SmartmanApps

Yeah, you clearly don’t even know what a convention is, and what are math conventions and math “rules” as you put it

Says person who actually doesn't know the difference, as per Maths textbooks

You’re wrong

oh no! you better start contacting all the textbook publishers and tell them that all Maths textbooks are wrong 😂

even a 2 minute Google search would show you that and explain why

Even a 2 minute Google search will bring up Maths textbooks which prove that Google is wrong 🙄

I’m done being Google for you

Maths teachers don't use Google - that's what Maths textbooks are for

when you’re not willing to Google it yourself

says person who was unwilling to use Google to find Maths textbooks 🙄

a*b and ab are both the product of a and b,

Nope. Only ab is the product of a and b. axb is Multiplication of 2 terms

As explained by the textbook you chose

If you had read more than 2 sentences of it, you would discover that you cannot use axb to show the product, only ab 🙄

a*b2 is ab2

No it isn't 😂 1/axb²=b²/a. 1/ab²=1/ab². Welcome to why we teach students about Terms 🙄

No textbook you’re grasping for contains your made-up exception

Law is the word you're looking for, and I posted dozens of them here in this post which you keep ignoring Mr. Ostrich

They all show what I’m rubbing your nose in. You’re just full of shit.

Nope, they all show you are full of shit Mr. Ostrich. See previous link

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 🙄

Multiplying two things makes them one term

You so nearly had it, look "two things"! Yes axb is 2 Terms being Multiplied to make them one 😂

Immediately before the definition you’re now lying about

Nope! Says exactly what I already said, and I have no idea why you think it says otherwise. Now read the next page, which tells you ab is one Term and doesn't say that axb is 1 Term. 🙄 You're proven wrong by the very textbook you're quoting from! 😂

Fuck your non-sequitur

Says person trying to disprove a(b+c)=(ab+ac) by dragging a(bc)²=ab²c² to try and make a false equivalence argument 😂

a(b+c)2 is a*(b+c)2

No it isn't! 😂 The first is one term, the second is two terms

for example - these four math textbooks.

Says Mr. Ostrich, still ignoring the dozens of textbooks I posted saying a(b+c)=(ab+ac)

No textbook will ever say it produces an a2 term

No, it produces an ab term and an ac term, a(b+c)=(ab+ac) 🙄

You made it up. You’re just full of shit

Says Mr. Ostrich, now completely full of shit, still ignoring the dozens of textbooks I posted, including ones written before I was even born

The result of a multiplication operation is called a product

Now you're getting it - axb=ab. axb is Multiplication of 2 Terms, ab is the single Product. It's the reason that 8/2(1+3) and 8/2x(1+3) give different answers 🙄

Show me one textbook where a(b+c)2 gets an a2 term

I already gave you many that tell you a(b+c)=(ab+ac) Mr. Ostrich - which part of a(b+c)=(ab+ac) are you having trouble understanding?

b*c is the product of b and c

Nope! bc is the product of b and c - it's right there in the textbook! 😂

that say you’re full of shit.

Says person yet again who has proven they are full of shit about the definition of Terms 😂

b*c is one term

No it isn't! 😂

say you’re full of shit.

says person who just proved they're full of shit about what constitutes a Term 😂

Every textbook with an answer key says you’re full of shit

Says person who can't find a Maths textbook that says a(bxc)=(abxac) 🙄

being wrong on purpose is the point

I'm gonna presume that's why you keep claiming a(bxc)=(abxac) 🙄

The answer in either case is shut the fuck up

says person still not doing that 😂

2(n)2 is 2n2

No it isn't! 😂 2xn² is

Anything else is an inane complication nobody else believes in or uses or needs

Except for authors of Maths textbooks 😂

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??

If you can simplify before distributing - and the PDFs you spam say you can

They say you can do that when there is Addition or Subtraction inside the Brackets. They also say you cannot Distribute over Multiplication, at all

then there is no difference

There is no difference between Addition and Multiplication?? 😂

You made it the fuck up

And yet, there it is in textbooks that were written before I was even born 😂

2(n)2 is 2n2 whether n=a+b or n=a*b=ab

Nope! a(b+c)=(ab+ac). a(bxc)=abc

If you want to square the 2, that’s (2n)2.

...or 2²xn², or 2(½n+½n)²

It’s not about the multiply sign, or grouping, or division

Yes it is! 😂 If there's a Multiply or a Divide, you cannot Distribute.

You fooled yourself into saying 2=1

Not me! 😂

Sorry but there is no math government that can enforce rules

Maths textbooks do. Try looking in some

the order of operations isn’t intrinsic either

Yes they are! 😂

It is just something people agreed upon volununtarily, aka a convention

Nope. Literally proven rules

Tell that obvious to over half the population who get this wrong

Way less than half actually. No teachers or students ever get this wrong, only adults who have forgotten the rules, and poll after poll puts this down around 40-45% of adults.

Ok, then explain prefix and postfix, where these conventions don’t apply

The conventions don't apply, the rules still apply. Maths notation and the rules of Maths aren't the same thing.

How can these be rules of math when they didn’t universally apply?

The rules do universally apply 🙄

The order of operations tells us how to interpret an equation without rearranging it

Yep, and you showed you don't know the rules 🙄

When you pick a different convention, you need to rearrange it to get the same answer

Not necessarily, though it makes it easier (but also leads a lot of people to make mistakes with signs, as you found out 😂 )

What you did was rearrange the equation

To show you how to correctly do "Multiplication first". 🙄

which you can only do if you are already following a specific convention

Which you didn't, hence why you ended up with a wrong answer. 🙄 There is no textbook which says put the multiplication in Brackets if doing "Multiplication first", none.

because the conventions are not laws of mathematics, they are conventions

And putting the Multiplication inside Brackets isn't a convention anywhere 🙄

They obey the laws of math. Conventions aren’t laws of math, they’re conventions

Yep, and you ignored both, hence your wrong answer 🙄

And a quick Google search will tell you that not everyone puts juxtaposition at a higher precedent than multiplication

And a quick look in the Google support forum will show you many people telling them that is wrong, and Google just closes the incident 🙄

it’s a convention

No it isn't. It's against the rules. 🙄 Again, you won't find this alleged "convention" in any Maths textbook

As long as people are using the same convention, they’ll agree on an answer and that answer is correct

Unless they disobeyed the rules, in which case they are all wrong 🙄

You can be mean all you like, that doesn’t change the nature of conventions

And you can be as ignorant of the rules and conventions of Maths as much as you want, and it's not going to change that your answer is wrong 🙄

My doctorate is irrelevant to the truth

It sure is. I've seen a PhD who didn't read the only textbook he had referenced in his thesis, which proved his idea that teachers were doing it wrong and he wasn't, was wrong. 😂 Should've listened to the people who teach it (or actually read the textbook he referenced 🙄 ).

which makes students of math feel inordinately inferior

They don't. All students get this correct. It's only adults who have forgotten the rules that get it wrong.

these gotcha-style math memes IMO deepen students’ belief that they’re just bad at math

Nope. Students never get these wrong.

proofs mean something very specific to me and I can’t yet imagine what that looks like WRT order of operations

All you have to do is see which way gives wrong answers for 2+3x4 and you've proven which ways don't work 😂

note that conventions aren’t necessarily “optional”

Yes they are.

when being understood is essential

You don't understand how to do 2+3x4-5 without knowing which conventions people use for the order of the plus and minus?

Here I am only concerned about the next generation of maths student and how viral content like this can discourage them unnecessarily

It doesn't. None of them get it wrong. 🙄

“No one” in this context meant “no one who actually does maths professionally.”

No it doesn't. Everyone who does Maths professionally does it the same way as in Maths textbooks 🙄

When I see 1+½ i can instantly say “one and a half”

And that would be wrong. It's 1 plus one half. 1½ is one and a half.

when I see 1 + 1 ÷ 2 i actually have to pause for a moment to think about order of operations

You don't know to Divide before Adding??

one I recognize the structure of the problem immediately, and one feels foreign.

Says person with "decades of maths experience outside of textbooks" 🙄

The point is that people who do maths for a living

That would be me

are probably above average in maths, tend to write things differently than people who are stopped their maths education in high school (or lower)

Nope. We all write it the same way as we were taught, even those who have done Maths at University (also me).

these types of memes are designed around making people who know high school maths feel smart

No, they're designed around getting those who have forgotten the rules to argue about it. i.e. engagement bait

and another which says “first multiply two by three, then add it to two”

No we don't. We have another notation which says to do paired operations (equivalent to being in brackets) first.

why on earth do the “rules” have anything further to say about order of operations?

Because if you don't obey them you get wrong answers 🙄

How are you gonna write 2 + 2 ÷ 2 with repeated addition?

You don't, because the second 2 is associated with a Division that has to be done before the addition. Maybe go back to school and learn how to do Maths 🙄

That doesn’t mean it has to be expanded first.

Yes it does. Everything has to be expanded before you do the addition and subtraction, or you get wrong answers 🙄

2+3x4=2+3+3+3+3=2+12=14 correct

2+3x4=5x4=5+5+5+5=20 wrong

You could expand 2 + 2 × 3 as (2+2)+(2+2)+(2+2)

Says someone who can't tell the difference between (2+2)x3=12 and 2+2x3=8 🙄

you are unable to tell me what mathematical law prohibits it

The order of operations rules 😂

reverse polish notation wouldn’t work as it does

It works because it treats every operation as bracketed without writing the brackets. Also that's only a Maths notation, not the Maths itself.

In RPL, 2 2 + 3 × is 12

Because the way it calculates that is (2+2)x3, not complicated. Same order of operations rules as other Maths notations - just a different way of writing the same thing

If you had to expand multiplication first, how would it work?

It works because Brackets - 2 2 + = (2+2) - are before Multiplication

The same can be done with prefix notation

Another Maths notation, same rules of Maths

Different programming languages have different orders of operations

Maths doesn't

those languages work just fine

They don't actually. Welcome to most e-calcs give wrong answers because the programmers failed to deal with it correctly.

Your argument amounts to saying that it makes the most sense to do multiplication before addition

No, my argument is it's a universal rule of Maths, as found in Maths textbooks 🙄

that only gives you a convention, not a rule

Left to right is a convention (as is not writing the brackets in RPN). Brackets before Multiplication before Addition are rules.

knowledge on this subject without qualification

I'm a Maths teacher with a Masters - thanks for asking - how about you?

while ignoring my larger point

You mean your invalid point, that I debunked?

what are conventions if not agreed upon rules?

Conventions are optional, rules aren't.

here is a history of how we actually came to agree upon the aforementioned rules which you may find interesting

He's well-known to be wrong about his "history", and if you read through the comments you'll find plenty of people telling him that, including references. Cajori wrote the definitive books about the history of Maths (notation). They're available for free on the Internet Archive - no need to believe some random crank and his blog.

The rules are about how you interpret the notation

No, the notation definitions are about how to interpret the notation. The rules are about how to do the Maths.

That’s not true

Yes it is

PEDMAS: 8÷2x4 = 4x4 = 16

Yep.

PEMDAS: 8÷2x4 = 8÷8 = 1

Nope. PEMDAS: 8x4÷2 = 32÷2 = 16. What you actually did is 8÷(2x4), in which you changed the sign in front of the 4 - 8÷(2x4)= 8÷2÷4 - hence your wrong answer

PE M|D A|S: 8÷2x4 = 4x4 = 16

Yep, same answer regardless of the order 🙄

And thats not even getting into juxtaposition operations,

Which I have no doubt you don't understand how to do those either, given you don't know how to even do Multiplication first in this example.

where fields like physics use conventions that differ from most other field

Nope! The obey all the rules of Maths. They would get wrong answers if they didn't

you’re missing the point

No, you are...

It could be SAMDEP and math would still work

No it can't because no it wouldn't 😂

you’d just rearrange the equation.

Says someone who didn't rearrange "PEMDAS: 8÷2x4 = 8÷8 = 1" and got the wrong answer 😂

The rules don’t change

Hence why "PEMDAS: 8÷2x4 = 8÷8 = 1" was wrong. You violated the rule of Left Associativity