The rules are socially agreed upon. They are not a mathematical truth. There is nothing about the order of multiple different operators in the definition of the operators themselves. An operator is simply just a function or mapping, and you can order those however you like. All that matters is just what calculation it is that you’re after
Just because a definition of an operator contains another operator, does not require that operator to take precedence. As you pointed out, 2+3*4 could just as well be calculated to 5*4 and thus 20. There’s no mathematical contradiction there. Nothing broke. You just get a different answer. This is all perfectly in line with how maths work.
You can think of operators as functions, in that case, you could rewrite 2+3*4 as add(2, mult(3, 4)), for typical convention. But it could just as well be mult(add(2, 3), 4), where addition takes precedence. Or, similarly, for 2*3+4, as add(mult(2, 3), 4) for typical convention, or mult(2, add(3, 4)), where addition takes precedence. And I hope you see how, in here, everything seems to work just fine, it just depends on how you rearrange things. This sort of functional breakdown of operators is much closer to mathematical reality, and our operators is just convention, to make it easier to read.
Something in between would be requiring parentheses around every operator, to enforce order. Such as (2+(3*4)) or ((2+3)*4)
Isn’t a Maths textbook, and has many mistakes in it
Just because a definition of an operator contains another operator, does not require that operator to take precedence
Yes it does 😂
2+3x4=2+3+3+3+3=14 by definition of Multiplication
2+3x4=5x4=20 Oops! WRONG ANSWER 😂
As you pointed out, 2+34 could just as well be calculated to 54 and thus 20
No, I pointed out that it can’t be calculated like that, you get a wrong answer, and you get a wrong answer because 3x4=3+3+3+3 by definition
There’s no mathematical contradiction there
Just a wrong answer and a right one. If I have 1 2 litre bottle of milk, and 4 3 litre bottles of milk, even young kids know how to count up how many litres I have. Go ahead and ask them what the correct answer is 🙄
Nothing broke
You got a wrong answer when you broke the rules of Maths. Spoiler alert: I don’t have 20 litres of milk
You just get a different answer
A provably wrong answer 😂
This is all perfectly in line with how maths work
2+3x4=20 is not in line with how Maths works. 2+3+3+3+3 does not equal 20 😂
add(2, mult(3, 4)), for typical
rule
But it could just as well be mult(add(2, 3), 4), where addition takes precedence
And it gives you a wrong answer 🙄 I still don’t have 20 litres of milk
And I hope you see how, in here, everything seems to work just fine
No, I see quite clearly that I have 14 litres of milk, not 20 litres of milk. Even a young kid can count up and tell you that
it just depends on how you rearrange things
Correctly or not
our operators is just convention
The notation is, the rules aren’t
Something in between would be requiring parentheses around every operator, to enforce order
No it wouldn’t. You know we’ve only been using brackets in Maths for 300 years, right? Order of operations is much older than that
Such as (2+(3*4))
Which is exactly how they did it before we started using Brackets in Maths 😂 2+3x4=2+3+3+3+3=14, not complicated.
I mean, it is pretty clear here that you do not really understand the purpose of notation, nor what maths is. Notation is just a constructed language to convey a mathematical idea, it’s malleable
Really though, maths is so much more than “3+5=8 because that’s the correct answer!” But why is it the correct answer? In what context? What is the definition of addition? How can you prove that 1+1=2 from fundamental axioms? This is harder to answer than you might think.
Read the comments and you’ll find multiple people telling him he is wrong, with references 😂 His usual comeback is “well, that doesn’t prove that it’s taught everywhere”, yeah only that they ALL say the same thing! 😂 And he even admitted at one point he couldn’t find his rule in any Maths textbooks. 😂 I even tried to tell him myself, and he deleted my comment because I proved he was wrong 😂
Is well-known to be overridden with people who do not know how to do order of operations 😂 On Mastodon I’ve seen people asking where is a better place to take Maths problems
If you want a book about this
I have plenty of Maths textbooks, which for some reason you refuse to look in
“comprehensive handbook” - so, yet again, not a Maths textbook 🙄
“first published in 1945 in Russia” - the order of operations rules are older than 1945 😂
“frequently used guide for scientists, engineers, and technical university students” - notably no mention of Mathematicians
I’m sure you could also find stuff about this in a set theory book
and you could find this in a high school Maths textbook
Though good luck understanding them without sufficient experience in high-level maths
You know teachers here are required to have a Masters in Maths right?? 😂
But why is it the correct answer?
Count up and find out, or use some Cuisenaire rods. This is how young kids learn to do it
In what context?
The context of Addition 🙄
What is the definition of addition?
1+1=2, then inductively proven for all subsequent numbers
How can you prove that 1+1=2 from fundamental axioms?
It’s true by definition
This is harder to answer than you might think
Not hard at all. 1+1=2 by definition, then the rest of the numbers are proven inductively. You know there are several species of animals that also know how to count, right?
Maths is so much more malleable and abstract than what you think it is. You really do not understand maths as well as you think you do, and I feel a bit sad for any student of yours that would wish to explore some deeper revelations of maths, just to be told “nope! That’s just how it is!” with no further thinking at all.
A lot of maths is chosen. Choices with good motivation, but choices nonetheless. So long as there not being contradictions or paradoxes, the formulation of a form of math is valid. Which is why you have different forms of maths with different rules.
And you really could use some more humility, it’s obnoxious when you act all so high and mighty and arrogant, with no interest in questioning your assumptions. Devolving into ridiculing the person you’re discussing with and a general vibe of “omfg I’m right you fucking idiot because I’m right how dumb can you get??”
Like, what is it that you want here, a book from the 700s of the one dude that invented arithmetics and told clearly “I chose this.”? You are making your arguments effectively unfalsifiable by just going “Nuh uh” all the time.
Get some humility and learn a bit about the foundations of maths. Like. Down to set theory. See for yourself what actually is the foundation. And, spoiler, it’s not a high school textbook. Hopefully I do not need to tell you how concepts are simplified for younger students, instead of overwhelming them with the complete knowledge of a subject.
Nope, rules arising from the definition of the operators in the first place.
It most certainly is a mathematical truth!
The mnemonics are conventions, the rules are rules
The rules are socially agreed upon. They are not a mathematical truth. There is nothing about the order of multiple different operators in the definition of the operators themselves. An operator is simply just a function or mapping, and you can order those however you like. All that matters is just what calculation it is that you’re after
Nope! Universal laws.
Yes they are! 😂
That’s exactly where it is. 2x3 is defined as 2+2+2, therefore if you don’t do Multiplication before Addition you get wrong answers
No you can’t! 😂 2+3x4=5x4=20, Oops! WRONG ANSWER 😂
And if you want the right answer then you have to obey the order of operations rules
That’s a very simplistic view of maths. It’s convention https://en.wikipedia.org/wiki/Order_of_operations
Just because a definition of an operator contains another operator, does not require that operator to take precedence. As you pointed out, 2+3*4 could just as well be calculated to 5*4 and thus 20. There’s no mathematical contradiction there. Nothing broke. You just get a different answer. This is all perfectly in line with how maths work.
You can think of operators as functions, in that case, you could rewrite 2+3*4 as add(2, mult(3, 4)), for typical convention. But it could just as well be mult(add(2, 3), 4), where addition takes precedence. Or, similarly, for 2*3+4, as add(mult(2, 3), 4) for typical convention, or mult(2, add(3, 4)), where addition takes precedence. And I hope you see how, in here, everything seems to work just fine, it just depends on how you rearrange things. This sort of functional breakdown of operators is much closer to mathematical reality, and our operators is just convention, to make it easier to read.
Something in between would be requiring parentheses around every operator, to enforce order. Such as (2+(3*4)) or ((2+3)*4)
The Distributive Law and Arithmetic is very simple.
Nope, a literal Law. See screenshot
Isn’t a Maths textbook, and has many mistakes in it
Yes it does 😂
2+3x4=2+3+3+3+3=14 by definition of Multiplication
2+3x4=5x4=20 Oops! WRONG ANSWER 😂
No, I pointed out that it can’t be calculated like that, you get a wrong answer, and you get a wrong answer because 3x4=3+3+3+3 by definition
Just a wrong answer and a right one. If I have 1 2 litre bottle of milk, and 4 3 litre bottles of milk, even young kids know how to count up how many litres I have. Go ahead and ask them what the correct answer is 🙄
You got a wrong answer when you broke the rules of Maths. Spoiler alert: I don’t have 20 litres of milk
A provably wrong answer 😂
2+3x4=20 is not in line with how Maths works. 2+3+3+3+3 does not equal 20 😂
rule
And it gives you a wrong answer 🙄 I still don’t have 20 litres of milk
No, I see quite clearly that I have 14 litres of milk, not 20 litres of milk. Even a young kid can count up and tell you that
Correctly or not
The notation is, the rules aren’t
No it wouldn’t. You know we’ve only been using brackets in Maths for 300 years, right? Order of operations is much older than that
Which is exactly how they did it before we started using Brackets in Maths 😂 2+3x4=2+3+3+3+3=14, not complicated.
I mean, it is pretty clear here that you do not really understand the purpose of notation, nor what maths is. Notation is just a constructed language to convey a mathematical idea, it’s malleable
And yeah, it’s easy to just say “this page is wrong!” without any further argument. Nothing you referenced proved the convention as law, and neither is there any mathematical basis for any proof, because it simply is nonsensical to “prove” a notation. Have another source for this being convention https://www.themathdoctors.org/order-of-operations-why/ or https://math.stackexchange.com/questions/884765/mathematical-proof-for-order-of-operations. If you want a book about this, then there’s https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev that is cited by wikipedia. I’m sure you could also find stuff about this in a set theory book. Though good luck understanding them without sufficient experience in high-level maths
Really though, maths is so much more than “3+5=8 because that’s the correct answer!” But why is it the correct answer? In what context? What is the definition of addition? How can you prove that 1+1=2 from fundamental axioms? This is harder to answer than you might think.
says person who doesn’t understand that there is only one possible answer to 2+3x4. Even kids who are still counting up know what it is
Yep, and the rules aren’t. 2+3x4 can only ever equal 14. In Germany it’s written 2+3.4, and it’s still equal to 14, because the rules are universal
says person ignoring the textbook screenshots explaining why it’s a Law 🙄
Yes there is. See textbook screenshots 🙄
It proves the rules 🙄
Read the comments and you’ll find multiple people telling him he is wrong, with references 😂 His usual comeback is “well, that doesn’t prove that it’s taught everywhere”, yeah only that they ALL say the same thing! 😂 And he even admitted at one point he couldn’t find his rule in any Maths textbooks. 😂 I even tried to tell him myself, and he deleted my comment because I proved he was wrong 😂
Is well-known to be overridden with people who do not know how to do order of operations 😂 On Mastodon I’ve seen people asking where is a better place to take Maths problems
I have plenty of Maths textbooks, which for some reason you refuse to look in
“comprehensive handbook” - so, yet again, not a Maths textbook 🙄
“first published in 1945 in Russia” - the order of operations rules are older than 1945 😂
“frequently used guide for scientists, engineers, and technical university students” - notably no mention of Mathematicians
and you could find this in a high school Maths textbook
You know teachers here are required to have a Masters in Maths right?? 😂
Count up and find out, or use some Cuisenaire rods. This is how young kids learn to do it
The context of Addition 🙄
1+1=2, then inductively proven for all subsequent numbers
It’s true by definition
Not hard at all. 1+1=2 by definition, then the rest of the numbers are proven inductively. You know there are several species of animals that also know how to count, right?
Maths is so much more malleable and abstract than what you think it is. You really do not understand maths as well as you think you do, and I feel a bit sad for any student of yours that would wish to explore some deeper revelations of maths, just to be told “nope! That’s just how it is!” with no further thinking at all.
A lot of maths is chosen. Choices with good motivation, but choices nonetheless. So long as there not being contradictions or paradoxes, the formulation of a form of math is valid. Which is why you have different forms of maths with different rules.
And you really could use some more humility, it’s obnoxious when you act all so high and mighty and arrogant, with no interest in questioning your assumptions. Devolving into ridiculing the person you’re discussing with and a general vibe of “omfg I’m right you fucking idiot because I’m right how dumb can you get??”
Like, what is it that you want here, a book from the 700s of the one dude that invented arithmetics and told clearly “I chose this.”? You are making your arguments effectively unfalsifiable by just going “Nuh uh” all the time.
Get some humility and learn a bit about the foundations of maths. Like. Down to set theory. See for yourself what actually is the foundation. And, spoiler, it’s not a high school textbook. Hopefully I do not need to tell you how concepts are simplified for younger students, instead of overwhelming them with the complete knowledge of a subject.
No it isn’t, as per Maths textbooks
says someone who doesn’t understand it at all
Just as well I’m their teacher then, hey? 😂 I showed you the textbooks, and you refused to look at them
Nope! Only the notation.
You mean so long as it obeys the laws of nature
But we don’t have different rules, only different notations. The rules of Maths are universal
says person who refuses to look in Maths textbooks
says person who refuses to look in Maths textbooks
there aren’t any. All the rules of Maths are explicitly spelt out in Maths textbooks, not to mention several of which are easy to prove.
Like the person who refuses to look in Maths textbooks
No-one chose it. There are even several species of animals that know how to count! 😂 It’s a universal law
Just as well I also provide the proof in the form of Maths textbooks. Oh wait, you keep refusing to look at them! 😂
says person who refuses to look in Maths textbooks
says person who knows nothing about it. Makes up fanciful stories like it was “chosen” when nature proves otherwise
It’s Arithmetic. Even some animals know how to do Arithmetic, none of them know how to do set theory! 😂
That’s right, it’s a Primary school textbook 😂
And yet you still manage to not understand them 🙄
Welcome to why Algebra isn’t taught until Year 7 😂