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 😂

A “teacher” who doesn’t know that all lessons are simplifications that get corrected at a higher level,

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 😂

refers to children’s textbook as an infallible source of college level information

A high school Maths textbook most certainly is an infallible source of "college level" information, given it contains the exact same rules 😂

A “teacher” incapable of differentiating between rules of a convention and the laws of mathematics

Well, that's you! 😂 The one who quoted Wikipedia and not a Maths textbook 😂

A “teacher” incapable of looking up information on notations of their own specialization

You again 😂 Wikipedia isn't a Maths textbook

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

Wikipedia

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

You don’t trust Wikipedia?

The site that you just quoted which is proven wrong by Maths textbooks, THAT Wikipedia?? 🤣🤣🤣

you’ve yet to explain why notations like prefix and postfix dont need these “rules”.

Umm, they do need the rules! 😂

how could they only apply to certain notations?

They don't, they apply to all notations 🙄

Do you teach classes like this? “That’s not a product, it’s a multiplication”

Yep! And if you read more than 2 sentences out of the textbook you would know why 🙄

those are the same thing.

Says person who only read 2 sentences out of a whole chapter 🙄

Shouldn’t you, as a teacher, be explaining the difference, if you say there is one?

Yep, and it's right there in the textbook! 🙄

I’m starting to believe you don’t think they’re is one

So you think if a=2 and b=3, then...

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

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

Are somehow the same answer?? 😂 Which one is it then? 1/6 or 3/2?? 😂

You could argue that “product” refers to the result of the multiplication rather than the operation

Yep by definition!

there’s no sense in which the formula “a × b” does not refer to the result of multiplying a and b

There's no sense in which it does refer to the result you mean. The result of axb is ab. If a=2, b=3, axb=ab. 2x3=6, axb=2x3, ab=6

you don’t bother to even make such an argument

Says someone revealing that they haven't read a word I've said 🙄

you’re not actuality smart enough to understand the words you’re using

says someone who has just proven they haven't been reading them 🙄

It’s interesting, isn’t it, that you never provide any reference to your textbooks to back up these strange interpretations

Yes I did, and you only read 2 sentences out of it 😂

Where in your textbook does it say explicitly that ab is not a multiplication

Read on dude, read on, like I have been telling you the whole time. Oh wait, that would prove you were wrong. Oh, I wonder why you haven't read it... 🙄

It doesn’t, does it?

The page that you only read one sentence from 🙄

You’re keen to cite textbooks any time you can, but here you can’t

I already did and you only read 2 sentences out of it 🙄

You complain that people don’t read enough of the textbook, yet they read more than you ever refer to

says person who has repeatedly proven they've only read 2 sentences 🙄

In the other thread I said I wouldn’t continue unless you demonstrated your good faith by admitting to a simple verifiable fact that you got wrong

And I pointed out that in fact you got it wrong, and Mr. Hypocrite has failed to admit it 🙄

provide an actual textbook example where any of the disputed claims you make are explicitly made

Same one I already told you and you only read 2 sentences out of a whole chapter

there should be some textbook somewhere which says that mathematics would not work with different orders of operations

It's easy enough to prove yourself, like I did. Go ahead and try it out and let me know how you go.

you’ve never found a textbook which says anything like this

No, I was able to prove it myself 🙄

only things like “mathematicians have agreed”

Because it was proven 🙄

where’s your textbook which says that “a × b is not a term”?

Same textbook that you only read 2 sentences from

Where is the textbook that says 5(17) requires distribution?

It tells you tight there on the same page that you must remove all brackets, 🙄 which you also haven't admitted to being wrong about yet, surprise, surprise, surprise

Where’s your textbook which says “ab is a product, not multiplication”?

Same one you only read 2 sentences from

there is a textbook reference saying “ab means the same as a × b”,

And you stopped reading at that point didn't even finish the page, never mind the chapter 🙄 Just started making false claims (contradicted by same textbook) that "means" means "equals", instead of realising they have explicitly not said equals 🙄

so your mental contortions are not more authoritative

Says person who made the mental contortion that "means" means "equals" instead of reading the rest of the page

your ability to interpret maths textbooks is poor

says person who only read 2 sentences out of a whole chapter 🙄

we can have a productive discussion

when you decide to read more than 2 sentences 🙄

My prediction: you’ll present some implicit references

Wrong, as usual

try to argue they mean what you want

says person trying to argue that "means" means "equals" 🙄