SmartmanApps comments on Math is not a democracy

[–] SmartmanApps@programming.dev 0 points 7 months ago (2 children)

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 🙄

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[–] PeriodicallyPedantic@lemmy.ca 0 points 7 months ago (1 child)

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

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[–] SmartmanApps@programming.dev 0 points 7 months ago (1 child)

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 🙄

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[–] PeriodicallyPedantic@lemmy.ca 1 point 7 months ago* (last edited 7 months ago) (2 children)

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

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.

For the 3rd time it does have order of operations 🙄You just do them in some random order do you?

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

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

How embarrassing for you.
Here are some more materials:

A post by Berkley university about popular ambiguous equations.
A published paper from Berkley that has been cited, with much stronger language on the matter.
Here is an article from the university of Melbourne
Article from the university of utah
A howstuffworks article on order of operations that explains it, doesn't have the pedigree of a university, but still clearly explained
Plus dozens of Quora answers, articles from online academies and learning centers, that I figured you'd just dismiss.

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.

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[–] FishFace@piefed.social 1 point 7 months ago (1 child)

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.

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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 🙄

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

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

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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 🤣🤣🤣

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

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!"

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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??? 🤣🤣🤣

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

You gave the defintion of one kind of proof.

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.

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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

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[–] FishFace@piefed.social 1 point 7 months ago

Hahaha ok sure thing buddy!

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[–] SmartmanApps@programming.dev -1 points 7 months ago (1 child)

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 🤣🤣🤣

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[–] PeriodicallyPedantic@lemmy.ca 0 points 7 months ago* (last edited 7 months ago) (1 child)

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.

I already told you 3 times they obey the same rules

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.

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

Right here:

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

Which you attempt to retort with

BTW this is completely wrong...

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.

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

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.

Note that I always cite Maths textbooks

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.

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[–] SmartmanApps@programming.dev 0 points 7 months ago* (1 child)

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 🤣🤣🤣

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[–] PeriodicallyPedantic@lemmy.ca 1 point 6 months ago* (last edited 6 months ago)

if PEDMAS is a law

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

THANK YOU. this is what I've been trying to tell you the entire fucking time. PEMDAS is not a law, its a convention.

but just in case you decide to go back on that, and since you seem to be obsessed with the idea that all notations adhere to PEMDAS - let me blow your mind:

here is the distributive law, written in the 3 notations we've been talking about:
prefix: *a+bc = +*ab*ac
infix: a(b+c) = ab+ac
postfix: abc+* = ab*ac*+

(not using juxtaposition multiplication for prefix/postfix for clarity)

so where does PEDMAS get involved in prefix or postfix notations?

regarding your textbook being the first google result... are you referring to the textbook from 1913? for someone talking about the importance of textbooks, thats a really strange choice. I can't find another with the same name and author of either Coll or Rich.
and hilariously, if you look at that text book, on page 90 it says the following:

Probably the most common error consists in breaking the laws of precedence of operations (§ 13). These laws were made arbitrarily, but are recognized the world over, and the student must accept and memorize them.

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

That screenshot calls it a convention you troll.

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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 🤣🤣🤣

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

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 🤔🤔🤔

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[–] SmartmanApps@programming.dev 0 points 7 months ago (1 child)

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

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.

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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 🤣🤣🤣

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

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

answer the question, deflecter :)

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

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.

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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.

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[–] FishFace@piefed.social 0 points 7 months ago (1 child)

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.

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[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child)

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 😂

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[–] FishFace@piefed.social 1 point 7 months ago* (last edited 6 months ago)

Property, not Law, yes

an old textbook (p78. Note, before quibbling about "products", that even though it is expressed by juxtaposition, on page 1 this textbook says that, "multiplication is indicated by the absence of a sign" and we are in the multiplication, not the non-existent "product" section. The following exercises are explicitly multiplication.)
a new textbook (p31) (Note that this time the law is expressed with × symbols. I also note that this textbook is the exact same publisher - CGP - that you have screenshotted in support of your own claims elsewhere, and indeed we used CGP textbooks at school.)
and a teacher resource (p5) (published by the University of Melbourne for teaching primary and secondary students)

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.

who proved them, yes
from proof of same

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?

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lemmy:	0.19.20
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