What makes non-PEMDAS answers invalid?
It seems to me that even the non-PEMDAS answer to an equation is logical since it fits together either way. If someone could show a non-PEMDAS answer being mathematically invalid then I’d appreciate it.
My teachers never really explained why, they just told us “This is how you do it” and never elaborated.
In: 834
OK, there are many good answers, but let me point out one more thing.
It has been mentioned that PEMDAS is a convention, not a “empirical rule” or “truth”. We agree on it.
Furthermore, it has been pointed out that it is necessary to agree on PEMDAS (or any other rule for priority of operands, which is what PEMDAS is), when two people want to talk to each other in math (or you want to talk to your future self, in that case it is evenly important!).
In a nutshell, when you change the rules, the result will change. It’s not wrong, it’s just that your formula means something different. The very simple and obvious example has already been given:
(2*3) + 4 is not the same as 2*(3+4). Both interpretations of 2*3+4 are “correct”, you just can’t switch back at forth at random. And if you add parenthesis, you can basically enforce operant priority without any rule except, solve parenthesis first. It just gets ugly. But it gets ugly – anyway 🙂
When you work in math (or in my case, logic, which is often pretty much the same, but… ah well anyway), when you talk higher mathematics, one of the first things to figure out when you read a paper/book/… is: what notation rules (including priority of operators) has been used.
Because there is no “standard”. Seriously, there isn’t. There are conventions, and schools that use conventions, and areas of maths (or logic) that prefer those or those conventions. Sometimes it’s continent based, but it also changed dramatically over time. Heck, even the symbols Gottlob Frege used 120 years ago are completely outdated, while what he wrote about is foundations of modern mathematics…
So, just be happy that for your everyday kitchen math, PEMDAS is quite sufficient because that’s what the world in general agrees upon. 🙂
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