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
The order isn’t arbitrary.
Parentheses kinda need to go first to promote a calculation, or they rapidly get wildly complicated to use and you’d often have to use a bunch of them to get to the same result that a single parentheses can achieve with our current notation where it brings a part of the calculation to the front.
Similar with exponents – if you don’t have the exponent have priority over MDAS then you’d need to use parentheses almost every time you have an exponent to get the answer you need.
Multiplication and Division – these are next and equal in priority, because division is fundamentally multiplication by the inverse of the number. Eg 4/3 = = 4 x 1/3 = 4 x 0.333r. It makes sense to have MD come before AD because MD are essentially batched addition/subtractions, also again if you prioritize these after addition/subtraction you need a bunch of parentheses.
Fundamentally though – math isn’t a homework assignment, it’s a way to represent real quantities and things that are happening, so you can’t just evaluate everything in a different order and as long as everyone agrees on the order it’s all correct, because you’re not going to get to the real world answer you’re aiming for. It might be possible to write math using an alternative order of precedence, but in many cases you’re going to get a very convoluted equation vs the order we have, because you’re working against what the numbers are actually doing.
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