SmartmanApps

But factorised terms are multiplications,

No, they're Distribution done in the Brackets step, a(b+c)=(ab+ac), now solve (ab+ac)

a(b+c) = a*(b+c)

Nope! a(b+c)=(ab+ac). 1/a(b+c)=1/(ab+ac), but 1/ax(b+c)=(b+c)/a.

23+25=16

(2x3+2x5) actually, or you'll get the wrong answer when it follows a Division sign. See previous point

Do you think you’re above them?

You know we're talking about Year 7 Maths, right? 😂

Elementary school teaches you the fundamentals to your future education

but NOT The Distributive Law, which is taught in high school, in Algebra

I didn’t say you were wrong about math

You said "I don’t think you’re right", and followed it up with "Ill informed", to a Maths teacher.

I said you were wrong about English that is used in relation to math

And you were wrong about that too

Clearly this isn’t a strong suit of yours

What you mean is you clearly can't rebut any of it

However, stop acting like you know everything

I know everything about high school Maths - I teach it

you clearly don’t

There you go again calling a Maths teacher wrong about Maths 😂

You’re using some very strange logic to argue you’re right

You think Maths textbooks use very strange logic??

it doesn’t make any sense

read this then. Contains Maths textbooks

Please read this section of Wikipedia which talks about these topics better than I could

Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there's plenty in here

It shows that there is ambiguity in the order of operations

and is wrong about that, as proven by Maths textbooks

especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication

That's because Multiplication and Division can be done in any order

It addresses everything you’ve mentioned

wrongly, as per Maths textbooks

Multiplication denoted by juxtaposition (also known as implied multiplication)

Nope. Terms/Products is what they are called. "implied multiplication" is a "rule" made up by people who have forgotten the actual rules.

s often given higher precedence than most other operations

Always is, because brackets first. ab=(axb) by definition

1 / 2n is interpreted to mean 1 / (2 · n)

As per the definition that ab=(axb), 1/2n=1/(2xn).

[2][10][14][15]

Did you look at the references, and note that there are no Maths textbooks listed?

the manuscript submission instructions for the Physical Review journals

Which isn't a Maths textbook

the convention observed in physics textbooks

Also not Maths textbooks

mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik

Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer

More complicated cases are more ambiguous

None of them are ambiguous.

the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)]

It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)

or [1 / (2π)] · (a + b).[18]

No, it can't mean that unless it was written (1 / 2π)(a + b), which it wasn't

Sometimes interpretation depends on context

Nope, never

more explicit expressions (a / b) / c or a / (b / c) are unambiguous

a/b/c is already unambiguous - left to right. 🙄

Image of two calculators getting different answers

With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.

6÷2(1+2) is interpreted as 6÷(2×(1+2))

6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)

(6÷2)×(1+2) by a TI-83 Plus calculator (lower)

Yep, Texas Instruments is the only one still doing it wrong

This ambiguity

doesn't exist, as per Maths textbooks

“8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations:

No there isn't - you MUST obey The Distributive Law, a(b+c)=(ab+ac)

Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”

And he was wrong about that. 🙄

calls such contrived examples

Which notably can be found in Maths textbooks

the creator of the universe tells this guy he’s being a hypocritical crank

The creator of the universe made the laws of nature, which gave rise to the rules of Maths, which can be found in Maths textbooks 😂

You’re very rude

What do you expect to happen when you call a Maths teacher wrong about Maths?

Ill informed

Maths teachers are ill informed about Maths?? 😂

Elementary means fundamental or basic

Which therefore contradicts your argument about it being part of Arithmetic, which is taught in elementary school, Algebra isn't

I’m talking programming languages

Written by people who forget the order of operations rules, hence MathGPT is the only e-calc which gives correct answers.

We are not the same

Yep, as well as being a programmer I'm also a Maths teacher

Most languages throw a syntax error if the multiplication symbol is missing

See first point

You are the brickest wall on lemmy

Says person who hasn't looked this up in a Maths textbook 😂

Either out of undiagnosed neurodivergence or some aggravating character gimmick

Neither, I'm a Maths teacher

you pretend there is one true way to do a thing

There's no pretending involved, it's in Maths textbooks

The commutative property means addition can happen in any order

Yep, and??

But multiplication and distribution are totally different

Nope! They can also be done in any order

you will never ever shut the fuck up about splitting that hair

Got no idea who you think you're talking to, but I never said Multiplication and Division are different

It’s dogma

No, it's the rules of Maths as found in Maths textbooks 😂

You’ve internalized one set of rigid instructions

ALL Mathematicians have, if you're going to put it like that.

declared them the rules of all mathematics

As found in Maths textbooks

to the point you insist Reverse Polish Notation has parentheses

It adds them in the background, so that you don't have to - if it didn't it would return wrong answers - you not having to type them in doesn't mean they aren't getting added

It literally cannot

...give correct answers without putting each paired operation into brackets

Yet it’s an equally valid way to write and do math

and obeys the EXACT SAME RULES 🙄

It gets the same results

because it obeys the same rules 🙄

despite distribution being impossible

Not impossible at all. Someone even wrote it in one of the other comments! 😂

Last time I tried wedging this uneniable fact through any gap in your mortar

you found there were no gaps 😂

you smugly declared you’d found a way

And as these very comments show, I'm not the only one to have done so! 😂

then explained multiplication, not distribution

No, Distribution.

Zero self-awareness

Well, you have zero awareness of what's in Maths textbooks anyway 😂

To this day, you are trying to be smug about a time you proudly contradicted yourself

I have never contradicted myself. You calling Distribution "Multiplication" doesn't make it Multiplication.

I feel sorry for students who can’t just tell you

My students do very well in their exams. How about you? 😂

Go away, patience vampire

Still can't admit you were wrong then 🙄

Adults who have forgotten the rules who I work with and read/write code where it’s important

And as a consequence of that, MathGPT is the only e-calc which gives correct answers to order of operations! 😂

This is like some pure maths vs real life engineering cliché

It's a Correct Maths vs. Programmers who have forgotten the rules cliche

You’re either being deliberately obtuse or you’re painfully naive

Neither, I'm a Maths teacher

Those aren’t ‘rules of maths’,

Yes they are 😂

because math would work with other orders of operations as well.

There aren't any "other" orders of operations.

They are conventions

Nope, rules of Maths

Other cultures could have different conventions and it would work as well

They do have other conventions, they do not have other rules. The rules of Maths are universal.

I don’t think you’re right

You don't think Maths textbooks are right??

The wiki page

is full of disinformation. Note that they literally never cite any Maths textbooks

as an example of “elementary arithmetic.”

And whichever Joe Blow My Next Door Neighbour wrote that is wrong

as an example in “elementary algebra.”

Algebra isn't taught until high school

That implies that yes, this is arithmetic,

No, anything with a(b+c) is Algebra, taught in Year 7

the introduction of variables is what makes it algebra

and the rules of Algebra, which includes a(b+c)=(ab+ac). There is no such rule in Arithmetic.

It doesn’t matter what course finally teaches it to you

It does if you're going to argue over whether it's Arithmetic or Algebra.

not by definition part of that domain

The Distributive Law is 100% part of Algebra. It's one of the very first things taught (right after pronumerals and substitution).

It’s been ages since I took it

I teach it. We teach it to Year 7, at the start of Algebra

More people evaluate 2+3x4 incorrectly than 2+(3x4)

The people who have forgotten the rules of Maths, and the mnemonics even! 😂

So, no, your answer does not hold up to my observed reality

So try observing a real Maths textbook then. Students have no trouble at all with this, only adults who've forgotten the rules.

I’m not humoring this again

STILL can't admit you're wrong then 😂 I guess you never bothered looking in any Maths textbooks since last time then (or you did and don't want to admit you found out you were wrong)