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
PEDMAS isn’t required. It’s always possible to write out a complex algebraic expression that isnt ambiguous about which operation to do first without PEDMAS. It might require a lot of brackets (and the understanding that everything inside brackets goes first) but it’s always possible.
What makes a non-PEDMAS answer invalid is that without it, 1+1×2 can either be 3 or 4 depending on which operation you do first. Its written ambiguously. I could write (1+1)x2 or 1+(1×2) to clarify, or we could agree that with PEDMAS rules, I always mean 1+(1×2). If I meant the other one, id have to revert to using brackets again.
PEDMAS was invented because mathematicians are inherently lazy and dont want to write so many brackets. It’s kind of a mathematician’s shorthand that is taught to be the right way to do it. It makes math a lot less ugly and cumbersome too, so I dont mind.
Edit: Here’s a (https://www.youtube.com/watch?v=y9h1oqv21Vs) from MinutePhysics explaining what I mean, courtesy of u/Necoras
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