In mathematics, a product is the result of multiplication,
or Factoristion, ab+ac=a(b+c) <== a Product of a and (b+c)
I mean, I don’t like to argue about this
And yet here you are arguing with someone who is and is a Maths teacher
there is an implied multiplication there.
Nope! It's a Term/Product. There's no such thing as "implied multiplication" - you won't find it in any Maths textbook
Which you said changed 130 years ago
The definition of Division changed more than 130 years ago. a+b/c+d originally meant (a+b)/(c+d), but that limited you to one division per expression, so they changed the definition to be a+b/c+d=a+(b/c)+d, which brought it into line with all the other operators - the underlying Maths never changed, just the way we write expressions did
isn't a Maths textbook
In mathematics and computer programming, the order of operations is a collection of conventions
and rules 🙄 Haven't even got past the first sentence you quoted and it's already wrong
These conventions
Rules
but some programming languages and calculators
May disobey the rules and give wrong answers, like Texas Instruments calculators
With math, you can invent your own notation if you like
Yep, but you cannot invent your own rules 🙄
This is done often.
No it isn't.
And if it makes sense, you can also change the order of operation
No you can't, or you get wrong answers, like Texas Instruments calculators
The notation you learn in school is just a common one, but other notations are equally valid and can be useful
But the rules are universal. You seem to be confusing notation with the rules
Therefore this kind of question is not a pure math question
Yes it is
what kind of conventions or notations people want to use
We can see for ourselves quite clearly what notation they have used. There's no mystery or debate about it
The context is what allows the math question to have a single answer
The rules of Maths is what gives it a single answer - that's what they're for! 😂
The rules of math itself are much more fundamental and they don’t care about how people decided to write formulas down.
Yep, one of which is The Distributive Law, a(b+c)=(ab+ac).
Yes it does
Says person who can't cite a single example of it depending on the language 🙄
Sorry, your realm does not extend into English
Sorry, it most definitely does when it comes to how English is used in Maths
It’s tangential to mathematics, but it isn’t mathematics
The way we say Mathematical things is 100% Maths
There’s absolutely nothing you can improve on?
I can improve some badly written textbooks. Probably every Maths teacher can.
Has a teacher ever been wrong (or just uninformed) about a topic in a subject they teach?
Yes, ones who haven't looked in the textbook which seems to be the case with a lot of unqualified U.S. Maths teachers
Does every English teacher know the content of every book?
Probably the content of every book they teach 🙄
No one knows everything about a subject
Teachers do. It comes from teaching the same thing year after year after year
Anyway, this isn’t your subject!
Yes it is! 😂
This is English, not math
It's Mathematical English
Do you see any formulas, proofs, or equations in these comments?
Do you see words in Maths textbooks? And the definitions of them? 🙄
What don’t you get?
Why you keep insisting that Maths textbooks are wrong
It being in an algebra textbook does not limit it to the realm of algebra
And NOT being in any arithmetic book means it's not part of Arithmetic 🙄
Numbers are in that textbook too
Yep, both Arithmetic and Algebra, as opposed to a(b+c) which is only in Algebra books.
If I’m wrong, I’d love to see the citation
Says person who can't cite any Arithmetic books it's in 🙄
Anyway, unless you provide that proof at the end there
Already gave it in the previous post... which you didn't look at 🙄
You already said that to me
And you're still ignoring it
Because division is multiplication
No it isn't.
and subtraction is addition
And you still have to do both
2/2 is the same as 2*½
They're equal in value, they're not the same
2-2 is the same as 2+(-2)
You got that the wrong way around. Brackets have only been used in Maths for a few centuries now
Well, as I already said multiple times: Division = Multiplication
And you were wrong every time you said it.
therefore they would be doing them together
Not if you left them out of the mnemonic and they didn't know when to do them
You’re not listening to me
Says person refusing to look in Maths textbooks 🙄
found the Commonwealther
Or more precisely, the non-USer 😜
I’m a software developer
So am I
adding extra parenthesis often adds clarity
Everyone I've seen add Brackets to it has done so in the WRONG place and given WRONG answers. Again this is an issue of programmers not checking the rules of Maths
that do not apply to what I’m talking about
The rules of Maths always apply to all Maths
I already said he was wrong about that. Quoting him saying it doesn't change that he's wrong about it
No, and I have no idea where you got that idea! 😂