This message appeared within moments of me making this post. It is a scam. Don't ever pay any attention to these messages.

especially for mixed division and multiplication, have changed over time

and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper

Supporting my point that these “rules” are not in fact rules of maths

says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂

instead rules of mathematicians

who proved them, yes

associative relations which obey the distributive law

Property, not Law, yes

may break one set of rules of precedence

there's only one set! 😂

those are rules made by mathematicians not by the fundamental working of the universe

says person failing to give a single example of such 😂

How do I know this?

Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂

at the time he was writing, there was “no agreement” over the order in which to perform divisions and multiplications if both occur in an expression

Yep, and why was that, or have you already forgotten the assignment? 😂

So here’s a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not?

Of course, and I, unlike you, know exactly what he was talking about 😂

do you then agree that, for there to be agreement now

There isn't, given he was talking about conventions, and now, same as then, different people use different conventions, but all of them obey the rules 🙄

that change must be through rules created by mathematicians

from proof of same

rules given to us from the universe itself?

NOW you're getting it!

Because the universe certainly didn’t change in the meantime, did it?

Nope, and neither have the rules 😂

If you don’t agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course.

And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂

The contents of the book day nothing about the “rules” only about the symbols

says person proving they didn't read it. Who woulda thought you might refuse to read something that would prove you wrong. 🙄

In general, responding to a question with “you haven’t read enough” is, indeed, deflection

says person revealing they don't know what deflection means either 🙄

a sign you can’t answer

I can answer if you go ahead and book some online tutoring with me to cover the history behind the comment.

If you could, you would! Simple

It's not my job to educate you dude, unless you book some online tutoring with me, in which case it is my job. I gave you a book which answers it, for free, in extreme detail, and you lied about what it even contains, cos you never even looked at it, simple.

answer the question, deflecter :)

I haven't deflected. I told you to go read up on the history of it and you would discover what was being talked about. Since you apparently don't know how to use Google either, here's a link for you

about a page saying “other rules may have been adopted” suggests anything others than that different rules may have been adopted?

says person revealing they haven't read about the history behind that comment 🙄

You know by know that no-one but you agrees with your interpretations.

All the textbooks agree dude, which you would know if you had read more, but you've chosen to remain an ignorant gaslighter

You can’t find a single explicit agreement with them

With what?

Reposting the same pages that you are misinterpreting is very silly, isn’t it

says person who can't post anything that agrees with their silly interpretation 🤣🤣🤣

just stop it it’s not cool its not funny its not impressing everyone

It's not meant to be cool, or funny, or impress anyone. It's fact-checking disinformation

you’re just going to feel badly about it later

Nope! Feels good every time I stop a gaslighter

All mathematical proofs can be written in that form, otherwise they are not proofs

says person confirming he doesn't know much about Mathematical proofs 🙄

All kinds of proof are merely special cases of the general kind I told you about

No they're not, and you even admitted at the time that it had limitations 🙄

You didn’t know this?? Yeesh

Yes, I knew you only knew about one kind of proof, hence why I told you to go back to high school and re-learn all the other types that we teach to students

I’ve given you the definition of a proof before

You gave the defintion of one kind of proof. I'll take that as an admission then that you can't fault any of my proofs, since you can't point out anything wrong with any of them, only that they don't use the only proof method you know of, having forgotten the other proof methods that were taught to you in high school 🤣🤣🤣

if you can’t work out why what you wrote doesn’t match

I already know why it doesn't match, that doesn't make it not a proof, DUUUUHHH!!! 🤣🤣🤣 You need to go back to high school and learn about the other methods of proof that we use. You only seem to know the one you use in your little bubble.

you just can’t do maths.

Says person who only knows of ONE way to prove anything in Maths! BWAHAHAHAHAHAHAHAHAHA! 🤣🤣🤣

Taken as an admission that I have indeed proved my points then, as I already knew was the case.

That’s ok, as Barbie taught us “math is hard!”

Is THAT why you only know ONE method of proof - you learnt from Barbie??? 🤣🤣🤣

And yet you were unable to reply with a proof. So sad

Says person unable to point out in what way it wasn't a proof, so sad 🤣🤣🤣

That’s some awful impressive goalpost shifting

BWAHAHAHAHAHAHA! Says person refusing to acknowledge that it's in textbooks the difference between conventions and rules 🤣🤣🤣

Gold medal mental gymnastics winner

Yep, I know you are. That's why you had to post known to be wrong blogs, because you couldn't find any textbooks that agree with you 🤣🤣🤣

And here you are, still unable to explain why prefix and postfix notation don’t have an operator precedence.

Speaking of goalpost shifting - what happened to they don't have rules?? THAT was your point before, and now you have moved the goalposts when I pointed out that the blog was wrong 🤣🤣🤣

I’m still waiting

says person who has still not posted any textbook at all with anything at all that agrees with them, to someone who has posted multiple textbooks that prove you are wrong, and now you are deflecting 🤣🤣🤣🤣

They literally don’t

they literally *do., That's why the rules get mentioned once at the start of the blog - it's the same rules duuuhhh!!! 🤣🤣🤣

I defy you to show me a single source that tells you that prefix or postfix notation use PEDMAS.

PEMDAS isn't the rules, it's a convention

I’ll even take Quora answers

I won't take anything but textbooks, and you've still come up with none

I’ll even take a reputable source talking about prefix/postfix that doesnt bring up how order of operations isn’t required for those notations.

That's exactly what the blog you posted does. I knew you hadn't read it! BWAHAHAHAHAHAHAHA! 🤣🤣🤣 I'll take that as an admission of being wrong then

No, you’ve show a screenshot from a random PDF

of a Maths textbook, with the name of the textbook in the top left, and the page number also in the top left. 🤣🤣🤣

Infix notation needs extra information to make the order of evaluation of the operators clear:

rules built into the language about operator precedence and associativity

Yep, says nothing about operator precedence being tied to the notation, exactly as I just said, so that's a fail from you then

But then you go on to say something to the effect of “anyone who knows the rules can the extra information”

derive the rules is what I said liar. The only thing you need to know is the definition of the operators, everything else follows logically from there.

Which is both unsubstantiated given the long history of not having PEDMAS

The order of operations rules are way older than PEMDAS. It even says it in one of the blogs you posted that PEMDAS is quite recent, again showing you didn't actually read any of it. 🙄

No, you’ve show a screenshot from a random PDF

Nothing random about it. The name of the textbook is in the top left. Go ahead and search for it and let me know what you find. I'll wait 🤣🤣🤣

What math textbook and what edition is it?

So, you're telling me you don't know how to look at the name of the PDF and search for it?? 🤣🤣🤣 I can tell you now it's the #1 hit on Google

The fact you think that factorization has to do with order of operations is shocking

says person revealing they don't know anything about order of operations 🤣🤣🤣 Make sure you let all the textbook authors know as well 🤣🤣🤣

Yes the multiplication is done first

No, Brackets are done first.

The law is about converting between a sum of a common product and a product of sums

Nope. That's the Distributive Property, and yes indeed, the Property has nothing to do with order of operations, but the Distributive Law has everything to do with order of operations.

No matter how you write them, it will always be about those things,

The Property will, the Law isn't

so the multiplication always happens first.

No, Brackets are always done first

It’s crazy that you’re not able to distinguish between mathematical concepts and the notation we use to describe them

says person who doesn't even know the difference between a Property and a Law, and, as far as I can tell, have never even heard of The Distributive Law, given they keep talking about the Property

But putting that aside, that’s not a proof of PEDMAS.

Right, it's a proof of the order of operations rules for Brackets 🙄

If PEDMAS is an actual law

It isn't, it's a convention

There are proofs for 1+1

It's true by definition. There's nothing complex about it. Just like ab=(axb) is true by definition

if PEDMAS is a law

It isn't, it's a convention. Not sure how many times you need to be told that 🙄

or an textbook snippet

You mean like textbook snippets stating that The Distributive Law is the reverse operation to Factorising?? See above 🤣🤣🤣

Has anyone tried TextTransform with a Button on Android? I originally tried all sorts of things to get my Android buttons to be lower-case, and nothing worked, it was always all-caps regardless of the original case, because "Material design on Android", 🙄 and I ended up giving up on it. Would love to try this out but I've recently reinstalled and haven't finished yet, so I haven't got anything ready to go to try it out and see if it works with Android Buttons.

Our friend doesn’t know what a mathematical proof is,

says person who doesn't know enough about Maths to prove the order of operations rules, which literally anyone can do for themselves if they know all the operator and grouping symbols definitions 🤣🤣🤣

will instead try to give you an example in which he posits a real-world calculation, writes down an arithmetic expression for it according to one convention, interprets it with another, gets a different answer, and tells you this is “proof” that it’s wrong

I have no idea who you're talking about, but it ain't me! 😂

writes down an arithmetic expression for it according to

the definitions of the operators 🙄

When I explained to him

was precisely nothing

how you could write down the expression according to a different convention, then interpret it with the same convention and get the same answer, he just denied, denied, denied

What you mean is I actually proved you wrong about "different conventions" (noted you still don't know the difference between conventions and rules), but you're pretending it never happened 🙄

A claim entirely unsupported by the textbook example you provided

says person who pointed out to begin with it was talking about conventions. BWAHAHAHAHAHA! I even underlined it for you. Ok, then, tell me which convention exactly they are talking about if it isn't left to right 😂

Nowhere does it say that one is a convention

It quite clearly states that left to right is a convention 🙄

but not the other

"the other" wasn't even the subject at hand. 🙄 Here you go then...

it only says that removing brackets changes the meaning in some situations, which is fully within the scope of a convention

But not within the scope of rules 🙄

There you go again, just admitting you don’t know what postfix and prefix notations are.

There you go again not being able to say what the RULES for them are! 🤣🤣🤣 I admitted nothing of the kind by the way. I already told you 3 times they obey the same rules 🙄

here is a great free article from Colorado State university

It's pretty rubbish actually - finding a blog post by someone as ill-informed as you doesn't make it "great". Note that I always cite Maths textbooks and thus have no need to ever quote blog posts? 😂

Note how it says the rules about operator precedence are for the notation

Because (sigh) the same rules apply to all notations 🙄

which itself is a convention, as all notations are

Yep, and are separate to the rules, which are the same for all notations

Note how it says the rules about operator precedence are for the notation

Nope. Doesn't say that anywhere. Go ahead and screenshot the part which you think says that. I'll wait

how prefix and postfix don’t need those rules

Doesn't say that either. 🙄 Again, provide a screenshot of where you think it says that

BTW this is completely wrong...

"Infix notation needs extra information to make the order of evaluation of the operators clear" - Anyone who knows the definitions of the operators and grouping symbols is able to derive the rules for themselves, no need for any "extra information" 🙄

"For example, the usual rules for associativity say that we perform operations from left to right" - The thing we just established is a convention, not rules 🙄

"so the multiplication by A is assumed to come before the division by D" - Which we've already established can be done in any order 🙄

How embarrassing for you

No, you actually. You know, the person who can't find a single textbook that agrees with them 😂

Here are some more materials

NONE of which were Maths textbooks, NOR Maths teachers 😂

A post by Berkley university about popular ambiguous equations

None of which are actually ambiguous. He should've looked in a Maths textbook before writing it 😂

"the 48/2(9+3) question" - 48/2(9+3)=48/(2x9+2x3), per The Distributive Law, as found in Maths textbooks 😂

A published paper from Berkley that has been cited, with much stronger language on the matter

Did you even read it?? Dude doesn't even know the definition of Terms, ab=(axb) 🤣🤣🤣

Here is an article from the university of Melbourne

"Without an agreed upon order" - Ummm, we have proven rules, which literally anyone can prove to themselves 😂

Article from the university of utah

"There is no mathematical reason for the convention" - There are reasons for all the conventions - talk about admitting right at the start that you don't know much about Maths 🙄

A howstuffworks article on order of operations that explains it

It only explains the mnemonics actually, not why the rules are what they are. 🙄

Did you read it?? 🤣🤣🤣

"The order of operations — as Americans know it today — was probably formalized in either the late 18th century" - Nope! Way older than that 🙄

doesn’t have the pedigree of a university, but still clearly explained

It actually did a better job than all of the university blogs you posted! 🤣🤣🤣

Plus dozens of Quora answers, articles from online academies and learning centers, that I figured you’d just dismiss.

Because not Maths textbooks, duuuuhhhh 🤣🤣🤣

But to top it all off, if this was truely a law of mathematics

Which it is as per Maths textbooks 🤣🤣🤣

then show me a proof, theorem, or even a mathematical conjecture, about order of operations.

The proof is it's the reverse operation to Factorising, thus must be done first 🙄

But since you hate Maths textbooks, go ahead and search for "reverse operation of distributive law" and let me know what you find. I'll wait 🤣🤣🤣

In your screenshot of a textbook, they refer to it as a convention twice

Left to right is a convention, yes, doing Multiplication and Division before Addition and Subtraction is a rule 🙄

And you still haven’t explained prefix or postfix notation not having order of operations

For the 3rd time it does have order of operations 🙄 You just do them in some random order do you? No wonder you don't know how Maths works

Get rekd idiot

says person who doesn't know the difference between conventions and rules, and thinks postfix notation doesn't have rules 🙄

That screenshot calls it a convention you troll

says the actual troll, who didn't notice it was talking about left to right,. which is indeed a convention which it is explaining 🤣🤣🤣

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 🙄

Microsoft lessons are like this...

Have to reply to your other post here, because you hit the maximum comment depth with your rubbish.

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

That's right, as per Page 36 of Modern Algebra, published in 1965, as opposed to Advanced Algebra, published in 1912., but if you think we still call it "Multiplication" you're more than welcome to find a modern textbook which calls it that, instead of relying on a 113 year old textbook 🙄

If you can find an explicit textbook example where writing a(b)²

What did you not understand about textbooks write ab² if they meant (axb²)?

that’s another way you can prove your good faith

I already proved it with all my other textbook references, which you keep ignoring 🙄

the exponent could be anything other than 1

In other words, you refuse to believe the rule that I have already quoted multiple times, because it proves you are wrong about this meme, and so trying to derail the argument, still, with your false equivalence argument, speaking of lacking good faith 🙄

Likewise, if you can find any explicit textbook example which specifically mentions an “exception” to the distributive law

There aren't any exceptions. I'm not sure why you're having trouble with that. You want me to find evidence of something I have said all along doesn't exist 😂

I’m not saying that such an explicit example is the only way to demonstrate your claim

says person who to date has refused to accept what any textbook has said about it 🙄

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

Since when do trolls post Maths textbooks backing them up? 🤣🤣🤣

that it’s possible to have a productive discussion.

says person who has rejected literally every Maths textbook I've posted. 🙄

You insist you’re talking about mathematical rules that cannot be violated

as per Maths textbooks 🙄

so it should be no problem to find an explicit mention of them

...and I already posted many of them, but for some reason you find them unacceptable (that reason being that they prove you are wrong 😂 )

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

Nope, liar. All calculators except for Texas Instruments and e-calcs are correct - certainly all my calculators are correct (as can be seen in the video in the thread). Same thread shows the reason that programmers are almost all wrong - they don't even all get it wrong in the same way - everyone gets it wrong in different ways, which debunks the whole idea of them following any rules 😂

that my interpretation of your own textbooks is wrong

Which you would've found out for yourself, had you read more than 2 sentences out of them. 🙄 Welcome to what happens when you only read the scaffolding part of a lesson, and not the new content part of the lesson 🙄

if you show no ability to admit error

says person who has failed to admit their error about the calculators. 🙄For me to do so would require me having made an error to begin with, which I haven't, which is why you've been unable to say where I've made an error 🙄

to admit that disagreement from competing authorities casts doubt on your claims

There isn't any disagreement from competing authorities, and yet you still refuse to admit you're wrong 🙄

to evince your controversial claims with explicit examples that are not subject to interpretational contortions,

says the only person who has made such contortions, such as "means" means "equals" 🙄

the likelihood is that you’re not willing to ever see truth

You you mean, as evidenced by the fact that you had already dismissed me as being good faith in your above post before I had even seen THIS post - something, something, judge, jury, and executioner 🙄

there’s no point arguing with such a person

I'm not arguing with you - I'm debunking your rubbish claims lest any reader fall prey to them

sorry for making multiple replies on the same point

Which at the end of it all you had still failed to make a point.

As my own show of good faith, I do see that one of your textbooks (Chrystal) has the convention that a number “carries with it” a + or -, which is suppressed in the case of a term-initial positive number

No, a show of good faith by you would be 1. accepting that axb and ab are different, as per the page you reference above, which I'll come back to in a tick, 2. accepting The Distributive Law, a(b+c)=(ab+ac), is a thing found in many Maths textbooks (all of which you ignored), otherwise all you have conceded was yet another side-quest on your part because you refuse to concede anything which is actually relevant

So, you started this post with referencing Page 6 of Advanced Algebra (as proven by you quoting the bit about "Multiplication", which explicitly shows that bxc and bc ARE NOT THE SAME THING, and yet here you are still not acknowledging this fact.

a÷bxc=12÷3x4=16, a÷bc=12÷(3x4)=1

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

It's not a convention, it's a rule 🙄

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

No-one cares 🙄 Most people don't go to university and learn niche rules, everyone goes to high school and learns the general rules

You failed to demonstrate any good faith

says the person who actually demonstrated no good faith 🙄 and was unable to back up anything they said with a textbook

so this is the end of this conversation

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

Your reply reveals that you even understand that you were wrong

Nope!

“it’s designed that way”

Yep, that shows I was correct about "simple" calculators, whereas chain calculators were designed that way, but that was used as moving goalposts by the person claiming this applied to "simple" calculators, which was disproven by the manual showing that it did indeed have a stack and obey the order of operations rules, hence the goalposts got moved, again 🙄

the language changed

You think it doesn't change?? BWAHAHAHAHAHA 🤣🤣🤣 But sure, Mr. I'm (not) showing good faith, go ahead and show us a modern textbook which calls Products "Multiplication". I'll wait. 😂 Oh wait. you said the conversation was over. Too bad you can't prove your point then... again

but are so prideful,

Correct is the word you're looking for

so averse to ceding ground,

says person who has failed to come up with a single valid point that I could therefore cede to 🙄

that you just… can’t… say it!

says person who has failed to admit they are wrong about things they have been proven wrong about 🙄

The children you really ought to stop teaching are more mature than this.

They're more mature than you yes. They have no problem at all with The Distributive Law and why it exists, and can see their calculators know this also.

You’re an embarrassment to the profession.

says the actual embarrassment who can't back up anything they say with any Maths textbook 🙄

Man, this whole post has been embarrassing for you

Nope. I'm the only one who has backed up what they've said with Maths textbooks 🙄

I can’t help but notice youve once again failed to address prefix and postfix notations.

What is it that you want addressed?

And that you’ve not actually made any argument other than “nuh uh”

Backed up by Maths textbooks 🙄

We can all tell you’re not a maths teacher

Says person who actually isn't a Maths teacher, hence no textbooks 😂