Comment on I dunno

• SmartmanApps@programming.dev ⁨3⁩ ⁨weeks⁩ ago

  There isn’t one true order of operations that is objectively correct

  Yes there is, as found in Maths textbooks the world over

  that’s hardly the way most people would write that

  Maths textbooks write it that way

  you wouldn’t use the / symbol

  Yes you would.

  You’d either use ÷

  Same same

  It’s a good candidate for nerd sniping.

  Here’s one I prepared earlier to save you the trouble

  I’d call that 36

  And you’d be wrong

  as written given the context you’re saying it in

  The context is Maths, you have to obey the rules of Maths. a(b+c)=(ab+ac), 5(8-5)=(5x8-5x5).

  But I’d say it’s ambiguous

  And you’d be wrong about that too

  you should notate in a way to avoid ambiguities

  It already is notated in a way that avoids all ambiguities!

  Especially if you’re in the camp of multiplication like a(b)

  That’s not Multiplication, it’s Distribution, a(b+c)=(ab+ac), a(b)=(axb).

  being different from ab

  Nope, that’s exactly the same, ab=(axb) by definition

  and/or a × b

  (axb) is most certainly different to axb. 1/ab=1/(axb), 1/axb=b/a

  source

  • JackbyDev@programming.dev ⁨3⁩ ⁨weeks⁩ ago

    Please read this section of Wikipedia which talks about these topics better than I could. It shows that there is ambiguity in the order of operations and that for especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication. It addresses everything you’ve mentioned.

    en.wikipedia.org/wiki/Order_of_operations#Mixed_d…

    There is no universal convention for interpreting an expression containing both division denoted by ‘÷’ and multiplication denoted by ‘×’. Proposed conventions include assigning the operations equal precedence and evaluating them from left to right, or equivalently treating division as multiplication by the reciprocal and then evaluating in any order;[10] evaluating all multiplications first followed by divisions from left to right; or eschewing such expressions and instead always disambiguating them by explicit parentheses.[11]

    Beyond primary education, the symbol ‘÷’ for division is seldom used, but is replaced by the use of algebraic fractions,[12] typically written vertically with the numerator stacked above the denominator – which makes grouping explicit and unambiguous – but sometimes written inline using the slash or solidus symbol ‘/’.[13]

    Multiplication denoted by juxtaposition (also known as implied multiplication) creates a visual unit and is often given higher precedence than most other operations. In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.[2][10][14][15] For instance, the manuscript submission instructions for the Physical Review journals directly state that multiplication has precedence over division,[16] and this is also the convention observed in physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz[c] and mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik.[17] However, some authors recommend against expressions such as a / bc, preferring the explicit use of parenthesis a / (bc).[3]

    More complicated cases are more ambiguous. For instance, the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)] or [1 / (2π)] · (a + b).[18] Sometimes interpretation depends on context. The Physical Review submission instructions recommend against expressions of the form a / b / c; more explicit expressions (a / b) / c or a / (b / c) are unambiguous.[16]

    Image of two calculators getting different answers: 6÷2(1+2) is interpreted as 6÷(2×(1+2)) by a fx-82MS (upper), and (6÷2)×(1+2) by a TI-83 Plus calculator (lower), respectively.

    This ambiguity has been the subject of Internet memes such as “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations: 8 ÷ [2 · (2 + 2)] = 1 and (8 ÷ 2) · (2 + 2) = 16.[15][19] Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”, and calls such contrived examples “a kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rules”.[12]

    source

    • SmartmanApps@programming.dev ⁨3⁩ ⁨weeks⁩ ago

      Please read this section of Wikipedia which talks about these topics better than I could

      Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there’s plenty in here

      It shows that there is ambiguity in the order of operations

      and is wrong about that, as proven by Maths textbooks

      especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication

      That’s because Multiplication and Division can be done in any order

      It addresses everything you’ve mentioned

      wrongly, as per Maths textbooks

      Multiplication denoted by juxtaposition (also known as implied multiplication)

      Nope. Terms/Products is what they are called. “implied multiplication” is a “rule” made up by people who have forgotten the actual rules.

      s often given higher precedence than most other operations

      Always is, because brackets first. ab=(axb) by definition

      1 / 2n is interpreted to mean 1 / (2 · n)

      As per the definition that ab=(axb), 1/2n=1/(2xn).

      [2][10][14][15]

      Did you look at the references, and note that there are no Maths textbooks listed?

      the manuscript submission instructions for the Physical Review journals

      Which isn’t a Maths textbook

      the convention observed in physics textbooks

      Also not Maths textbooks

      mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik

      Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer

      More complicated cases are more ambiguous

      None of them are ambiguous.

      the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)]

      It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)

      or [1 / (2π)] · (a + b).[18]

      No, it can’t mean that unless it was written (1 / 2π)(a + b), which it wasn’t

      Sometimes interpretation depends on context

      Nope, never

      more explicit expressions (a / b) / c or a / (b / c) are unambiguous

      a/b/c is already unambiguous - left to right. 🙄

      Image of two calculators getting different answers

      With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.

      6÷2(1+2) is interpreted as 6÷(2×(1+2))

      6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)

      (6÷2)×(1+2) by a TI-83 Plus calculator (lower)

      Yep, Texas Instruments is the only one still doing it wrong

      This ambiguity

      doesn’t exist, as per Maths textbooks

      “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations:

      No there isn’t - you MUST obey The Distributive Law, a(b+c)=(ab+ac)

      Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”

      And he was wrong about that. 🙄

      calls such contrived examples

      Which notably can be found in Maths textbooks

      source

      • JackbyDev@programming.dev ⁨3⁩ ⁨weeks⁩ ago

        If you believe the article is incorrect, submit your corrections to Wikipedia instead of telling me.

        source

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