this post was submitted on 31 Dec 2023
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I mean, that sounds like the reasoning behind the order of operations, to me. At least that's the only reason I've ever been given.
The order of operations is a convention created by humans so as to ensure a consistent understanding of mathematical expressions. The reason for them being the way they are is merely because that's what we've agreed upon.
To add, I believe regardless of order of operations if we used () for every part of the equation it would no longer matter, but that would get tedious so as you said humans agreed on a shorthand for consistency.
No, they have to be the way they are as a result of the way the operators have been defined. e.g. 2x3 is shorthand for 2+2+2, so if you don't do multiplication before addition then you get the wrong answer, hence the order of operations rules.
I wish I could have been in the room. You know someone was like, "Eh, just left to right. We'll use parentheses to specify an order when it's necessary." Then someone else said, "What if we use this system of various rules instead." If I were there, I would have killed that person to save mankind.
All order of operation rules are made up, but some of them are more useful than others. Rules that jive with associative and communtative laws are preferred.
Or come over to RPN and stop worrying about it.
None of them are made-up. They are all a natural consequence of the way things have been defined. e.g. 2x3 is shorthand for 2+2+2, so if you don't do multiplication before addition then you get the wrong answer, hence the order of operations rules.
The order of operations is made from consensus. Just like we all agree the first letter of the alphabet is "A". You could make the order of operations whatever you like, you would just need to rewrite equations to reflect that change.
No it isn't. It's a natural consequence of the definitions in the first place. e.g. 2x3 is shorthand for 2+2+2, so if you don't do multiplication before addition then you get the wrong answer, hence the order of operations rules.
Order of operations proof - Associativity and Terms/Expressions