority than explicit
    multiplication or explicit division, in which those operations are written
    explicitly with symbols like x * / or ÷. Under this more sophisticated
    convention, the implicit multiplication in 2(2 + 2) is given higher
    priority than the explicit division in 8÷2(2 + 2). In other words,
    2(2+2) should be evaluated first. Doing so yields 8÷2(2 + 2) = 8÷8 = 1.
    By the same rule, many commenters argued that the expression 8 ÷ 2(4)
    was not synonymous with 8÷2x4, because the parentheses demanded immediate
    resolution, thus giving 8÷8 = 1 again.

    This convention is very reasonable, and I agree that the answer is 1
    if we adhere to it. But it is not universally adopted.

    • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
      1·
      9 months ago

      […] the question is ambiguous. There is no right or wrong if there are different conflicting rules. The only ones who claim that there is one rule are the ones which are wrong!

      https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

      Yeah nah. Actual Maths textbooks and proofs - did you not notice the complete lack of references to textbooks in the blog? It’s funny that he mentions Cajori though, given Cajori has a direct reference to Terms #MathsIsNeverAmbiguous

    • Coreidan@lemmy.worldEnglish
      0·
      1 year ago

      Everyone in this threading referencing PEMDAS and still thinking the answer is 1 are completely ignoring the part of the convention is left to right. Only way to get 1 is to violate left to right on multiplication and division.

      • Zagorath@aussie.zone
        1·
        1 year ago

        The problem is that BIDMAS and its variants are lies-to-children. Real mathematicians don’t use BIDMAS. Multiplication by juxtaposition is extremely common, and always takes priority over division.

        Nobody in their right minds would saw 1/2x is the same as (1/2)x. It’s 1/(2x).

        That’s how you get 1. By following conventions used by mathematicians at any level higher than primary school education.

        • EndlessApollo@lemmy.world
          0·
          1 year ago

          Source? I have a hard ass time believing that nobody in their right mind would do pemdas the way you’re supposed to do it xD

          • Zagorath@aussie.zoneEnglish
            0·
            1 year ago

            The problem is that you’re thinking of BIDMAS as a set of hard rules, rather than the set of rough guidelines created in the early 20th century by one random teacher for the purposes of teaching 10-year-olds how to do the level of maths that 10-year-olds do.

            This video and this one point to some examples of style guides in academia as well as practical examples in the published works of mathematicians and physicists, which are pretty consistent.

            If you want to come up with a hard rule, doing BIJMDAS, adding in “multiplication indicated by juxtaposition” with the J, is a much better way to do it than what you learnt when you were 10. But even that’s still best to think of as a handy guideline rather than a hard and fast rule.

            • EndlessApollo@lemmy.world
              0·
              1 year ago

              That’s cool, but still wrong :3

              No fr I had no idea that those acronyms weren’t the whole picture, I just assumed some mathematicians a long time ago decided how that stuff should be written out and that BEDMAS/PEMDAS/whatever contained all the rules in it. Thank you for the info, Idk why this isn’t more widely taught, ig because those acronyms are what all the questions are already written for? It doesn’t seem that hard to just teach it as BEADMAS, where the A refers to numbers adjacent to variables

  • cRazi_man@lemm.ee
    1·
    1 year ago

    Ah damn it. It took me ages to find a calculator app that fits my needs… And now I find out it works like the one on the right.

  • Zummy@lemmy.world
    1·
    1 year ago

    I don’t understand why people say Maths. Math encompasses every single type of Math. Maths is just wrong.

  • Rentlar@lemmy.ca
    0·
    1 year ago

    I treat • and × differently, • I treat like the left side and × I treat like the right side calculation.

      • Rentlar@lemmy.ca
        1·
        9 months ago

        Yes they both are multiply, but…

        Calculate 8 ÷ 2a where a = 4. Then,

        Calculate 8 ÷ 2 × a where a = 4.

        See how in the first form a is implied to be part of the fraction where in the second it isn’t?

        A dot • could be between 2 and a and it would still follow the first example. In vector multiplication, dot and cross products produce different results.

        • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
          2·
          9 months ago

          Calculate 8 ÷ 2a where a = 4. Then,

          Calculate 8 ÷ 2 × a where a = 4.

          See how in the first form a is implied to be part of the fraction where in the second it isn’t?

          It’s not implied, it’s explicitly because of the definition of Terms.

          P.S. now substitute a=2 and you’ll see why it matters.

          A dot • could be between 2 and a and it would still follow the first example

          No, it wouldn’t. Inserting a dot (multiplication) makes it the same as your second example. i.e. 3 Terms, not 2 Terms.

          In vector multiplication, dot and cross products produce different results.

          This isn’t vector multiplication. This is Year 7 algebra.

          • Rentlar@lemmy.ca
            1·
            9 months ago

            We agree that the two situations are separate. You can call them terms or whatever, since we’re multiplying and dividing the idea of terms seems irrelevant here to me but I suppose for pedantry’s sake we can entertain it. It doesn’t matter what a is, but the first result is 4 ÷ a the second result is 4a.

            I use the dot as an expression of the same term rather than separate. This is matter of my notational convention, due to dot multiplication providing a single scalar result where cross multiplication resulting in a vector product. You can write 10 paragraphs telling me that my convention is wrong and why but I don’t really care that much, to save you some time.

            ETA: When I handwrite out non-Vector equations, you will rarely see me write a • or a × sign inside of a fraction anyway, it’s placement is generally clear enough for me, and I will put brackets where it’s confusing.

            • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
              1·
              9 months ago

              We agree that the two situations are separate

              Ok, that’s a start.

              but the first result is 4 ÷ a the second result is 4a

              Exactly! So when a=2 then 4÷a=2, and 4a=8, which isn’t the same thing. Welcome to why 2a and 2xa (and therefore also 2.a) aren’t the same thing.

              I use the dot as an expression of the same term rather than separate.

              But that is incorrect. A dot is used for multiplication. i.e. it separates terms. If you use a . for 2.a, then you are writing the same thing as 2xa, not the same thing as 2a.

              This is matter of my notational convention

              Well, that’s fine enough if you keep it to yourself, but don’t use it in anything anyone else is going to read, or you’re going to run into the issues I just pointed out

  • arisunz@lemmy.blahaj.zone
    0·
    1 year ago

    this comment section illustrates perfectly why i hate maths so much lmao

    love ambiguous, confusing rules nobody can even agree on!

    • 4am@lemm.ee
      1·
      1 year ago

      PEMDAS

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

      The rule is much older than me and they taught it in school. Nothing ambiguous about it, homie. The phone app is fucked up. Calculator nailed it.

    • onion@feddit.de
      1·
      1 year ago

      The problem isn’t math, it’s the people that suck at at it who write ambigous terms like this, and all the people in the comments who weren’t educated properly on what conventions are.

      • Swallowtail@beehaw.org
        0·
        1 year ago

        Yeah, you could easily make this more straightforward by putting parentheses around 8÷2. It’s like saying literature sucks because Finnegans Wake is incomprehensible.

        • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
          1·
          9 months ago

          you could easily make this more straightforward by putting parentheses around 8÷2

          But that would be a different expression with a different answer (16 rather than 1). This is the mistake made by the programmer of the e-calc - treats it as though there’s extra brackets there when there isn’t.

      • loops@beehaw.orgEnglish
        0·
        1 year ago

        Huge shout out to the jaded AF high school math teachers that don’t give a fuck any more!

        • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
          1·
          9 months ago

          They do care. The issue is everyone argues about it without even asking Maths teachers about it to being with! I guarantee (I’ve seen it myself) literally every blog you read which says this is “ambiguous”, without exception they never mention Maths textbooks or Maths teachers (because then they wouldn’t be able to bombastically declare “This is ambiguous!”).

    • UnRelatedBurner@sh.itjust.works
      0·
      1 year ago

      lol, math is literally the only subject that has rules set in stone. This example is specifically made to cause confusion. Division has the same priority as multiplication. You go from left to right. problem here is the fact that you see divison in fraction form way more commonly. A fraction could be writen up as (x)/(y) not x/y (assuming x and y are multiple steps). Plain and simple.

      The fact that some calculator get it wrong means that the calculator is wrongly configured. The fact that some people argue that you do () first and then do what’s outside it means that said people are dumb.

      They managed to get me once too, by everyone spreading missinformation so confidently. Don’t even trust me, look up the facts for yourself. And realise that your comment is just as incorrect as everyone who said the answer is 1. (uhm well they don’t agree on 0^0, but that’s kind of a paradox)

      • Primarily0617@kbin.social
        1·
        1 year ago

        math is literally the only subject that has rules set in stone

        go past past high school and this isn’t remotely true

        there are areas of study where 1+1=1

      • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
        1·
        9 months ago

        math is literally the only subject that has rules set in stone

        Indeed, it does.

        This example is specifically made to cause confusion.

        No, it isn’t. It simply tests who has remembered all the rules of Maths and who hasn’t.

        Division has the same priority as multiplication

        And there’s no multiplication here - only brackets and division (and addition within the brackets).

        A fraction could be writen up as (x)/(y) not x/y

        Neither of those. A fraction could only be written inline as (x/y) - both of the things you wrote are 2 terms, not one. i.e. brackets needed to make them 1 term.

        The fact that some people argue that you do () first and then do what’s outside it means that

        …they know all the relevant rules of Maths

        look up the facts for yourself

        You can find them here

        your comment is just as incorrect as everyone who said the answer is 1

        and 1 is 100% correct.

        well they don’t agree on 0^0

        Yes they do - it’s 1 (it’s the 5th index law). You might be thinking of 0/0, which depends on the context (you need to look at limits).

            • UnRelatedBurner@sh.itjust.works
              1·
              9 months ago

              Fuck it, I’m gonna waste time on a troll on the internet who’s necroposting in te hopes that they actually wanna argue the learning way.

              This example is specifically made to cause confusion.

              No, it isn’t. It simply tests who has remembered all the rules of Maths and who hasn’t.

              I said this because of the confusion around the division sign. Almost everyone at some point got it confused, or is just hell bent that one is corrent the other is not. In reality, it is such a common “mistake” that ppl started using it. I’m talking about the classic 4/2x. If x = 2, it is:

              1. 4/2*2 = 2*2 = 4
              2. 4/(2*2) = 4/4 = 1

              Wolfram solved this with going with the second if it is an X or another variable as it’s more intuitive.

              Division has the same priority as multiplication

              And there’s no multiplication here - only brackets and division (and addition within the brackets).

              Are you sure ur not a troll? how do you calculate 2(1+1)? It’s 4. It’s called implicit multiplication and we do it all the time. It’s the same logic that if a number doesn’t have a sign it’s positive. We could write this up as +2*(+1+(+1)), but it’s harder to read, so we don’t.

              A fraction could be writen up as (x)/(y) not x/y

              Neither of those. A fraction could only be written inline as (x/y) - both of the things you wrote are 2 terms, not one. i.e. brackets needed to make them 1 term.

              I don’t even fully understand you here. If we have a faction; at the top we have 1+2 and at the bottom we have 6-3. inline we could write this as (1+2)/(6-3). The result is 1 as if we simplify it’s 3/3.

              You can’t say it’s ((1+2)/(6-3)). It’s the same thing. You will do the orders differently, but I can’t think of a situation where it’s incorrect, you are just making things harder on yourself.

              The fact that some people argue that you do () first and then do what’s outside it means that

              …they know all the relevant rules of Maths

              You fell into the 2nd trap too. If there is a letter or number or anything next to a bracket, it’s multiplication. We just don’t write it out, as why would we, to make it less readable? 2x is the same as 2*x and that’s the same as 2(x).

              look up the facts for yourself

              You can find them here

              I can’t even, you linked social media. The #1 most trust worthy website. Also I can’t even read this shit. This guy talks in hashtags. I won’t waste energy filtering out all the bullshit to know if they are right or wrong. Don’t trust social media. Grab a calculator, look at wolfram docs, ask a professor or teacher. Don’t even trust me!

              your comment is just as incorrect as everyone who said the answer is 1

              and 1 is 100% correct.

              I chose a side. But that side it the more RAW solution imo. let’s walk it thru:

              • 8/2(2+2), let’s remove the confusion
              • 8/2*(2+2), brackets
              • 8/2*(4), mult & div, left -> right
              • 4*(4), let go
              • 4*4, the only
              • 16, answer

              BUT, and as I stated above IF it’d be like: 8/2x with x=2+2 then, we kinda decided to put implicit brackets there so it’s more like 8/(2x), but it’s just harder to read, so we don’t.

              And here is the controversy, we are playing the same game. Because there wasn’t a an explicit multilication, you could argue that it should be handled like the scenario with the x. I disagree, you agree. But even this argument of “like the scenario with the x” is based of what Wolfram decided, there are no rules of this, you do what is more logical in this scenario. It can be a flaw in math, but it never comes up, as you use fractions instead of inline division. And when you are converting to inline, you don’t spear the brackets.

              well they don’t agree on 0^0

              Yes they do - it’s 1 (it’s the 5th index law). You might be thinking of 0/0, which depends on the context (you need to look at limits).

              You said it yourself, if we lim (x->0) y/x then there is an answer. But we aren’t in limits. x/0 in undefined at all circumstances (I should add that idk abstract algebra & non-linear geometry, idk what happens there. So I might be incorrect here).

              And by all means, correct me if I’m wrong. But link something that isn’t an unreadable 3 parted mostodon post like it’s some dumb twitter argument. This is some dumb other platform argument. Or don’t link anything at all, just show me thru, and we know math rules (now a bit better) so it shouldn’t be a problem… as long as we are civilised.

              side note: if I did some typos… it’s 2am, sry.

              • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
                1·
                9 months ago

                I’m talking about the classic 4/2x. If x = 2, it is:

                4/2x2 = 2x2 = 4

                4/(2x2) = 4/4 = 1

                It’s the latter, as per the definition of Terms. There are references to this definition being used going back more than 100 years.

                Wolfram solved this with going with the second if it is an X or another variable as it’s more intuitive

                Yes, they do if it’s 2x, but not if it’s 2(2+2) - despite them mathematically being the same thing - leading to wrong answers to expressions such as the OP. In fact, that’s true of every e-calculator I’ve ever seen, except for MathGPT (Desmos used to handle it correctly, but then they made a change to make it easier to enter fractions, and consequently broke evaluating divisions correctly).

                how do you calculate 2(1+1)? It’s 4. It’s called implicit multiplication

                No, it’s not called implicit multiplication. It’s distribution.

                We could write this up as +2*(+1+(+1))

                No, you can’t. Adding that multiplication has broken it up into 2 terms. You either need to not add the multiply, or add another set of brackets if you do, to keep it as 1 term.

                I can’t think of a situation where it’s incorrect

                If a=2 and b=3, then…

                1/axb=3/2

                1/ab=(1/6)

                If there is a letter or number or anything next to a bracket, it’s multiplication

                No, it’s distribution. Multiplication refers literally to multiplication signs, of which there aren’t any in this expression.

                2x is the same as 2*x

                No, 2A is the same as (2xA). i.e. it’s a single Term. 2xA is 2 Terms (multiplied).

                If a=2 and b=3, then…

                axb=2x3 (2 terms)

                ab=6 (1 term)

                This guy talks in hashtags.

                Only in the first post in each thread, so that people following those hashtags will see the first post, and can then click on it if they want to see the rest of the thread. Also “this guy” is me. :-)

                Grab a calculator, look at wolfram docs, ask a professor or teacher

                I’m a Maths teacher with a calculator and many textbooks - I’m good. :-) Also, if you’d clicked on the thread you would’ve found textbook references, historical Maths documents, proofs, the works. :-)

                8/2(2+2), let’s remove the confusion

                8/2*(2+2), brackets

                8/2*(4), mult & div, left -> right

                4*(4), let go

                2 mistakes here. Adding the multiplication sign in the 2nd step has broken up the term in the denominator, thus sending the (2+2) into the numerator, hence the wrong answer (and thus why we have a rule about Terms). Then you did division when there was still unsolved brackets left, thus violating order of operations rules.

                it’s more like 8/(2x), but it’s just harder to read, so we don’t

                But that’s exactly what we do (but no extra brackets needed around 2x nor 2(2+2) - each is a single term).

                you could argue that it should be handled like the scenario with the x

                Which is what the rules of Maths tells us to do - treat a single term as a single term. :-)

                there are no rules of this

                Yeah, there is. :-)

                you use fractions instead of inline division

                No, never. A fraction is a single term (grouped by a fraction bar) but division is 2 terms (separated by the division operator). Again it’s the definition of Terms.

                And by all means, correct me if I’m wrong

                Have done, and appreciate the proper conversation (as opposed to those who call me names for simply pointing out the actual rules of Maths).

                link something that isn’t an unreadable

                No problem. I t doesn’t go into as much detail as the Mastodon thread though, but it’s a shorter read (overall - with the Mastodon thread I can just link to specific parts though, which makes it handier to use for specific points), just covering the main issues.

                as long as we are civilised

                Thanks, appreciated.

                • UnRelatedBurner@sh.itjust.works
                  1·
                  9 months ago

                  Idk where you teach, but I’m thankful you didn’t teach me.

                  Let me quizz you, how do you solve 2(2+2)^2? because acording to your linked picture, because brackets are leftmost you do them first. If I were to believe you:

                  • (2*2+2*2)^2
                  • (4+4)^2, = 64

                  but it’s just simply incorrect.

                  • 2(4)^2, wow we’re at a 2x^2
                  • 2*16 = 32

                  The thing that pisses me off most, is the fact that, yes. Terms exists, yes they have all sorts of properties. But they are not rules, they are properties. And they only apply when we have unknows and we’re at the most simplified form. For example your last link, the dude told us that those terms get prio because they are terms!? There are no mention of term prio in the book. It just simply said that when we have a simplified expression like: 2x^2+3x+5 we call 2x^2 and 3x and 5 terms. And yes they get priority, not because we named them those, but because they are multiplications. These help us at functions the most. Where we can assume that the highest power takes the sign at infinity. Maybe if the numbers look right, we can guess where it’d switch sign.

                  I don’t even want to waste energy proofreading this, or telling you the obvious that when we have a div. and a mult. and no x’s there really is no point in using terms, as we just get a single number.

                  But again, I totally understand why someone would use this, it’s easier. But it’s not the rule still. That’s why at some places this is the default. I forgot the name/keywords but if you read a calculator’s manual there must be a chapter or something regarding this exact issue.

                  So yeah, use it. It’s good. Especially if you teach physics. But please don’t go around making up rules.

                  As for your sources, you still linked a blog post.

      • Zagorath@aussie.zone
        0·
        1 year ago

        If we had 1/2x, would you interpret that as 0.5x, or 1/(2x)?

        Because I can guarantee you almost any mathematician or physicist would assume the latter. But the argument you’re making here is that it should be 0.5x.

        It’s called implicit multiplication or “multiplication indicated by juxtaposition”, and it binds more tightly than explicit multiplication or division. The American Mathematical Society and American Physical Society both agree on this.

        BIDMAS, or rather the idea that BIDMAS is the be-all end-all of order of operations, is what’s known as a “lie-to-children”. It’s an oversimplification that’s useful at a certain level of understanding, but becomes wrong as you get more advanced. It’s like how your year 5 teacher might have said “you can’t take the square root of a negative number”.

        • vithigar@lemmy.ca
          2·
          1 year ago

          An actual mathematician or physicist would probably ask you to clarify because they don’t typically write division inline like that.

          That said, Wolfram-Alpha interprets “1/2x” as 0.5x. But if you want to argue that Wolfram-Alpha’s equation parser is wrong go ahead.

          https://www.wolframalpha.com/input?i=1%2F2x

            • vithigar@lemmy.ca
              1·
              9 months ago

              Dude, this thread is four months old and I’ve gotten several notifications over the past week from you sporadically responding to comments I barely remember making. Find something better to do with your time than internet argument archeology. I’ll even concede the point if it helps make you go away.

              Thanks for the correction, you are right.

          • Zagorath@aussie.zone
            0·
            1 year ago

            I will happily point out that Wolfram Alpha does this wrong. So do TI calculators, but not Casio or Sharp.

            Go to any mathematics professor and give them a problem that includes 1/2x and ask them to solve it. Don’t make it clear that merely asking “how do you parse 1/2x?” is your intent, because in all likelihood they’ll just tell you it’s ambiguous and be done with it. But if it’s written as part of a problem and they don’t notice your true intent, you can guarantee they will take it as 1/(2x).

            Famed physicist Richard Feynman uses this convention in his work.

            In fact, even around the time that BIDMAS was being standardised, the writing being done doing that standardisation would frequently use juxtaposition at a higher priority than division, without ever actually telling the reader that’s what they were doing. It indicates that at the time, they perhaps thought it so obvious that juxtaposition should be performed first that it didn’t even need to be explained (or didn’t even occur to them that they could explain it).

            According to Casio, they do juxtaposition first because that’s what most teachers around the world want. There was a period where their calculators didn’t do juxtaposition first, something they changed to because North American teachers were telling them they should, but the outcry front the rest of the world was enough for them to change it back. And regardless of what teachers are doing, even in America, professors of mathematics are doing juxtaposition first.

            I think this problem may ultimately stem from the very strict rote learning approach used by the American education system, where developing a deeper understanding of what’s going on seems to be discouraged in favour of memorising facts like “BIDMAS”.

            • vithigar@lemmy.ca
              1·
              1 year ago

              To be clear, I’m not saying 1/2x being 1/(2x) rather than 0.5x is wrong. But it’s not right either. I’m just pretty firmly in the “inline formulae are ambiguous” camp. Whichever rule you pick, try to apply it consistently, but use some other notation or parenthesis when you want to be clearly understood.

              The very fact that this conversation even happens is proof enough that the ambiguity exists. You can be prescriptive about which rules are the correct ones all you like, but that’s not going to stop people from misunderstanding. If your goal is to communicate clearly, then you use a more explicit notation.

              Even Wolfram Alpha makes a point of restating your input to show how it’s being interpreted, and renders “1/2x” as something more like

              1
- x
2

              to make very clear what it’s doing.

              • Zagorath@aussie.zoneEnglish
                0·
                1 year ago

                Even Wolfram Alpha makes a point of restating your input to show how it’s being interpreted

                This is definitely the best thing to do. It’s what Casio calculators do, according to those videos I linked.

                My main point is that even though there is theoretically an ambiguity there, the way it would be interpreted in the real world, by mathematicians working by hand (when presented in a way that people aren’t specifically on the lookout for a “trick”) would be overwhelmingly in favour of juxtaposition being evaluated before division. Maybe I’m wrong, but the examples given in those videos certainly seem to point towards the idea that people performing maths at a high level don’t even think twice about it.

                And while there is a theoretical ambiguity, I think any tool which is operating counter to how actual mathematicians would interpret a problem is doing the wrong thing. Sort of like a dictionary which decides to take an opinionated stance and say “people are using the word wrong, so we won’t include that definition”. Linguists would tell you the job of a dictionary should be to describe how the word is used, not rigidly stick to some theoretical ideal. I think calculators and tools like Wolfram Alpha should do the same with maths.

                • vithigar@lemmy.ca
                  0·
                  1 year ago

                  Linguists would tell you the job of a dictionary should be to describe how the word is used, not rigidly stick to some theoretical ideal. I think calculators and tools like Wolfram Alpha should do the same with maths.

                  You’re literally arguing that what you consider the ideal should be rigidly adhered to, though.

                  “How mathematicians do it is correct” is a fine enough sentiment, but conveniently ignores that mathematicians do, in fact, work at WolframAlpha, and many other places that likely do it “wrong”.

                  The examples in the video showing inline formulae that use implicit priority have two things in common that make their usage unambiguous.
                  First, they all are either restating, or are derived from, formulae earlier in the page that are notated unambiguously, meaning that in context there is a single correct interpretation of any ambiguity.

                  Second, being a published paper it has to adhere to the style guide of whatever body its published under, and as pointed out in that video, the American Mathematical Society’s style guide specifies implicit priority, making it unambiguous in any of their published works. The author’s preference is irrelevant.

                  Also, if it’s universally correct and there was no ambiguity in its use among mathematicians, why specify it in the style guide at all?

      • kpw@kbin.social
        0·
        1 year ago

        Off topic, but the rules of math are not set in stone. We didn’t start with ZFC, some people reject the C entirely, then there is intuitionistic logic which I used to laugh at until I learned about proof assistants and type theory. And then there are people who claim we should treat the natural numbers as a finite set, because things we can’t compute don’t matter anyways.

        On topic: Parsing notation is not a math problem and if your notation is ambiguous or unclear to your audience try to fix it.

    • RickRussell_CA@lemmy.worldEnglish
      0·
      1 year ago

      It doesn’t have to be confusing. This particular formula is presented in a confusing way. Written differently, the ambiguity is easily resolved.

    • darthelmet@lemmy.world
      0·
      1 year ago

      This is more language/writing style than math. The math is consistent, what’s inconsistent is there are different ways to express math, some of which, quite frankly, are just worse at communicating the mathematical expression clearly than others.

      Personally, since doing college math classes, I don’t think I’d ever willingly write an expression like that exactly because it causes confusion. Not the biggest issue for a simple problem, much bigger issue if you’re solving something bigger and need combine a lot of expressions. Just use parentheses and implicit multiplication and division. It’s a lot clearer and easier to work with.

        • darthelmet@lemmy.world
          1·
          9 months ago

          Something about the way this thread was written was kind of confusing, so I don’t really get what their point was. Is it just that the terminology is wrong? Or am I missing something?

          Like, whatever you call it, a x b, a*b, ab, and a(b) are all acceptable notations to describe the operation “multiply a and b.” Some are nicer to use than others depending on the situation.

          • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
            1·
            9 months ago

            Something about the way this thread was written was kind of confusing,

            Ok, sorry about that. I’m more than happy to update it if you want to give me some constructive feedback on what was confusing about it. Note though that this was the 3rd part in the series, and maybe you didn’t go back and read the previous 2 parts? They start here

            Is it just that the terminology is wrong? Or am I missing something?

            Yes and yes. :-) The 2 actual rules of Maths that apply here are Terms and The Distributive Law. These are 2 different rules of Maths - neither of which is “multiplication” - and so when lumping them together as “implicit multiplication” you end up with unpredictable, and usually wrong, answers. The only way to always get the right answer is to follow the actual rules of Maths.

            a x b, a*b, ab, and a(b) are all acceptable notations to describe the operation “multiply a and b.”

            No, they’re not. The first two are multiplications, the second two are Terms. Note that a Term is a product, the result of a multiplication. In the mnemonics, “Multiplication”" refers literally to multiplication signs, and nothing else.

            • darthelmet@lemmy.world
              2·
              9 months ago

              Ok, sorry about that. I’m more than happy to update it if you want to give me some constructive feedback on what was confusing about it. Note though that this was the 3rd part in the series, and maybe you didn’t go back and read the previous 2 parts? They start here

              NP. I’m not really great at giving writing advice, so can’t really help there. Something about it just didn’t click when I read it. The extra context you linked did help a bit.

              As far as the issue: After reading it I think it does just seem to be a matter of terminology mixed with problems that arise with when you need to write math expressions inline in text. If you can write things out on paper or use a markdown language, it’s really easy to see how a fractional expression is structured.

              8

              2(1+3)

              is a lot easier to read than 8/2(1+3) even if they technically are meant to be evaluated the same. There’s no room for confusion.

              And as for distributive law vs multiplication, maybe this is just taking for granted a thing that I learned a long time ago, but to me they’re just the same thing in practice. When I see a(x+1) I know that in order to multiply these I need to distribute. And if we fill in the algebraic symbols for numbers, you don’t even need to distribute to get the answer since you can just evaluate the parentheses then use the result to multiply by the outside.

              Conversely, if I was factoring something, I would need to do division.

              ax + a

              a

              = x+1, thus: a(x+1)

              I think we’re basically talking about the same thing, I’m just being a bit lose with the terminology.

              And while we’re at it, the best way to make sure there’s no misunderstanding is to just use parenthesis for EVERYTHING! I’m mostly kidding, this can rapidly get unreadable once you nest more than a few parens, although for these toy expressions, it would have the desired effect.

              (8)/(2(1+3)) is obviously different than (8/2)(1+3)

              • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.devEnglish
                1·
                9 months ago

                8/2(1+3) even if they technically are meant to be evaluated the same

                But 8/2(1+3) isn’t a fraction. The / - the computing equivalent of ÷ (which can only be written using Unicode on a computer, so a bit of a pain to use compared to / )- is an operator, which means they’re 2 separate terms. A fraction bar is a grouping symbol, which means it’s 1 term. In this particular case it doesn’t matter, but if it appeared in a bigger expression then it absolutely does matter. The way to write 8/2(1+3) as a fraction inline is to add extra brackets. i.e. (8/2(1+3)) - because brackets are also a grouping symbol.

                And as for distributive law vs multiplication, maybe this is just taking for granted a thing that I learned a long time ago, but to me they’re just the same thing in practice

                Bu they’re not, for the same reason. Firstly, the Distributive Law isn’t multiplication at all - which only applies literally to multiplication symbols - it applies to bracketed terms (i.e. is a single term which needs to be distributed) - and secondly it applies to a single term, whereas multiplication applies to 2 terms (one before and one after). Anyone who talks about 2(1+3) needing to be “multiplied” has already made the mistake that is going to lead to a wrong answer (unless they just happen to “multiply” before they divide, which is an accidental way to get the right answer).

                if I was factoring something

                Indeed, that is the precise reason the Distributive Law exists - they are the opposite operation to each other! Anyone who adds a multiplication symbol has broken up the factorised term, again leading to the wrong answer.

                I’m just being a bit lose with the terminology

                Yeah, and that’s all I was pointing out in the first place - please don’t use “implicit multiplication”. The term itself - i.e. it includes “multiplication” - leads people to do it wrong (because they treat it as multiplication, not brackets, then argue about the precedence of “multiplication”!). It needs to die!

                this can rapidly get unreadable once you nest more than a few parens,

                Well that’s why the rules of Terms ab=(axb) and The Distributive Law a(b+c)=(a*(b+c))=(ab+ac) exist to begin with - less brackets! :-) Imagine having to write a fraction as (1/(axb)) all the time!

                (8)/(2(1+3)) is obviously different than (8/2)(1+3)

                Correct, though a lot of people treat it as the latter (yet another way to do it wrong - doing division before brackets) because they figure the 8/2 is “outside the brackets”, but in fact only the 2 is, because the slash separates them as being 2 terms.