💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

It’s what is actually taught in high school, so there are those who remember and those who don’t.

You are correct with your definition - Terms are separated by operators and joined by grouping symbols - and it’s consequently not ambiguous at all (using so-called “weak juxtaposition” breaks that rule).

enforce writing math without ambiguity

It already is written without ambiguity.

were taught in third grade

This is actually taught in Year 7 - the people who only remember the 3rd Grade version of the rules are the ones getting it wrong.

There isn’t ambiguity to begin with - just people who have forgotten the rules of Maths.

I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts

And I wrote a bunch of fact checks pointing out there is consensus amongst the actual experts - high school Maths teachers and textbook authors, the 2 groups who you completely ignored in your blog post.

FACT CHECK 1/5

If you are sure the answer is one… you are wrong

No, you are. You’ve ignored multiple rules of Maths, as we’ll see…

it’s (intentionally!) written in an ambiguous way

Except it’s not ambiguous at all

There are quite a few people who are certain(!) that their result is the only correct answer

…and an entire subset of those people are high school Maths teachers!

What kind of evidence/information would it take to convince you, that you are wrong

A change to the rules of Maths that’s not in any textbooks yet, and somehow no teachers have been told about it yet either

If there is nothing that would change your mind, then I’m sorry I can’t do anything for you.

I can do something for you though - fact-check your blog

things that contradict your current beliefs.

There’s no “belief” when it comes to rules of Maths - they are facts (some by definition, some by proof)

How can math be ambiguous?

#MathsIsNeverAmbiguous

operator priority with “implied multiplication by juxtaposition”

There’s no such thing as “implicit multiplication”. You won’t find that term used anywhere in any Maths textbook. People who use that term are usually referring to Terms, The Distributive Law, or most commonly both! #DontForgetDistribution

This is a valid notation for a multiplication

Nope. It’s a valid notation for a factorised Term. e.g. 2a+2b=2(a+b). And the reverse process to factorising is The Distributive Law. i.e. 2(a+b)=(2a+2b).

but the order of operations it’s not well defined with respect to regular explicit multiplication

The only type of multiplication there is is explicit. Neither Terms nor The Distributive Law is classed as “multiplication”

There is no single clear norm or convention

There is a single, standard, order of operations rules

Also, see my thread about people who say there is no evidence/proof/convention - it almost always ends up there actually is, but they didn’t look (or didn’t want you to look)

The reason why so many people disagree is that

…they have forgotten about Terms and/or The Distributive Law, and are trying to treat a Term as though it’s a “multiplication”, and it’s not. More soon

conflicting conventions about the order of operations for implied multiplication

Let me paraphrase - people disagree about made-up rule

Weak juxtaposition

There’s no such thing - there’s either juxtaposition or not, and if there is it’s either Terms or The Distributive Law

construct “viral math problems” by writing a single-line expression (without a fraction) with a division first and a

…factorised term after that

Note how none of them use a regular multiplication sign, but implicit multiplication to trigger the ambiguity.

There’s no ambiguity…

multiplication sign - multiplication

brackets with no multiplication sign (i.e. a coefficient) - The Distributive Law

no multiplication sign and no brackets - Terms (also called products by some. e.g. Lennes)

If it’s a school test, ask you teacher

Why didn’t you ask a teacher before writing your blog? Maths tests are only ever ambiguous if there’s been a typo. If there’s no typo’s then there’s a right answer and wrong answers. If you think the question is ambiguous then you’ve not studied enough

maybe they can write it as a fraction to make it clear what they meant

This question already is clear. It’s division, NOT a fraction. They are NOT the same thing! Terms are separated by operators and joined by grouping symbols. 1÷2 is 2 terms, ½ is 1 term

BTW here is what happened when someone asked a German Maths teacher

you should probably stick to the weak juxtaposition convention

You should literally NEVER use “weak juxtaposition” - it contravenes the rules of Maths (Terms and The Distributive Law)

strong juxtaposition is pretty common in academic circles

…and high school, where it’s first taught

(6/2)(1+2)=9

If that was what was meant then that’s what would’ve been written - the 6 and 2 have been joined together to make a single term, and elevated to the precedence of Brackets rather than Division

written in an ambiguous way without telling you what they meant or which convention to follow

You should know, without being told, to follow the rules of Maths when solving it. Voila! No ambiguity

to stir up drama

It stirs up drama because many adults have forgotten the rules of Maths (you’ll find students get this right, because they still remember)

Calculators are actually one of the reasons why this problem even exists in the first place

No, you just put the cart before the horse - the problem existing in the first place (programmers not brushing up on their Maths first) is why some calculators do it wrong

“line-based” text, it led to the development of various in-line notations

Yes, we use / to mean divide with computers (since there is no ÷ on the keyboard), which you therefore need to put into brackets if it’s a fraction (since there’s no fraction bar on the keyboard either)

With most in-line notations there are some situations with conflicting conventions

Nope. See previous comment.

different manufacturers use different conventions

Because programmers didn’t check their Maths first, some calculators give wrong answers

More often than not even the same manufacturer uses different conventions

According to this video mostly not these days (based on her comments, there’s only Texas Instruments which isn’t obeying both Terms and The Distributive Law, which she refers to as “PEJMDAS” - she didn’t have a manual for the HP calcs). i.e. some manufacturers who were doing it wrong have switched back to doing it correctly

P.S. she makes the same mistake as you, and suggests showing her video to teachers instead of just asking a teacher in the first place herself (she’s suggesting to add something to teaching which we already do teach. i.e. ab=(axb)).

none of those two calculators is “wrong”

ANY calculator which doesn’t obey all the rules of Maths is wrong!

Bugs are – by definition – unintended behaviour. That is not the case here

So a calculator, which has a specific purpose of solving Maths expressions, giving a wrong answer to a Maths expression isn’t “unintended behaviour”? Do go on

No, it doesn’t. It never talks about Terms, nor The Distributive Law (which isn’t the same thing as the Distributive Property). These are the 2 rules of Maths which make this 100% not ambiguous.

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. 😂

You can’t prove something with incomplete evidence

If something is disproven, it’s disproven - no need for any further evidence.

BTW did you read my thread? If you had you would know what the rules are which are being broken.

the article has evidence that both conventions are in use

I’m fully aware that some people obey the rules of Maths (they’re actual documented rules, not “conventions”), and some people don’t - I don’t need to read the article to find that out.

I have never encountered strong juxtaposition

There’s “strong juxtaposition” in both Terms and The Distributive Law - you’ve never encountered either of those?

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.

Mathematical notation however can be.

Nope. Different regions use different symbols, but within those regions everyone knows what each symbol is, and none of those symbols are in this question anyway.

Because it’s conventions as long as it’s not defined on the same page

The rules can be found in any high school Maths textbook.

No it isn’t dotnet.social/@SmartmanApps/110819283738912144

are reacting from their gut

As was the person who wrote the article. Did you not notice the complete lack of Maths textbooks in it?

You probably missed the part where the article talks about university level math,

This is high school level Maths. It’s not taught at university.

Why would I read something that I know is wrong? #MathsIsNeverAmbiguous

Because as a high school Maths teacher as soon as I saw the assertion that it was ambiguous I knew the article was wrong. From there I scanned to see if there were any Maths textbooks at any point, and there wasn’t. Just another wrong article.