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.
Actually, it is. Written by a PhD and used in a college course.
Yeah there’s an issue with them having forgotten the basic rules, since they don’t actually teach them (except in a remedial way). Why do you think I keep trying to bring you back to actual Maths textbooks?
May want to work on your own reading comprehension.
Nope. It’s still not a textbook. Sounds more like a higher education version of Wikipedia.
The facts disagree
With you, yes.
it doesn’t change the underlying issue that it’s defined by man.
The notation is, the rules aren’t.
In the absence of all your books (which you clearly don’t understand anyway based on our discussion of unary vs binary)
Says person who doesn’t understand the difference between unary and binary. Apparently EVERYTHING is binary according to you (and your website). 😂
order of operations only exists because we all agree to it
It exists whether we agree with it or not. Don’t obey it, get wrong answers.
You keep mentioning textbooks but haven’t actually shown any that support you. I have. I’ll trust the PhD teaching a university course on the subject over the nobody on the internet who just keeps saying “trust me bro” and then being condescending while also being embarrassingly wrong.
Says person who doesn’t understand the difference between unary and binary.
Talking about yourself in the third person is weird. Even your nonsense about a silent “+” is really just leaving off the leading 0 in the equation 0+2. Because addition is a binary operator.
Apparently EVERYTHING is binary according to you (and your website). 😂
Only the ones that operate on two inputs. Some examples of unary operators are factorial, absolute value, and trig functions. The laughing face when you make a fool of yourself isn’t really as effective as you think it is.
But we’re getting off topic again. I can’t keep trying to explain the same thing to you, so I would say this has been fun, but it’s been more like talking to an unusually obnoxious brick wall. Next time you want to engage with someone try being less of a prick, or at least less wrong. You’re not nearly as smart as you seem to think you are.
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.
Yeah there’s an issue with them having forgotten the basic rules, since they don’t actually teach them (except in a remedial way). Why do you think I keep trying to bring you back to actual Maths textbooks?
Nope. It’s still not a textbook. Sounds more like a higher education version of Wikipedia.
With you, yes.
The notation is, the rules aren’t.
Says person who doesn’t understand the difference between unary and binary. Apparently EVERYTHING is binary according to you (and your website). 😂
It exists whether we agree with it or not. Don’t obey it, get wrong answers.
It is though. Here’s a link to buy a printed copy: https://libretexts.org/bookstore/order?math-7309
You keep mentioning textbooks but haven’t actually shown any that support you. I have. I’ll trust the PhD teaching a university course on the subject over the nobody on the internet who just keeps saying “trust me bro” and then being condescending while also being embarrassingly wrong.
And because I can’t help it, I’ll also trust Wolfram over you: Examples of binary operation on A from A×A to A include addition (+), subtraction (-), multiplication (×) and division (÷). Here, you can buy a copy of this too: https://www.amazon.com/exec/obidos/ASIN/1420072218/weisstein-20
Talking about yourself in the third person is weird. Even your nonsense about a silent “+” is really just leaving off the leading 0 in the equation 0+2. Because addition is a binary operator.
Only the ones that operate on two inputs. Some examples of unary operators are factorial, absolute value, and trig functions. The laughing face when you make a fool of yourself isn’t really as effective as you think it is.
But we’re getting off topic again. I can’t keep trying to explain the same thing to you, so I would say this has been fun, but it’s been more like talking to an unusually obnoxious brick wall. Next time you want to engage with someone try being less of a prick, or at least less wrong. You’re not nearly as smart as you seem to think you are.