How did we discover PEMDAS? If math is just representative of real things, why does it matter the order? I know that going out of order yields the wrong answer, but why does going through PEMDAS yield the right one?
In: Mathematics
It’s arbitrary, an artifact of writing mathemathical expressions as we do in everyday use (“infix notation”). The only thing that matters is that everybody uses the same order or stuff goes tits up.
As an example of a notation that doesn’t *have* the concept of “order of operations”, there is the Reverse Polish Notation / Postfix Notation:
1 2 + 4 *
means the same thing as (1+2)*4 and
1 2 4 * +
is the same as 1+2*4
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