snipping replies into tiny segments and replying shortly to each makes the discussion much harder to follow

Says person who did it in a random order, and included stuff that wasn’t even in this thread to begin with, thus making it impossible to follow 🙄

this is the most interesting thing you’ve said

You on the other hand haven’t said anything interesting, so do us all a favour and give it a rest

you can write your 14 litres of milk as 2 + 3 x 4

You “can” write it the way it’s always been written, yes 😂

But if you had right-to-left order of operations

Which we don’t 🙄

you could not write this as 2 + 2 x 3 = 8 litres

Right, you would write 3x2+3x2 😂

you’d have to insert brackets: (2 + 2) x 3 = 12 litres

Or you just write it correctly to begin with, then Factorise

But with left-to-right order you could write this as 2 + 2 x 3 = 12

No you can’t. As you already pointed out 2+2x3=8. 😂 Have you forgotten that we already do evaluate left to right??

where one translates readily to BODMAS order without brackets

Dating back many centuries before we even started using brackets in Maths 😂

the other translates readily to L2R order without brackets

Umm, it’s the same one 😂

interpreted correctly

Welcome to the order of operations rules - so glad you could finally join us

Yes, if you incorrectly translate my scenario as 2 + 2 x 3 with BODMAS order, you get the wrong answer

What you mean is you get the wrong answer, having written it out wrongly to begin with 🙄

the problem into mathematical notation using L2R order, then evaluated the expression using BODMAS order

They’re the same order 😂

the problem with one convention then evaluating that with another is wrong!

No it isn’t! 😂 All conventions give the same answer. Disobeying the rules on the other hand…

axiomatisation and write the proof

Umm, there’s no axioms involved, and I already showed you the proof 🙄

order of operations is about notation

Nope. It’s about rules. That’s why everyone the world over gets the same answers regardless of the notation they use in the different countries

constitutes a proof. It does not

says someone revealing they only know about the two types of proof, not all the others ones as well 🙄

Here is the mathematical definition of a proof in a first order theory

Which is one type of proof 🙄

no room for milk and bottles in a proof

There’s room for Cuisenaire rods though. Welcome to even a 3rd grader can prove it 😂

trying to establish that it’s wrong

I already proved it’s wrong 🙄

it’s adding nothing beyond restating what you’re already saying

And yet, you keep ignoring that it’s been proven correct Mr. Ostrich, hence I need to keep repeating it 🙄

imaginary third-grader

I can assure you that they aren’t imaginary! 😂

writing down 2 + 2 x 3 = 12

Ah, nope! They would write 3x2+3x2

if you taught him or her the right-to-left convention

We taught them first how to use Cuisenaire rods, then the order of operations rules, which follows on logically from there 🙄

all confidently incorrect.

says person about to prove that they are the one who is confidently incorrect… 😂

Note especially the phrase: “Many simple calculators without a stack”

Note the lack of a reference 🙄

chain calculation mode) is commonly employed on most general-purpose calculators

No it isn’t. It’s only employed by calculators designed to use chain calculations, which is another specialist, niche market, like RPN calculators. Note again the lack of a reference

an example of a calculator manual from the 70s showing (in Example 6) that the order of operations is left-to-right

BWAHAHAHAHAHAHA! No it doesn’t! 🤣🤣🤣 It shows you to press the +/= button after the bracketed part in order to evaluate that first, because, if you don’t, it will evaluate the Multiplication first, as per the order of operations rules, which it will use the stack for. 😂 When you press the x button, the parser know you meant the previous button press to be used as an equals and not as addition. You need to work on your reading/comprehension skills dude

the successor

A chain calculator, so this is just you rehashing your RPN argument with a different, niche notation

you have forgotten these old, basic calculators

says person who forgot to check that the manual agrees before posting it, leading to proof that they are the ones who have forgotten how they work! 🤣🤣🤣

now we’ve established that you’re confidently incorrect

No, we’ve established that you are the one who is confidently incorrect 😂

Windows calculator being “wrong” in its emulation of stackless calculators

We’ve established that isn’t what it’s doing, given it’s not called Chain mode, it’s called Standard mode, which it most definitely isn’t! 😂

let’s bring this back to the point

Yep, that point being that simple calculators, like the first one, will say 2+3x4=14. To get 20 you have to do 2+3=x4 😂

even though their order of operations is left-to-right

only chain calculators do it left to right. You’re making a false equivalence argument, just like RPN was a false equivalence argument

I said before: it had a different convention for a sensible reason

Which you just proved the first one doesn’t have a “different convention”. 😂 The second one does, but again that’s a false equivalence argument to all other calculators (same for RPN)

if you expect something different it is you who are using the device wrong

You proved they both do exactly what I expect 😂

How to use the device is written in the manual

Which you didn’t read carefully 🤣🤣🤣

so every user of it can use it correctly

As I have been, the whole time

if you want to continue this discussion, please acknowledge that you were wrong about this.

Except you just proved that you were the one who was wrong about this! 🤣🤣🤣 I expect you are now going to acknowledge that you were wrong about this, because otherwise you’re exposing yourself as a hypocrite

This is a simple, verifiable matter of fact that you’ve been shown to be wrong about

Nope, you were shown to be wrong 🤣🤣🤣

as above, the different calculators have different conventions

As above, only niche calculators like RPN and Chain have different conventions, and it’s right there in their manual, that you didn’t read carefully

all through this that order of operations is not merely a convention, but a rule. So, it’s not actually about textbooks

Which part didn’t you understand about the rules can be found in Maths textbooks?

your spilled milk establishes the opposite of what you want it to

Umm, no it doesn’t. It establishes that there is only one correct answer to 2+3x4, that being 14

textbooks are all you have

and calculators, and Cuisenaire rods, and counting up, and proofs 😂

if all the textbooks were edited overnight to teach L2R order of operations

They already do teach left to right! 😂

Children would learn that to add 2 litres of milk to 3 bottles of 4 litres, they ought to write 2 + (3 x 4)

No, they would learn the same thing they learn now 2+3x4. You know they haven’t been taught about brackets yet, right? They don’t learn about brackets until Year 5

The textbooks are, in fact, how you can see that this is just a convention

No, Cuisenaire rods show that this is a rule. 🙄 That’s why kids are shown how to use them before they first learn how to multiply

If the textbooks changed, only what people write would change

Because notations change but the rules don’t 🙄

you’ve been linking haven’t been about order of operations

There’s dozens here - knock yourself out! 😂

There is no “definition of multiplication” here

In other words, not the right tool for the job. Glad you finally worked that out! 😂

a convention is a social construct

And the rules aren’t 🙄

The definition exists

In your mind maybe, not in Maths textbooks, as I would’ve told you at the time (wherever it was - you’re now referring to something that isn’t even in this thread originally, so I don’t even know what you’re talking about anymore)

Saying “we don’t have it” doesn’t make sense

And I still don’t know where you’re having trouble in understanding that

I’ve told it to you

And I told you that we don’t have that definition 🙄

so now you have it;

And I told you that you were wrong 🙄

the choice of convention I’m saying you’re making

I’ve been talking about rules the whole time Mr. Ostrich

what is it then?

Proof by disproof 🙄

first-order arithmetic, the + symbol is a binary operation

So now you’re resorting to the minority of the population that has studied that at University. Way to admit you’re wrong in the general case 😂

We’re not “leaving it out” in front of the 2

High school Maths textbooks, which everyone does, explicitly say it’s there

So far you have not even tried to write down what it would mean for the test to be wrong

What part didn’t you understand in 20 litres is the wrong answer?

I can lay out my definition of “it’s a matter of convention” easily

Because you keep ignoring that they are proven rules Mr. Ostrich 🙄

everything could be done another way

Actually it can’t. Go ahead and try, and you’ll find that out eventually

be consistent with itself and with physical reality

That’s the exact thing which prevents it from being done another way 🙄