Left to right is a convention, yes, doing Multiplication and Division before Addition and Subtraction is a rule 🙄
A claim entirely unsupported by the textbook example you provided. Nowhere does it say that one is a convention but not the other, it only says that removing brackets changes the meaning in some situations, which is fully within the scope of a convention.
For the 3rd time it does have order of operations 🙄You just do them in some random order do you?
There you go again, just admitting you don't know what postfix and prefix notations are.
If you're ordering your operations based what the operator is, like PEDMAS, then what you're doing isn't prefix or postfix.
I'll tell you what, here is a great free article from Colorado State university talking about prefix, postfix, and infix notations.
Note how it says the rules about operator precedence are for the notation which itself is a convention, as all notations are, and how prefix and postfix don't need those rules
says person who doesn't know the difference between conventions and rules, and thinks postfix notation doesn't have rules 🙄
How embarrassing for you.
Here are some more materials:
- A post by Berkley university about popular ambiguous equations.
- A published paper from Berkley that has been cited, with much stronger language on the matter.
- Here is an article from the university of Melbourne
- Article from the university of utah
- A howstuffworks article on order of operations that explains it, doesn't have the pedigree of a university, but still clearly explained
- Plus dozens of Quora answers, articles from online academies and learning centers, that I figured you'd just dismiss.
But to top it all off, if this was truely a law of mathematics, then show me a proof, theorem, or even a mathematical conjecture, about order of operations.