There’s a useful distinction to be made. The order of operations is different between conventional written maths, calculators, reverse polish notation, python, etc. In contrast there is no disagreement over what the result of any individual binary operations is
So if you have one “notation definition” as you call it which says that 2+2*3 means ”first add two to two, then multiply by three" and another which says “first multiply two by three, then add it to two”, why on earth do the “rules” have anything further to say about order of operations?
There’s a useful distinction to be made. The order of operations is different between conventional written maths, calculators, reverse polish notation, python, etc. In contrast there is no disagreement over what the result of any individual binary operations is
The notation might be different, but the rules are universal
The rules are about how you interpret the notation, so that makes no sense.
No, the notation definitions are about how to interpret the notation. The rules are about how to do the Maths.
So if you have one “notation definition” as you call it which says that 2+2*3 means ”first add two to two, then multiply by three" and another which says “first multiply two by three, then add it to two”, why on earth do the “rules” have anything further to say about order of operations?
No we don’t. We have another notation which says to do paired operations (equivalent to being in brackets) first.
Because if you don’t obey them you get wrong answers 🙄