You insist they’re not the same. How?

Not difficult, I already did in another post. If a=2 and b=3...

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

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

So is 3xy

That's right

That doesn’t mean 3xy2 is 9y2x2.

That's right. It means 3abb=(3xaxbxb)

The power only applies to the last element

Factor yes, hence the special rule about Brackets and Exponents that only applies in that context

like how (8)22 only squares the 2

It doesn't do anything, being an invalid syntax to follow brackets immediately with a number. You can do ab, a(b), but not (a)b

not (6ab)(6ab)(6ab)

Yep, as opposed to 6(a+b), which is (6a+6b)

3(x+1)2 for x=-2 is 3, not 9

No it isn't. See previous point. Do we have an a(b+c), yes we do. Do we have an a(bc)²? No we don't.

2(x-b)2 has a 2b2 term

No, it has a a(b-c) term, squared

shut the fuck up

says someone still trying to make the special case of Exponents and Brackets apply to a Factorised Term when it doesn't. 😂 I'll take that as your admission of being wrong about a(b+c)=ax(b+c) then. Thanks for playing

For a=8, b=1, that’s 2*(81)(8*1).

Only if you had defined it as such to begin with, otherwise the Brackets Exponents rule doesn't apply if you started out with 2(8)², which is different to 2(8²) and 2(ab)²

..and there's still no exponent in a(b+c) anyway, Mr. False Equivalence

You realize a calculator doesn’t need to be a dedicated hardware, right?

You realise the calculator manufacturers have much more riding on their calculators being correct, right? 😂

Windows calculator, MacOS calculator, Android calculator, and all web-based calculators count as well.

Nope. Programmed by... programmers, who aren't earning any money from the calculator, and put the corresponding amount of effort into it.

You have no clue what you’re talking about.

says someone who just claimed that e-calcs count as much as actual, buy from a store, calculators 🤣

Alpha is a commercial product (with a free-tier as is usual nowadays)

Also well known to give wrong answers

uses the same engine as Mathematica, which is used extensively in industry, academic institutions

Nope! Academia warns against using it

None of your sources has exponents in them

In other words, you're admitting to trying to deflect from what's in Maths textbooks! 😂

that’s very convenient for your mistake of mixing up juxtaposition and your invented rule

It's the same rule, duh! Here it is in a textbook from more than 100 years ago when everything was still in brackets...

We've since then dropped the brackets from Factors which are a single Term. i.e. (a)(b+c) is now a(b+c), and (a)(b) is now ab. BTW would you like to explain how "my invented rule" appears in a textbook from more than 100 years ago? 🤣

Btw, ask yourself this as well: why would your invented interpretation of distributive law be necessary at all?

It's not invented, it's required as the reverse rule to Factorising, duh 😂 And I don't need to ask myself - as usual, all you have to do is look in Maths textbooks for the reason 😂

It brings no benefit to the table at all.

Being able to reverse the process of Factorising brings no benefit to the table?? 🤣

Juxtaposition arguably does

It's the same thing duh 🤣 ab=(a)(b), a(b+c)=(a)(b+c) notice how they are the same thing, expanding BRACKETS?? 🤣

Maybe you've forgotten about FOIL...

Now, think carefully about this, what happens when b=0, and what happens when d=0, you got it yet?? 🤣

because it allows shorter notation

AKA Factorised Terms and Products 😂

your invention doesn’t.

Again, explain how "my invention" appears in textbooks that are more than 100 years old. I'll wait 🤣

because it’s the only correct answer

Have you noticed yet that everything you think is correct is actually wrong as per Maths textbooks?? 🤣

I’ll consider your argument defeated

says person who has been comprehensively defeated by Maths textbooks and is now trying to deflect away from that 🤣

ignore further engagement from your part

I'll take that as an admission that you're wrong then, having been unable to debunk any Maths textbooks. See ya

5 isn’t a valid function name, is obviously the right answer.

5 is a coefficient of the Term 5(8-5) is the correct answer

an implied multiplication

There's no such thing. It's a Term/Product.

is the normal thing you learn in (I think?) somewhere between 5th to 7th grade

Yes, you learn that it's a Term/Product in Year 7

You only add an operator if it’s something else

You never add an operator, or you end up with wrong answers.

Google implied multiplication

There's no such thing. It's a Term/Product. Google is a prime source of Maths disinformation (yes, they have been told it's wrong, repeatedly, so it's disinformation).

Do you write 2x or do you write 2 • x?

2a=(2xa) by definition, and 5(8-5)=(5x8-5x5).

That’s implied multiplication

No, that's a Term/Product.

Implied multiplication

Terms/Products

I’ll never understand these approaches to learning. They require remembering the phrase, and then require remembering how the phrase translates to the rules you need to remember

Yeah, exactly, but the U.S. seems to have a chip on it's shoulder about always doing everything differently to the whole rest of the world. "Maths? We're not going to use BEDMAS, and we're not going to call them Brackets, and...".

Both of those Youtubes debunked in this thread.

dead communities

None of the communities you have mentioned are dead. In fact according to the January stats, all the communities you mentioned have above average usage.

Noted that you ignored this comment of mine...

it’s been worthwhile

Take your gaslighting somewhere else...

Notation isn’t semantics

Correct, the definitions and the rules define the semantics.

Mathematical proofs are working with

...the rules of Maths. In fact, when we are first teaching proofs to students we tell them they have to write next to each step which rule of Maths they have used for that step.

Nobody doubts that those are unambiguous

Apparently a lot of people do! But yes, unambiguous, and therefore the article is wrong.

But notation can be ambiguous

Nope. An obelus means divide, and "strong juxtaposition" means it's a Term, and needs The Distributive Law applied if it has brackets.

In this case it is: weak juxtaposition vs strong juxtaposition

There is no such thing as weak juxtaposition. That is another reason that the article is wrong. If there is any juxtaposition then it is strong, as per the rules of Maths. You're just giving me even more ammunition at this point.

Read the damn article

You just gave me yet another reason it's wrong - it talks about "weak juxtaposition". Even less likely to ever read it now - it's just full of things which are wrong.

How about read my damn thread which contains all the definitions and proofs needed to prove that this article is wrong? You're trying to defend the article... by giving me even more things that are wrong about it. 😂

unable to agree on an universal standard for anything

And yet the order of operations rules have been agreed upon for at least 100 years, possibly at least 400 years.

unscientific and completely ridiculous reason refuse to read

The fact that I saw it was wrong in the first paragraph is a ridiculous reason to not read the rest?

Let me just tell you one last time: you’re wrong

And let me point out again you have yet to give a single reason for that statement, never mind any actual evidence.

you should know that it’s possible that you’re wrong

You know proofs, by definition, can't be wrong, right? There are proofs in my thread, unless you have some unscientific and completely ridiculous reason to refuse to read - to quote something I recently heard someone say.

try not to ruin your students too hard

My students? Oh, they're doing good. Thanks for asking! :-) BTW the test included order of operations.

Go read the article, it’s about you

The article is wrong dotnet.social/@SmartmanApps/110897908266416158