6÷2(1+2)

zeta.one/viral-math/

I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.

It’s about a 30min read so thank you in advance if you really take the time to read it, but I think it’s worth it if you joined such discussions in the past, but I’m probably biased because I wrote it :)

panicnow,

This is a very nice piece that had so much information I did not know. Toward the top of the article I was wishing for footnotes, references or something that would indicate it was not just your opinion, but as I got further into the piece you provided so many great references. I thought the calculator manuals were particularly accessible and convincing. Thanks for a great read!

dgmib,

You state that the ambiguity comes from the implicit multiplication and not the use of the obelus.

I.e. That 6 ÷ 2 x 3 is not ambiguous

What is your source for your statement that there is an accepted convention for the priority of the iinline obelus or solidus symbol?

As far as I’m aware, every style guide states that a fraction bar (preferably) or parentheses should be used to resolve the ambiguity when there are additional operators to the right of a solidus, and that an obelus should never be used.

Which therefore would make it the division expressed with an obelus that creates the ambiguity, and not the implicit multiplication.

(Rest of the post is great)

wischi, (edited )

In this case it’s actually the absence of sources. I couldn’t find a single credible source that states that ÷ has somehow a different operator priority than / or that :

The only things there are a lot of are social media comments claiming that without any source.

My guess is that this comes from a misunderstanding that the obelus sign is forbidden in a lot of standards. But that’s because it can be confused with other symbols and operations and not because the order of operations is somehow unclear.

dgmib,

What is your source for the priority of the / operator?

i.e. why do you say 6 / 2 * 3 is unambiguous?

Every source I’ve seen states that multiplication and division are equal priority operations. And one should clarify, either with a fraction bar (preferably) or parentheses if the order would make a difference.

wischi, (edited )

Same priority operations are solved from left to right. There is not a single credible calculator that would evaluate “6 / 2 * 3” to anything else but 9.

But I challenge you to show me a calculator that says otherwise. In the blog are about 2 or 3 dozend calculators referenced by name all of them say the same thing. Instead of a calculator you can also name a single expert in the field who would say that 6 / 2 * 3 is anything but 9.

dgmib,

Will you accept wolfram alpha as credible source?

mathworld.wolfram.com/Solidus.html

Special care is needed when interpreting the meaning of a solidus in in-line math because of the notational ambiguity in expressions such as a/bc. Whereas in many textbooks, “a/bc” is intended to denote a/(bc), taken literally or evaluated in a symbolic mathematics languages such as the Wolfram Language, it means (a/b)×c. For clarity, parentheses should therefore always be used when delineating compound denominators.

wischi,

Did you read the blog post? I also quoted the exact same thing.

Aussiemandeus, (edited )
@Aussiemandeus@aussie.zone avatar

I guess if you wrote it out with a different annotation it would be

‎ ‎ 6

-‐--------‐--------------

2(1+2)

=

6

-‐--------‐--------------

2×3

=

6

–‐--------‐--------------

6

=1

I hate the stupid things though

velox_vulnus,

Markdown fucked your comment. Use escape symbols.

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

Escape symbols?

onion, (edited )

Lemmy interprets some symbols as formatting commands, for example putting a # at the start of a line turns it into a header:

header

You can tell it to not do that by putting a backslash before the symbol:

# not a header

The backslash is called the escape symbol.

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

Cheers mate

velox_vulnus, (edited )

Never mind, here’s another better way to do this:

^6^⁄2(1+2) ⇒ ^6^⁄2*3 ⇒ ^6^⁄6 ⇒ 1

Works on the web page, but looks weird on some mobile app. Markdown is a fucking mess. Some implementation has MathJax support, some have special syntaxes.

Rustmilian, (edited )
@Rustmilian@lemmy.world avatar

Lemmy* markdown is a fuckin mess. It’s way better elsewhere. & <>

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

Yeah connect for lemmy didn’t sort the out very well.

Brak,
@Brak@hexbear.net avatar

oooh this looks very pretty on hexbear, thanks friend!

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

I guess if you wrote it out with a different annotation it would be

‎ 6

–‐--------‐-------------- 2(1+2)

= 6 –‐--------‐-------------- 2×3

= 6 –‐--------‐-------------- 6

=1

I hate the stupid things though

Abnorc,

Don’t forget math with fruits! imgur.com/JOuRhQ3

wischi, (edited )

Just saw the image you posted and it’s awesome :-) I’m part of the group that can’t solve it, because I don’t know the 🌭 function from the top of my head. I also found the choice of symbols interesting that 🌭 is analytical continuation of 🍔 and not the other way round 🤣

CrushKillDestroySwag,

Very cool article on an aspect of math that I’ve never thought too deeply about before 👍

Portosian,

Honestly, I do disagree that the question is ambiguous. The lack of parenthetical separation is itself a choice that informs order of operations. If the answer was meant to be 9, then the 6/2 would be isolated in parenthesis.

chuckleslord,

It’s covered in the blog, but this is likely due to a bias towards Strong Juxtaposition rules for parentheses rather than Weak. It’s common for those who learned math into advanced algebra/ beginning Calc and beyond, since that’s the usual method for higher math education. But it isn’t “correct”, it’s one of two standard ways of doing it. The ambiguity in the question is intentional and pervasive.

Portosian,

My argument is specifically that using no separation shows intent for which way to interpret and should not default to weak juxtaposition.

Choosing not to use (6/2)(1+2) implies to me to use the only other interpretation.

There’s also the difference between 6/2(1+2) and 6/2*(1+2). I think the post has a point for the latter, but not the former.

chuckleslord,

I don’t know what you want, man. The blog’s goal is to describe the problem and why it comes about and your response is “Following my logic, there is no confusion!” when there clearly is confusion in the wider world here. The blog does a good job of narrowing down why there’s confusion, you’re response doesn’t add anything or refute anything. It’s just… you bragging? I’m not certain what your point is.

Portosian,

None of this has a point. We’re talking over a shitpost rant about common use of math symbols. Even the conclusion boils down to it being a context dependent matter of preference. I’m just disagreeing that the original question as posed should be interpreted with weak juxtaposition.

atomicorange, (edited )

I originally had the same reasoning but came to the opposite conclusion. Multiplication and division have the same precedence, so I read the operations from left to right unless noted otherwise with parentheses. Thus:

6/2=3

3(1+2)=9

For me to read the whole of 2(1+2) as the denominator in a fraction I would expect it to be isolated in parentheses: 6/(2(1+2)).

Reading the blog post, I understand the ambiguity now, but i’m still fascinated that we had the same criticism (no parentheses implies intent) but had opposite conclusions.

wischi,

Did you read the blog post?

Kowowow,

Nope it’s bedmas since everything is brackets

wischi,

Sorry but I don’t follow. Did you read the blog post?

Kowowow,

Those hoity toity with their parentheses don’t know what it is to struggle

ExLisper,

The fuck? I’m getting 15.

wischi,

If you are not kidding, can you show your steps I can try to help you, but I can’t currently think of a way how you’d end up with 15.

agni,

.

wischi,

?

Iapar,

!

Peter_Arbeitslos,
@Peter_Arbeitslos@feddit.de avatar

,

Opitech,

MinekPo1,
@MinekPo1@lemmygrad.ml avatar

I’ve seen a calculator interpret 1 ÷ 2π as ½π which was kinda funny

wischi,

All calculators that are listed in the article as following weak juxtaposition would interpreted it that way.

Lemmygradwontallowme, (edited )
@Lemmygradwontallowme@hexbear.net avatar

The real question here is BODMAS or PEMDAS?

hashbrowns4life, (edited )

Up here in the canada, we did BEDMAS

Brackets, Exponents, Division/Multiplication, Addition/Subtraction

Lemmygradwontallowme,
@Lemmygradwontallowme@hexbear.net avatar

Exponents, Oxponents, I honestly could give less of a shit until now…

keepcarrot,

Also PIMDAS (we had this conversation in my class this semester as we had a very wide range of ages and regions present in the class) (I is for indices) (I don’t remember what the Colombian students said, for some reason we had a group of 3 Colombians in our class of 12 nowhere near Colombia)

That said, the question is ambiguously written. Maybe the popularity of this will result in calculators being more consistent with how they interpret implicit multiplication signs.

(my preference is to show two lines, one with the numerator and one with the divisor)

Lemmygradwontallowme,
@Lemmygradwontallowme@hexbear.net avatar

PIMDAS? Isn’t that the same as PEMDAS?

keepcarrot,

So’s BOMDAS etc.? Just different words for things

Lemmygradwontallowme,
@Lemmygradwontallowme@hexbear.net avatar

Mutiplication or Division first then? Thus, BEDMAS or PEMDAS?

TankieTanuki,

POOTIS or PINGAS?

comrade_pibb,
@comrade_pibb@hexbear.net avatar

Hey this is interesting, thanks for sharing!

Alcatorda,

Hi! Nice blog post. Since you asked for feedback I’ll point out the one thing I didn’t really understand. You explain the difference between the calculators by showing excerpts from the manuals and you highlight that in the first manual, implicit multiplication is prioritised. But the text you underlined only refers to implicit multiplication involving special expressions(?) like pi, e, sqrt or log, and nothing about “regular” implicit multiplication like 2(1+3). So while your photos of the calculator results are great proof that the two models use a different order of operations, to me the manuals were a bit confusing since they did not actually seem to prove your point for the example math problems you are discussing. Or maybe I missed something?

wischi,

You are right the manual isn’t very clear here. My guess is that parentheses are also considered Type B functions. I actually chose those calculators because I have them here and can test things and because they split the implicit multiplication priority. Most other calculators just state “implicit multiplication” and that’s it.

My guess is that the list of Type B functions is not complete but implicit multiplication with parentheses should be considered important enough for it to be documented.

Pulptastic,

Negative reviews for the calculator that does OOO wrong.

wren,
@wren@sopuli.xyz avatar

Great read! Easy for everyone to understand, but also thorough. I loved the breakdown into the calculators functionality

wischi,

Thank you for taking the time reading it.

ConfusedPossum,

Who gives a shit about order of operations. In a real world scenario you'll know what to do

MrVilliam,

This is why you’re a confused possum.

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