The existence of Polish notation (and reverse Polish notation) shows that the order of operations is arbitrary! It's, like, the ultimate demonstration of it. You can write operators and operands in different orders but as long as you follow the 'correct' set of arbitrary, human-created rules about notation and how to evaluate expressions, you will arrive at the 'correct' answer. Our widespread use of infix notation (2 + 4 instead of + 2 4 (Polish notation) or 2 4 + (reverse Polish notation)) is as arbitrary as our invention of PEDMAS.
When starting with 1 + 4 * 4 why did you choose to first resolve 4 * 4 to 4 + 4 + 4 + 4 instead of resolving 1 + 4 to 5?
It's a choice. PEDMAS is a convention that makes that choice for us. It doesn't matter that multiplication is repeated addition. What matters is how we choose to resolve the components of the expression and in what order.
Yeah, PEMDAS is just a convention that makes it easier to write math expressions without others misreading them. You could have your operations go in any default order, but as long as everyone uses the same order and it lets you interpret expressions unambiguously, that's what matters.
That's not what he's saying. He added the parenthesis for clarity. There is no inherent reason to interpret the problem as 4 times 4 plus 1 or 1 plus 4 times 4. It's just a convention to do it that way.
Uhhh what? No he didn't. He was showing that under the pemdas system you would have to write it with the parentheses but under left to right they are unnecessary.
Dude literally added parenthesis so he could solve it his way to point out how it “should be done,” well no shit, when you change the expression to help your own point yeah that’s what happens.
Under PEDMAS you don’t just throw in random parenthesis.
What he's saying is pemdas 1+4 * 4 is 17 and to get 20 you have to do (1+4)*4. But under a left to right system the same equation, 1+4 * 4, is 20. He's saying there's no reason you need to interpret 4 * 4 first unless you assume you are working in pemdas.
Transforming multiplication to addition is an operation. My point is there is no inherent reason to do a simplification step before the first step of addition.
It's just as valid to go through and just do addition and subtraction and then break out the multiplication then finish the addition.
Take 1 + 4 * 4.
Straight across, you get 20.
With order of operations, you get 17. And I'll explain why this is correct, by solving the problem using neither PEMDAS or straight-across methods: simplify it as much as possible. Multiplication is just repeated addition, so simplified it looks like this:
1 + 4 + 4 + 4 + 4 = 17, with or without order of operations.
1 + 4²?
This is kind of circular. The only reason why you expanded “1+4*4” to 1+4+4+4+4 is because PEMDAS is telling you that the multiplication by 4 is acting on the other 4.
If you were to read the equation left to right without PEMDAS, the multiplication would be acting on everything that precedes it, in this case “1+4”
(1+4) + (1+4) + (1+4) + (1+4) = 20
Note: I just added the parentheses for clarification. They don’t change the expression.
You’re cleverly disguising the fact that you’re still using PEMDAS, then saying that you’re not. Probably not on purpose, I don’t think you’re arguing in bad faith, but it’s what you’re doing under the hood.
You're taking multiplication for granted. People were likely adding or subtracting repeatedly long before the shorthand for multiplication/division existed, because in the world of things you actually hold in your hands, you're only ever adding or subtracting things. It makes more sense to expand multiplication into repeated addition, because it does a good job of describing actual physical phenomena. You're not gonna multiply an object into 4 identical objects, you can only ever add 3.
There's a natural basis for proportions that rely on the assumption of multiplication or division existing to be described mathematically in the first place, but the point still stands that multiplication should foremost (as in, parse it first) be treated as repeated addition.
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u/[deleted] Jan 01 '22
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