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I want to ask some things about the order of operation. Of course I have heard and used PEMDAS! First of all i want to make this clear: we say that first we should calculate the parentheses: in order to do so we also use PEMDAS in each parenthesis to calculate it's value? I am almost sure about the answer but just want to confirm it. And the most important thing: how was the "right" order of operations decided? Is it just a convention that always gives right results in connection with the axioms that we have set for addition and multiplication? Can it be proved?

Thank you

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# Order of operations

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