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SmartmanApps@programming.dev ⁨3⁩ ⁨days⁩ 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

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JackbyDev@programming.dev ⁨3⁩ ⁨days⁩ 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]

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- SmartmanApps@programming.dev ⁨3⁩ ⁨days⁩ 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
  
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  - JackbyDev@programming.dev ⁨3⁩ ⁨days⁩ ago
    If you believe the article is incorrect, submit your corrections to Wikipedia instead of telling me.
    
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    SmartmanApps@programming.dev ⁨2⁩ ⁨days⁩ ago
    
    If you believe the article is incorrect, submit your corrections to Wikipedia
    
    You know they’ve rejected corrections by actual Maths Professors right? Just look for Rick Norwood in the talk section. Everyone who knows Maths knows Wikipedia is wrong, and looks in the right place to begin with - Maths textbooks
    
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