Right, so you cannot derive precedence order from the definition of the operations.
Yes you can. I’m not sure what you’re not understanding about Division before Addition 😂
Your argument based on the definition of multiplication as repeated addition is wrong
No it isn’t! 😂
We are discussing whether the answers are flat wrong or whether there is a layer of interpretation
Flat wrong, as per the rules Of Maths 🙄
Repeating that they are wrong does nothing for this discussion, so there’s no need to bother
So stop doing wrong things and I can stop saying you’re doing it wrong 😂
why they ought to qualify as “wrong” even though maths works regardless
If you have 1 2 litre bottle of milk, and 4 3 litre bottles of milk, even a 3rd grader can count up and tell you how many litres there are, and that any other answer is wrong. 🙄 2+3x4=2+3+3+3+3=14 correct 2+3x4=5x4=5+5+5+5=20 wrong See how the Maths doesn’t work regardless? 😂
you’ve just heard a school-level maths teacher tell you it’s done one way and believe that’s the highest possible authority
Nope, I’ve proven it myself - that’s the beauty of Maths, that anyone at all can try it for themselves and find out. I’m guessing that you didn’t try it yourself 😂
lots of things we get taught in high school are wrong
says person failing to give a single such example 🙄
it’s actually your job to understand maths at a higher level than the level at which you teach it
No it isn’t. I’m required to to get the Masters degree which is required to be a teacher here, and that’s the end of it.
It may be easier to to teach high school maths this way
The correct way, yes 😂
When I hear the word “rules”, I think you’re talking either about a rule of inference in first order logic or an axiom in a first-order system
Nope, neither.
So what are you talking about?
What don’t you understand about 20 being a wrong answer for 2+3x4??
whatever it is you mean by “rule”
Thing which results in wrong answers if disobeyed - like 2+3x4=20 - not complicated. This is what we teach to students - if you always obey all the rules then you will always get the correct answer.
arithmetic modulo 17, and say that’s an “alternative convention”
Of course not, just a different function of Maths, that doesn’t involve Arithmetic at all (other than the steps along the way in doing the long division), unlike 2+3x4 🙄
I contend that is all convention
Nope! Just a different rule to Arithmetic 🙄
What does it mean to be “bracketed without writing brackets”?
Same thing as we’re adding the 2 in 2+3 without writing a plus (or a zero) in front of the 2 - all Arithmetic starts from zero on the number-line. Maths textbooks explicitly teach this, that we can leave the sign omitted at the start if it’s a plus.
the symbols themselves - but we’re not writing them! So this isn’t relevant
Just like we aren’t writing the plus sign in 2+3 🙄
So what you’re admitting with these phantom brackets is that a notation can evaluate operations in a different order, even though there are no written brackets.
Nope. Same order as though we did write it in a notation using Brackets, same as we always start with adding the 2 even though we didn’t write a plus sign in 2+3.
So I can specify these fake brackets to always wrap the left-most operation first: (2 + 3) x 5
No you can’t, because you get a wrong answer 🙄
this notation now has left-to-right order of evaluation
No it doesn’t, Multiplication before Addition 🙄
If you prefer to think of there being invisible brackets there
You know we were writing this without brackets for several centuries before we started using brackets in Maths, right?? 😂
So, how do we decide whether our usual notation “has bogus brackets” or not? Convention
Nope. proven rules 🙄
We could choose one way or the other.
No we can’t. Even a 3rd grader who is counting up can tell you that 🙄
Nothing breaks if we choose one or the other.
Yes it does. Again ask the 3rd grader how many litres we have, and then try doing Addition first to get that answer 😂
we could say that left-to-right evaluation is the notation “without bogus brackets”
No we can’t. Ask the 3rd grader, or even try it yourself with Cuisenaire rods
Which choice we make is entirely arbitrary
Nope. proven rules 🙄
That is, unless you can find a compelling reason why one is right and the other wrong, rather than just saying it once again
Count up how many litres we have 🙄
What problems does it cause?
wrong answers 😂
you’re trying to establish that it’s a fundamental law of maths that you must do multiplication before addition
As per Maths textbooks 😂
you’ve written a post in which you document how some calculators don’t follow this
rule
said that they’re wrong is not evidence of that
says person ignoring the Maths textbooks I quoted and the actual calculators giving the correct answer 🙄
It’s just your opinion
Nope! proven rules as found in Maths textbooks 🙄
it’s really (weak) evidence that your opinion is wrong,
says person ignoring the Maths textbooks I quoted and the actual calculators giving the correct answer 🙄
you’re less of an authority than the manufacturers of calculators
Demonstrably not 😂
basic, non-scientific, non-graphing calculators all have left-to-right order of operations
No they don’t! 😂
e.g. windows calculator in “standard” mode
The Windows calculator is an e-calc which was written by a programmer who didn’t check that their Maths was correct. 🙄 Now try it with any actual calculator 🙄
Why is it different?
Written by a different programmer, but one who didn’t know The Distributive Law, so even in Scientific mode it gives wrong answers to 8/2(1+3) 🙄
Because “standard” mode is emulating a basic calculator
No it isn’t. All basic calculators obey Multiplication before Addition, 🙄 and if the programmer had tried it then they would’ve found that out
performs operations on that accumulated value
Instead of using the stack, to store the Multiplication first, like all actual calculators do 🙄
When you type “x 2” you are multiplying the accumulator by 2
No, the dumb programmer is. All actual calculators did the Multiplication first and put the result on the stack
the calculator has already forgotten everything that you typed to get the accumulator
But actual calculators have put that result on the stack 🙄
This was done in the early days of calculators
No it wasn’t. All calculators “in the early days” used the stack
It has a different convention for a sensible reason
Nope, it’s just disobeying the rules of Maths because dumb programmer didn’t check their Maths was correct 🙄
it was more practical when memory looked like this:
And even then the stack existed 🙄
the fact is that this isn’t “wrong”
Yes it is! 😂 Again, ask the 3rd grader to count up and tell you the correct answer
if you expect something different then it is you who
knows the rules of Maths 🙄
What do you mean “we don’t”?
What don’t you understand about “we don’t”?
I just made the definition
Of the notation, not the rules 🙄
We have another notation which says to do paired operations (equivalent to being in brackets) first
And this notation says to do paired operations first, same as if they were in Brackets. You so nearly had it 🙄
plain english (like “convention”)
says person who keeps calling the rules “convention” 🙄
mathematical (like “axiom”, “definition”, etc)
You know we have Mathematical definitions of the difference between conventions and rules, right??
Yes you can. I’m not sure what you’re not understanding about Division before Addition 😂
No it isn’t! 😂
Flat wrong, as per the rules Of Maths 🙄
So stop doing wrong things and I can stop saying you’re doing it wrong 😂
If you have 1 2 litre bottle of milk, and 4 3 litre bottles of milk, even a 3rd grader can count up and tell you how many litres there are, and that any other answer is wrong. 🙄 2+3x4=2+3+3+3+3=14 correct 2+3x4=5x4=5+5+5+5=20 wrong See how the Maths doesn’t work regardless? 😂
Nope, I’ve proven it myself - that’s the beauty of Maths, that anyone at all can try it for themselves and find out. I’m guessing that you didn’t try it yourself 😂
says person failing to give a single such example 🙄
No it isn’t. I’m required to to get the Masters degree which is required to be a teacher here, and that’s the end of it.
The correct way, yes 😂
Nope, neither.
What don’t you understand about 20 being a wrong answer for 2+3x4??
Thing which results in wrong answers if disobeyed - like 2+3x4=20 - not complicated. This is what we teach to students - if you always obey all the rules then you will always get the correct answer.
Of course not, just a different function of Maths, that doesn’t involve Arithmetic at all (other than the steps along the way in doing the long division), unlike 2+3x4 🙄
Nope! Just a different rule to Arithmetic 🙄
Same thing as we’re adding the 2 in 2+3 without writing a plus (or a zero) in front of the 2 - all Arithmetic starts from zero on the number-line. Maths textbooks explicitly teach this, that we can leave the sign omitted at the start if it’s a plus.
Just like we aren’t writing the plus sign in 2+3 🙄
Nope. Same order as though we did write it in a notation using Brackets, same as we always start with adding the 2 even though we didn’t write a plus sign in 2+3.
No you can’t, because you get a wrong answer 🙄
No it doesn’t, Multiplication before Addition 🙄
You know we were writing this without brackets for several centuries before we started using brackets in Maths, right?? 😂
Nope. proven rules 🙄
No we can’t. Even a 3rd grader who is counting up can tell you that 🙄
Yes it does. Again ask the 3rd grader how many litres we have, and then try doing Addition first to get that answer 😂
No we can’t. Ask the 3rd grader, or even try it yourself with Cuisenaire rods
Nope. proven rules 🙄
Count up how many litres we have 🙄
wrong answers 😂
As per Maths textbooks 😂
rule
says person ignoring the Maths textbooks I quoted and the actual calculators giving the correct answer 🙄
Nope! proven rules as found in Maths textbooks 🙄
says person ignoring the Maths textbooks I quoted and the actual calculators giving the correct answer 🙄
Demonstrably not 😂
No they don’t! 😂
The Windows calculator is an e-calc which was written by a programmer who didn’t check that their Maths was correct. 🙄 Now try it with any actual calculator 🙄
Written by a different programmer, but one who didn’t know The Distributive Law, so even in Scientific mode it gives wrong answers to 8/2(1+3) 🙄
No it isn’t. All basic calculators obey Multiplication before Addition, 🙄 and if the programmer had tried it then they would’ve found that out
Instead of using the stack, to store the Multiplication first, like all actual calculators do 🙄
No, the dumb programmer is. All actual calculators did the Multiplication first and put the result on the stack
But actual calculators have put that result on the stack 🙄
No it wasn’t. All calculators “in the early days” used the stack
Nope, it’s just disobeying the rules of Maths because dumb programmer didn’t check their Maths was correct 🙄
And even then the stack existed 🙄
Yes it is! 😂 Again, ask the 3rd grader to count up and tell you the correct answer
knows the rules of Maths 🙄
What don’t you understand about “we don’t”?
Of the notation, not the rules 🙄
And this notation says to do paired operations first, same as if they were in Brackets. You so nearly had it 🙄
says person who keeps calling the rules “convention” 🙄
You know we have Mathematical definitions of the difference between conventions and rules, right??