Your argument you haven’t made is backed up by math textbooks you haven’t provided written for children

That's quite a word salad. You wanna try that again, but make sense this time?

Your argument you haven’t made

If I didn't make it then it's not my argument, it's somebody else's 😂

is backed up by math textbooks you haven’t provided

as well as the textbooks I have provided 😂

written for children

All my textbooks are for teenagers and adults

How can that specific order of operations be a law of mathematics if it only applies to infix notation, and not prefix or postfix notations

I already addressed that here. I knew you were making up that I hadn't addressed something 🙄

Laws of mathematics are universal across notations

Correct, they do.

also says that order of operations is a law of mathematics.

If you think it's not a Law, then all you have to do is give an example which proves it isn't. I'll wait

You don’t have it

You mean you don't have a counter-example which proves it's not a Law

you also aren’t a maths teacher

says liar

Just because you say it a lot doesn’t make it true.

You know you just saying it's not true doesn't make it not true, right? 🤣🤣🤣

BTW, going back to when you said

8÷2x4 PEMDAS: 8÷2x4 = 8÷8 = 1

Here it is from a textbook I came across this week which proves I was right that you did it wrong 😂

Therefore, doing Multiplication first for 8÷2x4 is {(8x4)÷2}, not 8÷(2x4) - whatever you want to do first, you write first - exactly as I told you to begin with 🙄

I explained why here

And you were proven wrong elsewhere (since you ran your rubbish to the maximum comment depth), but admitted to not reading it, speaking of proving you were the bad faith one all along 🙄

So, now that I've found a place I can reply to your other non-repliable posts...

Even if you corner them on something

Which no-one ever has 🙄

they absolutely will not budge

See how many Mathematicians and Maths teachers you can gaslight into believing that they and Maths textbooks are all wrong, I'll wait.

I like many others brought up calculators and how common basic calculators only evaluate from left to right

And you hilariously provided a manual that proved you were wrong about that! 😂

He asserted (without evidence) that the first does not operate in this way

It's right there in the manual, as I pointed out 😂

even though the manual says that you must re-order some expressions so that bracketed sub-expressions come first

That's right, because it doesn't have brackets keys 🙄 So you have to enter that first, then press the equals key to make it evaluate that first, because it doesn't evaluate from left to right otherwise, it will do the multiplication first 🙄

still will not admit that he was wrong about his claim

says person who still will not admit he was wrong about his claim that all basic calculators working that way, even though the manual proves there are some that don't 😂

you will not convince him of anything no matter what the evidence is

Says person refusing to believe all evidence, including the calculator manual 😂

he fundamentally cannot separate mathematics from the notation

Nope liar. I'm the one who keeps pointing out they are different 🙄 Go ahead and find a screenshot of me saying they're the same, I'll wait

He calls a×b multiplication and ab a product.

As per Maths textbooks, which you keep ignoring 🙄

These are, of course, the exact same thing

says person who not only can't give a single textbook which says that, but refused to answer my question about

For a=2, b=3

1/ab=1/(2x3)=1/6

1/axb=1/2x3=3/2

which of those, according to you, is the correct answer, given you insist they are "the same thing" 🙄

implicit multiplication

There's no such thing. Go ahead and find a Maths textbook that says so, I'll wait

ab can, by some conventions, have a higher precedence than does the explicit multiplication in a×b

Literally always does, as per the rules of Maths, as found in Maths textbooks 🙄

he has taken that to mean that they are fundamentally different

So go ahead and explain how "the same thing", according to you, can give different answers in all textbooks. I'll wait

He thinks that a(b+c)=ab+bc is something to do with notation

The Distributive Law actually, another rule of Maths 🙄

not a fundamental relationship between multiplication and addition

There's no multiplication in The Distributive Law, only in The Distributive Property 🙄

I will say that no author would distinguish those two terms

Except, of course, for all the ones who do 😂

because they’re just too easily confused

says person confused about the difference between a Law and a Property 😂

And many authors explicitly say that one is also known as the other

says person who can't even cite a single example of such

He says that a×(b+c) = ab + bc is an instance of the “distributive property”

ax(b+c)=axb+axc actually.

You seem to think notation is only correct at exactly the level you claim to teach

Nope, every level after Primary school

Elementary school children get taught parentheses means you do stuff inside parentheses first

Because they haven't been taught The Distributive Law yet, and there is no outside brackets for them - they don't learn that until Year 7

college calculus students get taught parentheses mean you do stuff inside parenthesis first

No they don't.

despite two centuries of textbooks showing that is in fact how parentheses work

You're the one ignoring the 2 centuries of textbooks dude 😂

All published textbooks and all pragmatic mathematics operate as though your pet peeve does not exist

says person who can't cite a single such example, again 🙄

It’s almost like the shit you insist upon is completely made-up, and does not matter to anyone besides you

says person who actually made up that Multiplication and Products are the same thing 🙄

I thought they were called “products” not “multiplications”

That's right. You know you're referring to a 1912 textbook, right? Terminology has moved on since then, as demonstrated by the 1965 textbook 😂

I’m just trying to give you more opportunities to prove that you’re not just a troll

says person who ignored all the textbooks I posted, whilst not citing any themselves 🙄

You insist you’re talking about mathematical rules that cannot be violated, so it should be no problem to find an explicit mention of them

I provided many, which you ignored 🙄

you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong

Nope, liar. All my calculators give correct answers (Sharp, Casio, Omron - only Texas Instruments breaks the mold these days), and programmers disobeying the rules of Maths doesn't prove they not rules of Maths. 🙄 You are the one claiming that Sharp and Casio calculators are giving wrong answers. 🙄 I'm guessing that your calculator, if you even have one (which seems doubtful from what I've seen) is a Texas Instruments one.

that you are right

My caclulators and textbooks are correct, yes. 🙄

that my interpretation of your own textbooks is wrong

says person who read one sentence and stopped there and did some mental gymnastics with it, ignoring that the whole rest of the book contradicts that interpretation 🙄

if you show no ability to admit error

says the person who actually made errors.

admit that disagreement from competing authorities

There isn't any "disagreement from competing authorities". 😂 Every single textbook, not just Maths, but Physics, Chemistry, Engineering, etc., obeys the exact same rules 😂

As my own show of good faith, I

didn't look at any of the examples about Distribution and Terms, speaking of proving you are the bad faith person 🙄

I’ll explain why I think this is a bad convention

and you would be wrong, just like you are about everything else

why the formal first-order language of arithmetic doesn’t have this convention

No-one cares why a niche topic, only taught at University, is different to the general rules taught to everyone at high school 🙄

the distributive law is something you must do instead of a property of multiplication that you can use to aid in the manipulation of algebraic expressions but don’t have to

That's right, as per Maths textbooks

Folded into their inability to understand that some aspects of maths are custom and convention

Says person who has an inability to tell the difference between a convention and the rules 🙄

Somewhere along the way he seems to think that distributivity is something to do with brackets instead of something to do with addition and multiplication

Law Vs. Property, not complicated!

if I can get him to actually cop to any of his verifiable mistakes

Of which there are none as opposed to you who has several verifiable mistakes 🙄

back up any of his whackadoodle claims with direct references

You've been given them, and you ignored them

Tomorrow I’m expecting another wall of text responding to every single word except the ones where I ask for such an admission

says person who has still failed to show anywhere that I was mistaken 🙄 On the other hand you have refused to admit to your mistakes

I’ll have satisfied myself he’s a lost cause

Actually, you admitted to not even reading it - that's something which people who know they are wrong do 🙄

been pushing his wrong ideas of what the distributive law are, since 2023

says person again ignoring the Maths textbooks 🙄

Notice how the text never says “you MUST use the distributive law”?

I notice how you have comprehension and/or honesty issues

It always says some variation of “in order to simplify, you must…”?

Which part of the word "must" don't you understand? 😂 Also, which part of simplifying Brackets is part of the order of operations don't you understand? 😂

No, you don’t notice, because you’re blind

cough cough 😂 Here's another one, in case you're still in any doubt...

don’t understand what distributivity actually is.

says the person who actually doesn't understand what The Distributive Law is

You also got me confused with someone else trying to explain in short words how you’re wrong

Nope. Tweedle Dum and Tweedle Dee say very similar things, but one can still tell them apart.

bye

Don't let the door hit you on the way out! 😂

I love how confident you are about something you clearly have no knowledge of.

says person confidently proving they have no knowledge of it to a Maths teacher 🤣

At least if we’re judging by word count

from Maths textbooks, which for you still stands at 0

My dude sit in a university lecture for math majors

You know I have a Masters in Maths, right? 🤣

Your school books arent gospel

Proofs are, and these things are very easy to prove 🙄

You have declined to admit to a simple error you made

Not me, must be you! 😂

that early calculators lacked a stack,

They didn't 🙄

that basic four function calculators all did and still do

Have a stack, yes. I have one and it quite happily says that 2+3x4=14, something it can't do without putting "2+" on the stack while it does the 3x4 first 🙄

There’s no point having a discussion with someone so stubborn that they can’t admit a single mistake.

says someone too stubborn to admit making a mistake 🙄

I’m not sure whether you’re trying to wind people up or just a bit dim

Neither. I'm the one doing fact-checks with actual, you know, facts, like my simple calculator having a stack and correctly evaluating 2+3x4=14. It's the one I had in Primary school. The one in the first manual works the exact same way

this conversation is like trying to explain something to a particularly stuck-up dog

So maybe start listening to what I've been trying to tell you then. 🙄 It's all there in textbooks, if you just decide to read more than 2 sentences out of them.

The real tragedy is that you claim to be out there teaching kids this overcomplicated and false drivel.

Facts, as per the syllabus and Maths textbooks. Again, you need to read more than 2 sentences to discover that 🙄

only if you show that you’re not just a troll.

says person who has thus far refused to read more than 2 sentences out of the textbook 🙄

You can do that by admitting that you were wrong to say that all calculators have stacks

I wasn't wrong 🙄 The first manual that was linked to proved it. If you don't press the +/= button before the multiply then it will put the first part on the stack and evaluate the multiplication first, something it doesn't do if you press the +/= first to make it evaluate what you have typed in so far. 🙄 Every calculator will evaluate what you have typed in so far if you press the equals button, as pointed out in the first manual

because I showed you two examples

The first of which had a stack 🙄 the second of which was a chain calculator, designed to work that way. You're the one being dishonest

you were wrong

No I wasn't

that this screenshot

Which is a 1912 textbook. It also calls Factorising "Collections", and The Distributive Law "The Law of Distribution", and Products "Multiplication". Guess what? The language has changed a little in the last 110 years 🙄

it’s from Advanced Algebra by J.V. Collins, pg 6

Yep, published in 1912

On page 3, the concept of juxtaposition is introduced

And we now call them Products. 🙄 You can see them being called that in Modern Algebra, which was published in 1965. In fact, in Lennes' infamous 1917 letter, he used the word Product (but didn't understand, as shown by his letter), so the language had already changed then

admitting to an error on your part

There was no error. The language has changed since 1912 🙄

you actually are capable of admitting error

Of course I am. Doesn't mean I'm going to "admit" to an error when there is none 🙄

Fuck where this started

I'll take that as an admission that you're wrong. Thanks for playing

‘If a+b equals b+a, why is 1/a+b different from 1/b+a?’

Because they're not identically equal 🙄 Welcome to you almost getting the point

ab means a*b

means, isn't equal

That’s why 1/ab=1/(a*b)

Nope, it's because ab==(axb) <== note the brackets duuuhhh!!! 😂

But we could just as easily say 1/ab = (1/a)*b

No you can't! 😂

because that distinction is only convention

Nope! An actual rule, as found not only in Maths textbooks (see above), but in all textbooks - Physics, Engineering, Chemistry, etc. - they all obey ab==(axb)

None of which excuses your horseshit belief that a(b)2

says person still ignoring all these textbooks

You sneered about 1/ab five minutes ago

Yet again, I have no idea what you're talking about

Troll

says person who can't back up anything they say about Terms with textbook references 🙄

That’s convention for notation

Nope, still rules

not a distinction between a*b and ab

says person who only read 2 sentences out of the book, the book which proves the statement wrong 😂

a*b and ab both being the product of a and b

Nope, only ab is the product, and you would already know that if you had read more than 2 sentences 😂

You have to slap 1/ in front of things and pretend that’s the subject

"identically equal", which you claimed it means, means it will give the same answer regardless of what's put in front of it. You claimed it was identical, I proved it wasn't.

avoid these textbooks telling you

It kills you actually, but you didn't read any of the parts which prove you are wrong 🙄just cherry pick a couple of sentences out of a whole chapter about order of operations 🙄

They are the same thing. They are one term

Nope! If they were both 1 term then they would give the same answer 🙄

1/ab=1/(axb)=1/(2x3)=1/6

1/axb=1/2x3=3/2=1.5

Welcome to why axb is not listed as a Term on Page 37, which if you had read all the pages up until that point, you would understand why it's not 1 Term 🙄

You poor thing…

You don't know what Maths textbooks say because you were too poor to go to school? I'm sorry to hear that

You can’t keep your own horseshit straight

No idea what you're talking about, again, I've been saying the same thing the whole time

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 🙄