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• SmartmanApps@programming.dev ⁨3⁩ ⁨weeks⁩ ago

  Order of operations is not a hard rule

  Yes it is.

  It is a convention.

  Left to right is a convention. Left Associativity is a hard rule. Left to right is a convention which obeys the rule of Left Associativity.

  It’s something agreed upon

  It’s something that is a natural consequence of the definitions of the operators in the first place. As soon as Multiplication was defined in terms of Addition, that guaranteed we would always have to do Multiplication before Addition to get right answers.

  is it not something that is universally true

  Yes it is! All of Maths is universally true! 😂

  Solve for X X^2=4

  You know that’s no longer order of operations problem, right?

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  • Melvin_Ferd@lemmy.world ⁨3⁩ ⁨weeks⁩ ago

    What proof do you have that using a left to right rule is universally true?

    From my understanding It’s an agreed convention that is followed which doesn’t make it a universal truth. If we’re all doing it just to make things easier to understand, that implies we could have a right to left rule. It’s also true that not all cultures right in the same way.

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    But here is an interesting quote from Florian Cajori in his book a history of mathematical notations.

    Lastly here is an article that also highlights the issue.

    scienceblogs.com/…/the-horror-of-pemdas

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    • SmartmanApps@programming.dev ⁨3⁩ ⁨weeks⁩ ago

      What proof do you have that using a left to right rule is universally true?

      From my understanding It’s an agreed convention that is followed

      Read what I wrote again. I already said that left to right is a convention, and that Left Associativity is a rule. As long as you obey the rule - Left Associativity - you can follow whatever convention you want (but we teach students to do left to right, because they often make mistakes with signs when they try doing it in a different order, as have several people in this thread).

      that implies we could have a right to left rule

      You can have a right to left convention if the rule is Right Associativity.

      It’s also true that not all cultures right in the same way

      Yeah, I don’t know how they do Maths - if they do it the same as us or if they just flip everything back-to-front (or top to bottom - I guess they would). In either case all the rules on top stay the same once the direction is established (like I guess exponents would now be to the top left not the top right? but in any case the evaluation of an exponent would stay the same).

      But here is an interesting quote from Florian Cajori in his book a history of mathematical notations

      Yeah, he’s referring to the conventions - such as left to right - not the rule of Left Associativity, which all the conventions must obey. For a while Lennes was doing something different - because he didn’t understand Terms - and was disobeying Left Associativity, (which meant his rules were at odds with everyone else), but his rule died out within a generation of his death,. Absolutely all textbooks now obey Left Associativity, same as before Lennes came along.

      Lastly here is an article that also highlights the issue

      Not really. Just another person who has forgotten the rules.

      “as it happens, the accepted convention says the second one is correct”

      No it isn’t. The Distributive Law says the first is correct (amongst 4 other rules of Maths which also say the answer is only 1). The second way they did it disobeys The Distributive Law (and 4 other rules) and is absolutely wrong.

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