As far as I know, the only reason multiplication and division come first is that we’ve all agreed to it. But it can’t be derived in a vacuum as that other dude contends it should be.
No, only multiply and divide are. 2+3 is really +2+3, but we don’t write the first plus usually (on the other hand we do always write the minus if it starts with one).
As far as I know, the only reason multiplication and division come first is that we’ve all agreed to it.
No, they come first because you get wrong answers if you don’t do them first. e.g. 2+3x4=14, not 20. All the rules of Maths exist to make sure you get correct answers. Multiplication is defined as repeated addition - 3x4=3+3+3+3 - hence wrong answers if you do the addition first (just changed the multiplicand, and hence the answer). Ditto for exponents, which are defined as repeated multiplication, a^2=(axa). Order of operations is the process of reducing everything down to adds and subtracts on a number line. 3^2=3x3=3+3+3
Very confidently getting basic facts wrong doesn’t inspire confidence in the rest of your comments.
Your example still doesn’t give a reason why 2 + 3 * 4 is 2 + 3 + 3 + 3 +3 instead of 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 other than that we all agree to it.
And you can shove the condescension up your ass until you understand the difference between unary and binary operators.
But to original point. I’m not disagreeing with anything and you’re proving my point for me. There is no fundamental law of the universe that says multiplication comes first. It’s defined by man and agreed to. If we encounter aliens someday, the area of their triangles are still going to be half the width times the height, the ratios of their circles circumference to diameter are still going to be pi, regardless of how they represent those values. But they could very well prioritize addition and subtraction over multiplication and division.
Actually, it is. Written by a PhD and used in a college course. It just happens to be distributed for free because Canada is cool like that.
The LibreTexts libraries are Powered by NICE CXone Expert and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program
May want to work on your own reading comprehension.
It’s not me who doesn’t understand the difference.
The facts disagree.
You can keep saying defined all you want, it doesn’t change the underlying issue that it’s defined by man. In the absence of all your books (which you clearly don’t understand anyway based on our discussion of unary vs binary) order of operations only exists because we all agree to it.
Nothing. And that’s why people don’t write equations like that: You either see
46 + ---2
or
6 + 4
-------
2
If you wrote 6 + 4 / 2 in a paper you’d get reviewers complaining that it’s ambiguous, if you want it to be on one line write (6+4) / 2 or 6 + (4/2) or 6 + ⁴⁄₂ or even ½(6 + 4) Working mathematicians never came up with PEMDAS, which disambiguates it without parenthesis, US teachers did. Noone else does it that way because it does not, in the slightest, aid readability.
What fundamental property of the universe says that
6 + 4 / 2 is 8 instead of 5?
The fundamental property of Maths that you have to solve binary operators before unary operators or you end up with wrong answers.
But +, -, *, and / are all binary operators?
As far as I know, the only reason multiplication and division come first is that we’ve all agreed to it. But it can’t be derived in a vacuum as that other dude contends it should be.
No, only multiply and divide are. 2+3 is really +2+3, but we don’t write the first plus usually (on the other hand we do always write the minus if it starts with one).
No, they come first because you get wrong answers if you don’t do them first. e.g. 2+3x4=14, not 20. All the rules of Maths exist to make sure you get correct answers. Multiplication is defined as repeated addition - 3x4=3+3+3+3 - hence wrong answers if you do the addition first (just changed the multiplicand, and hence the answer). Ditto for exponents, which are defined as repeated multiplication, a^2=(axa). Order of operations is the process of reducing everything down to adds and subtracts on a number line. 3^2=3x3=3+3+3
Typical examples of binary operations are the addition ( + {\displaystyle +}) and multiplication ( × {\displaystyle \times }) of numbers and matrices
Very confidently getting basic facts wrong doesn’t inspire confidence in the rest of your comments.
Your example still doesn’t give a reason why 2 + 3 * 4 is 2 + 3 + 3 + 3 +3 instead of 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 other than that we all agree to it.
…says person quoting Wikipedia and NOT a Maths textbook! 😂
Yes it does., need to work on your comprehension…
You can disagree as much as you want and 3x4 will still be defined as 3+3+3+3. It’s been that way ever since Multiplication was invented.
The arithmetic operations, addition + , subtraction − , multiplication × , and division ÷
That better? Or you can find one you like all by yourself: https://duckduckgo.com/?q=binary+operator&ko=-1&ia=web
And you can shove the condescension up your ass until you understand the difference between unary and binary operators.
But to original point. I’m not disagreeing with anything and you’re proving my point for me. There is no fundamental law of the universe that says multiplication comes first. It’s defined by man and agreed to. If we encounter aliens someday, the area of their triangles are still going to be half the width times the height, the ratios of their circles circumference to diameter are still going to be pi, regardless of how they represent those values. But they could very well prioritize addition and subtraction over multiplication and division.
Is it a Maths textbook?
I already have dozens of Maths textbooks thanks.
It’s not me who doesn’t understand the difference.
Still need to work on your comprehension then. I did nothing of the sort.
Yes there is. The fact that it’s defined as repeated addition. You don’t do it first, you get wrong answers.
It’s been defined and man has no choice but to agree with the consequences of the definition, or you get wrong answers.
No they couldn’t. It gives wrong answers.
Actually, it is. Written by a PhD and used in a college course. It just happens to be distributed for free because Canada is cool like that.
May want to work on your own reading comprehension.
The facts disagree.
You can keep saying defined all you want, it doesn’t change the underlying issue that it’s defined by man. In the absence of all your books (which you clearly don’t understand anyway based on our discussion of unary vs binary) order of operations only exists because we all agree to it.
Nothing. And that’s why people don’t write equations like that: You either see
4 6 + --- 2or
6 + 4 ------- 2If you wrote
6 + 4 / 2in a paper you’d get reviewers complaining that it’s ambiguous, if you want it to be on one line write(6+4) / 2or6 + (4/2)or6 + ⁴⁄₂or even½(6 + 4)Working mathematicians never came up with PEMDAS, which disambiguates it without parenthesis, US teachers did. Noone else does it that way because it does not, in the slightest, aid readability.Says someone who clearly hasn’t looked in any Maths textbooks
Only if their Maths was very poor. #MathsIsNeverAmbiguous
Yes they did.
It was never ambiguous to begin with.
Says someone who has never looked in a non-U.S. Maths textbooks - BIDMAS, BODMAS, BEDMAS, all textbooks have one variation or another.