this post was submitted on 18 Dec 2025
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isn't a Maths textbook 🙄 far out, did you learn English from Wikipedia too? You sure seem to have trouble understanding the words Maths textbook
The site that you just quoted which is proven wrong by Maths textbooks, THAT Wikipedia?? 🤣🤣🤣
Umm, they do need the rules! 😂
They don't, they apply to all notations 🙄
I love how confident you are about something you clearly have no knowledge of.
Adorable.
Well, you made a good effort. At least if we're judging by word count.
says person confidently proving they have no knowledge of it to a Maths teacher 🤣
from Maths textbooks, which for you still stands at 0
To a "maths teacher"
Yeah sure
A "teacher" who doesn't know that all lessons are simplifications that get corrected at a higher level, and confidentiality refers to children's textbook as an infallible source of college level information.
A "teacher" incapable of differentiating between rules of a convention and the laws of mathematics.
A "teacher" incapable of looking up information on notations of their own specialization, and synthesizing it into coherent response.
Uh huh, sounds totally legit
Don't bother mate. Even if you corner them on something, they absolutely will not budge.
I like many others brought up calculators and how common basic calculators only evaluate from left to right. They contend that this is not true and that calculators have always been able to obey order of operations. I even linked the manuals of two different calculators which both had this operation.
He asserted (without evidence) that the first does not operate in this way (even though the manual says that you must re-order some expressions so that bracketed sub-expressions come first). He then characterised the second as a "chain calculator" for "niche purposes". So he admits it works left-to-right, but still will not admit that he was wrong about his claim.
This calculator thing is not central to the discussion on order of operations, but it goes to show: you will not convince him of anything no matter what the evidence is.
By the way, after reading a few of his comments, I believe I can summarise his whackadoodle understanding if you want to continue tilting at windmills: he fundamentally cannot separate mathematics from the notation. Thus he distinguishes many things which are the same but which are written differently.
As opposed to a Maths teacher who knows there are no corrections made at a higher level. Go ahead and look for a Maths textbook which includes one of these mysterious "corrections" that you refer to - I'll wait 😂
A high school Maths textbook most certainly is an infallible source of "college level" information, given it contains the exact same rules 😂
Well, that's you! 😂 The one who quoted Wikipedia and not a Maths textbook 😂
You again 😂 Wikipedia isn't a Maths textbook
Man, this whole post has been embarrassing for you. Oof.
I can't help but notice youve once again failed to address prefix and postfix notations.
And that you've not actually made any argument other than "nuh uh"
Not to mention the other threads you've been in. Yikes.
We can all tell you're not a maths teacher.
Nope. I'm the only one who has backed up what they've said with Maths textbooks 🙄
What is it that you want addressed?
Backed up by Maths textbooks 🙄
Says person who actually isn't a Maths teacher, hence no textbooks 😂
Your argument you haven't made is backed up by math textbooks you haven't provided written for children.
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? Laws of mathematics are universal across notations.
Show me a textbook that discusses other notations and also says that order of operations is a law of mathematics.
You don't have it, and you also aren't a maths teacher, or a teacher at all. Just because you say it a lot doesn't make it true.
That's quite a word salad. You wanna try that again, but make sense this time?
If I didn't make it then it's not my argument, it's somebody else's 😂
as well as the textbooks I have provided 😂
All my textbooks are for teenagers and adults
I already addressed that here. I knew you were making up that I hadn't addressed something 🙄
Correct, they do.
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 mean you don't have a counter-example which proves it's not a Law
says liar
You know you just saying it's not true doesn't make it not true, right? 🤣🤣🤣
BTW, going back to when you said
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 🙄
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 🤣🤣🤣
Strange that this way of assigning meaning to a string of mathematical symbols is a convention then, but not the other part that is mentioned in the same paragraph 🤔🤔🤔
And what, my dear, about a page saying "other rules may have been adopted" suggests anything others than that different rules may have been adopted?
You know by know that no-one but you agrees with your interpretations. You can't find a single explicit agreement with them. Reposting the same pages that you are misinterpreting is very silly, isn't it.
says person revealing they haven't read about the history behind that comment 🙄
All the textbooks agree dude, which you would know if you had read more, but you've chosen to remain an ignorant gaslighter
With what?
says person who can't post anything that agrees with their silly interpretation 🤣🤣🤣
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
The contents of the book day nothing about the "rules" only about the symbols, so lining this book doesn't answer the question.
In general, responding to a question with "you haven't read enough" is, indeed, deflection, and is a sign you can't answer. If you could, you would! Simple.
says person proving they didn't read it. Who woulda thought you might refuse to read something that would prove you wrong. 🙄
says person revealing they don't know what deflection means either 🙄
I can answer if you go ahead and book some online tutoring with me to cover the history behind the comment.
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.
Hey, you're right, Cajori does talk about operator precedence.
Unfortunately, it talks about how the rules, especially for mixed division and multiplication, have changed over time. Supporting my point that these "rules" are not in fact rules of maths, but instead rules of mathematicians.
That is why Cajori includes them in a book about the history of how we write mathematics. No matter how you write multiplication and addition, they must always be commutative, associative relations which obey the distributive ~~law~~; if they didn't, they wouldn't be multiplication and addition. However, you can write them down in different ways, by using different symbols for example. Using different symbols for multiplication changes what a sequence of mathematical symbols means, but it doesn't change what multiplication is. Doing the operations described by a sequence of mathematical symbols in one order or another order may break one set of rules of precedence, but those are rules made by mathematicians not by the fundamental working of the universe.
How do I know this? Because Cajori says that, 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. 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?
If you do agree that there was no such agreement, do you then agree that, for there to be agreement now, such as there may be, that change must be through rules created by mathematicians, rather than by rules given to us from the universe itself? Because the universe certainly didn't change in the meantime, did it?
If you don't agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course.
and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper
says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂
who proved them, yes
Property, not Law, yes
there's only one set! 😂
says person failing to give a single example of such 😂
Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂
Yep, and why was that, or have you already forgotten the assignment? 😂
Of course, and I, unlike you, know exactly what he was talking about 😂
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 🙄
from proof of same
NOW you're getting it!
Nope, and neither have the rules 😂
And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂
All call it the "distributive law". The second textbook uses the term interchangeably with "distributive property" (p34). A five-second google can find numerous webpages, with an introductory paragraph which starts, "the distributive law, also called the distributive property..." and Encylopedia Britannica says too that they are the same thing. All three resources make no distinction as far as distribution goes between an expression written with a multiplication symbol like 2×(4+5) and one without like 2(x+3).
There is no difference between the two terms. I'd ask you for your reference, but I'm sure it's in the same place as your references to your other nonsense that you tried and failed to find references for, so you needn't bother: the evidence above is all that's needed to dismiss this bollocks anyway. So stop repeating this stupid claim; nobody except a complete moron is going to use these two terms - which certainly sound like synonyms - to refer to two closely related, but different things. It's asking for confusion. I don't intend to discuss this point again.
So, you're saying that, some time after 1928, a mathematician proved that a ÷ b × c = (a ÷ b) × c? Where was this result published? What's the citation? Who was the author (or authors)? Or maybe you don't have the citation to hand, but know the proof off the top of your head? Please, let me see it.
Does it not seem weird to you that such a basic aspect of mathematics as multiplication and division remained undiscovered until the 20th century? It's hardly Fermat's Last Theorem. If the meaning of a ÷ b × c were not a matter of choice but instead an open question, why were mathematicians using the notation at all when its meaning was not known?
And what of the textbooks like High School Algebra, Elementary Course (1917) which used the convention - err oops, rule - of performing multiplication first? See page 212, example 155. (Would be 810, not 90, if using strict left-to-right priority for division and multiplication)
If it were proved that this ~~convention~~ is wrong, then you will surely be able to find some serious error that flows from doing division in this order. After all, from any contradiction, you can prove anything.
Of course you won't be able to do this because the question that you are saying was proved is "what does the sequence of symbols a ÷ b × c mean". The meaning of sequences of symbols is not a fundamental aspect of the universe, is it. They could have different meanings to different people, in different places, or at different times, couldn't they?
In your screenshot of a textbook, they refer to it as a convention twice.
And you still haven't explained prefix or postfix notation not having order of operations.
Get rekd idiot
Left to right is a convention, yes, doing Multiplication and Division before Addition and Subtraction is a rule 🙄
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
says person who doesn't know the difference between conventions and rules, and thinks postfix notation doesn't have rules 🙄
A claim entirely unsupported by the textbook example you provided. Nowhere does it say that one is a convention but not the other, it only says that removing brackets changes the meaning in some situations, which is fully within the scope of a convention.
There you go again, just admitting you don't know what postfix and prefix notations are.
If you're ordering your operations based what the operator is, like PEDMAS, then what you're doing isn't prefix or postfix.
I'll tell you what, here is a great free article from Colorado State university talking about prefix, postfix, and infix notations.
Note how it says the rules about operator precedence are for the notation which itself is a convention, as all notations are, and how prefix and postfix don't need those rules
How embarrassing for you.
Here are some more materials:
But to top it all off, if this was truely a law of mathematics, then show me a proof, theorem, or even a mathematical conjecture, about order of operations.
Our friend doesn't know what a mathematical proof is, and 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.
When I explained to him 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, with no sign of understanding.
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 🤣🤣🤣
I have no idea who you're talking about, but it ain't me! 😂
the definitions of the operators 🙄
was precisely nothing
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 🙄
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 🤣🤣🤣
I've given you the definition of a proof before, if you can't work out why what you wrote doesn't match you just can't do maths.
That's ok, as Barbie taught us "math is hard!"
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 🤣🤣🤣
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.
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.
Is THAT why you only know ONE method of proof - you learnt from Barbie??? 🤣🤣🤣
All mathematical proofs can be written in that form, otherwise they are not proofs. All kinds of proof are merely special cases of the general kind I told you about. You didn't know this?? Yeesh.
says person confirming he doesn't know much about Mathematical proofs 🙄
No they're not, and you even admitted at the time that it had limitations 🙄
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
Hahaha ok sure thing buddy!
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 😂
It quite clearly states that left to right is a convention 🙄
"the other" wasn't even the subject at hand. 🙄 Here you go then...
But not within the scope of rules 🙄
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 🙄
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? 😂
Because (sigh) the same rules apply to all notations 🙄
Yep, and are separate to the rules, which are the same for all notations
Nope. Doesn't say that anywhere. Go ahead and screenshot the part which you think says that. I'll wait
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 🙄
No, you actually. You know, the person who can't find a single textbook that agrees with them 😂
NONE of which were Maths textbooks, NOR Maths teachers 😂
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 😂
Did you even read it?? Dude doesn't even know the definition of Terms, ab=(axb) 🤣🤣🤣
"Without an agreed upon order" - Ummm, we have proven rules, which literally anyone can prove to themselves 😂
"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 🙄
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 🙄
It actually did a better job than all of the university blogs you posted! 🤣🤣🤣
Because not Maths textbooks, duuuuhhhh 🤣🤣🤣
Which it is as per Maths textbooks 🤣🤣🤣
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 🤣🤣🤣
That's some awful impressive goalpost shifting. Gold medal mental gymnastics winner.
And here you are, still unable to explain why prefix and postfix notation don't have an operator precedence. I'm still waiting.
They literally don't, and I defy you to show me a single source that tells you that prefix or postfix notation use PEDMAS. I'll even take Quora answers.
Heck, 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.
Right here:
Which you attempt to retort with
But then you go on to say something to the effect of "anyone who knows the rules can the extra information". Which is both unsubstantiated given the long history of not having PEDMAS, but also kind of a nothingburger.
It's literally the whole thing. Did you notice how they never discuss the need for operator precedence, or use operator precedence?
Build for me a prefix or postfix equation that you think is changed by adding parentheses (eg overriding the natural order of operations), and then go ahead and find a prefix or postfix calculator and show me the results of removing those parentheses.
If you read the rules for those notations, you'll see pretty clearly that operator precedence is purely positional, and has nothing to do with which operator it is.
No, you've show a screenshot from a random PDF. What math textbook and what edition is it?
The fact you think that factorization has to do with order of operations is shocking.
Yes the multiplication is done first, but not because PEDMAS. The law is about converting between a sum of a common product and a product of sums. No matter how you write them, it will always be about those things, so the multiplication always happens first. It doesn't depend on PEDMAS because without PEDMAS you'd simply write the equation differently and factorization would still work.
It's crazy that you're not able to distinguish between mathematical concepts and the notation we use to describe them.
But putting that aside, that's not a proof of PEDMAS.
If PEDMAS is an actual law, then there will be a formal proof or theorem about it. There are proofs for 1+1, if PEDMAS is a law then there will be an actual proof specifically about it. Not just some law and then you claim it follows that PEDMAS is true, an actual proof or theorem, or an textbook snippet explain how it is an unprovable statement.
BWAHAHAHAHAHAHA! Says person refusing to acknowledge that it's in textbooks the difference between conventions and rules 🤣🤣🤣
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 🤣🤣🤣
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 🤣🤣🤣
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 *do., That's why the rules get mentioned once at the start of the blog - it's the same rules duuuhhh!!! 🤣🤣🤣
PEMDAS isn't the rules, it's a convention
I won't take anything but textbooks, and you've still come up with none
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
of a Maths textbook, with the name of the textbook in the top left, and the page number also in the top left. 🤣🤣🤣
Yep, says nothing about operator precedence being tied to the notation, exactly as I just said, so that's a fail from you then
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.
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. 🙄
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 🤣🤣🤣
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 know it's the #1 hit on Google
says person revealing they don't know anything about order of operations 🤣🤣🤣 Make sure you let all the textbook authors know as well 🤣🤣🤣
No, Brackets are done first.
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.
The Property will, the Law isn't
No, Brackets are always done first
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
Right, it's a proof of the order of operations rules for Brackets 🙄
It isn't, it's a convention
It's true by definition. There's nothing complex about it. Just like ab=(axb) is true by definition
It isn't, it's a convention. Not sure how many times you need to be told that 🙄
You mean like textbook snippets stating that The Distributive Law is the reverse operation to Factorising?? See above 🤣🤣🤣