The answer realistically is determined by where you place implicit multiplication (or "multiplication by juxtaposition") in the order of operations.
Some place it above explicit multiplication and division, meaning it gets done before the division giving you an answer of 1
But if you place it as equal to it's explicit counterparts, then you'd sweep left to right giving you an answer of 9
Since those are both valid interpretations of the order of operations dependent on what field you're in, you're always going to end up with disagreements on questions like these...
But in reality nobody would write an equation like this, and even if they did, there would usually be some kind of context (I.e. units) to guide you as to what the answer should be.
Edit: Just skimmed that article, and it looks like I did remember the last explanation I heard about these correctly. Yay me!
Exactly. With the blog post I try to reach people who already heared that some people say it’s ambiguous but either down understand how, or don’t believe it. I’m not sure if that will work out because people who “already know the only correct answer” probably won’t read a 30min blog post.
Unfortunately these types of viral problems are designed the attract people who think they "know it all", so convincing them that their chosen answer isn't as right as they think it is will always be an uphill challenge
yeah, our math profs taught if the 2( is to be separated from that bracket for the implied multiplication then you do that math first, because the 2(1+2) is the same as (1+2)+(1+2) and not related to the first 6.
if it was 6÷2x(2+1) they suggested do division and mult from left to right, but 6÷2(2+1) implied a relationship between the number outside the parenthesis and inside them, and as soon as you broke those () you had to do the multiplication immediately that is connected to them. Like some models of calculatora do. wasn’t till a few yeara ago that I heard people were doing it differently.
I read the whole article. I don’t agree with the notation of the American Physical Society, but who am I to argue that? 😄
I started out thinking I knew how the order of operations worked and ended up with a broader view of the subject. Thank you for opening my mind a bit today. I will be more explicit in my notations from now on.
Thank you so much for taking the time. I’m also not convinced that APS’s notation is a very good choice but I’m neither american nor a physisist 🤣
I’d love to see how the exceptions work that the APS added, like allowing explicit multiplications on line-breaks, if they still would do the multiplication first, but I couldn’t find a single instance where somebody following the APS notation had line-break inside an expression.
That’s the correct answer if you follow one of the conventions. There are actually two conflicting but equally valid conventions. The blog explains the full story but this math problem is really ambiguous.
Ooh now I get you, sry. True. But sadly you now know the truth and you have to be careful with the implicit multiplications on your tax forms from now on ;-)
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.
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.
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.
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.
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.
Forgot the algebra using fruit emoji or whatever the fuck.
Bonus points for the stuff where suddenly one of the symbols has changed and it's "supposedly" 1/2 or 2/3 etc. of a banana now, without that symbol having been defined.
This is not a math problem but a calculator engineering problem. Some solve the sub operations from right to left while other do it from left to right.
It’s not really a calculator engineering problem. If you don’t have time to read the entire blog you should definitely check out the section “But my calculator says…”. It’s actually about order of operations regarding implicit multiplication.
I feel like if a blog post presents 2 options and labels one as the “scientific” one… And it is a deserved Label. Then there is probably a easy case to be made that we should teach children how to understand scientific papers and solve the equation in it themselves.
Honestly I feel like it reads better too but that is just me
I’m not sure if I’d call it the “scientific” one. I’d actually say that the weak juxtaposition is just the simple one schools use because they don’t want to confuse everyone. Scientist actually use both and make sure to prevent ambiguity. IMHO the main takeaway is that there is no consensus and one has to be careful to not write ambiguous expressions.
“If you are a student at university, a scientist, engineer, or mathematician you should really try to ask the original author what they meant because strong juxtaposition is pretty common in academic circles, especially if variables are involved like in $a/bc$ instead of numbers.”
I’m a scientist and I’ve only ever encountered strong juxtaposition in quick scribbles where everyone knows the equation already. Normally we’re very careful to use fraction notation (or parentheses) when there’s any possibility of ambiguity. I read the equation and was shocked that anyone would get an answer other than 9.
My comment was directed to the blog post and the claims contained in it.
The blog post claims it is popular in academy, if that is a deserved label, then I don’t understand how the author of the post lands on “there is no good or bad way, they are all valid”. I am in favor of strong juxtaposition but that is not the case that I am making here. Sorry for the confusion.
No one says “me are going”, but lots of people say “me and X are going”, indicating that for native speakers, coordination of noun phrases functions differently than a single noun phrase.
In a contrasting case, people might think the phrase “I and John are here” sounds wrong, though they’d accept “John and I are here.” If you’re going by the “pure grammar” rule of “remove one subject from the phrase and check the grammar”, you’d have to accept either of those as equally viable, but many people don’t.
Close but not quite: the correct grammar is to always mention yourself last (with second person coming first if present in the sentence and then third person) and, as you say, use I or me depending on which one it would be if the others weren’t in the sentence.
Wrong
“Me and Dave are going spelunking”
“Remember that Dave, you, and I are going spelunking”
“This is a picture of Dave and I spelunking”
Right
“Dave and I are going spelunking”
“Remember that you, Dave, and I are going spelunking”
the correct grammar is to always mention yourself last
That was exactly why I mentioned this case. What exactly separates the grammar of “I (and Dave) am going” vs “Dave (and I) is going”? They’re both “subject plus verb”, indicating that the order of the coordinations is a matter of style, not grammar.
As to the subjective vs objective cases, the reasons I brought that up is that grammar seeks to explain the rules of language as native speakers use it. Therefore, the only “wrong” grammar is constructions that natives wouldn’t use, such as (eg) mimicking a Japanese grammar structure and saying “I the house to go.” Since native speakers often use cases like “Me and Dave are going spelunking”, it’s not wrong, merely a different register of speaking.
Accepting only prestige dialects as “correct” grammar is why people continue to think things like “black people don’t speak right”, despite the fact that African American English has the same consistency of grammar that the prestige dialect does.
I would encourage people to code switch rather than adhere to one style of language over another in every case. Imho, it’s kind of problematic that language itself has become racialized in America to the point where people can actually be criticized or made fun of for speaking in the “wrong” style associated with their perceived ethnic background.
What exactly separates the grammar of “I (and Dave) am going” vs “Dave (and I) is going”?
The same thing that seperates the first one from “going Dave am I and”. Word order matters.
the order of the coordinations is a matter of style, not grammar.
Categorically false
Therefore, the only “wrong” grammar is constructions that natives wouldn’t use
Wrong again. Plenty of native speakers of just about every single language there is have atrocious grammar. Native ≠ correct grammar.
It’s not wrong, merely a different register of speaking
It’s wrong when it comes to grammar. Whether or not gramatically incorrect colloquial speech is acceptable and sometimes even preferable to being gramatically correct (it is in most cases, but in some it can be very grating) is a different matter entirely.
Accepting only prestige dialects as “correct” grammar
Nobody said anything about dialect
people continue to think things like "black people don’t speak right
As I mentioned earlier, colloquial speech can be as good as or better than gramatically correct speech in some cases.
You’re mixing up a whole lot of things that aren’t grammar and just generally being wildly wrong all over the place.
Just because there is no central authority does not mean there is no general consensus. English classes from elementary school to university aren’t accidentally in line with each other by some weird coincidence.
Descriptivism has a place in the evolution of language, but not in a wholesale “everything native speakers might say is grammatically correct if they are understood”.
English classes from elementary school to university aren’t accidentally in line with each other by some weird coincidence.
So who has the authority when experts disagree? Like I said, no one is saying “I house go” but some people think “Give this to whomever comes here first” is correct while others argue for “whoever”. Descriptivism by definition seeks to explain how language functions. Prescriptivism only works within a narrowly defined framework, like APA or MLA for example, but even within those there’s disagreement.
Cassandra uses epoch milliseconds for timestamping snapshots. This means that each node will have a different name for the same snapshot. Trivially solved with truncating the timestamp with * wildcard, but just… why?
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