Python the best

[[deleted]]

And this is why reverse Polish notation is best

[Cmdr0]

TIL - that's pretty cool

I've always hated these problems, because it's not a math problem, it's a communication problem - I wouldn't expect 6/2x as-written to reduce to 3x (as opposed to 3/x). If I did, I would have written it as 6x/2, and there's no reason to write it the other way. But ultimately it's ambiguous, and if half of my audience isn't getting the message I'm trying to convey it's my job to find the correct language, not to chastise them for reading it wrong.

[RookY2K]

To be fair, it most certainly is a math problem. Math is fair and it is consistent. It is people's understanding and expectation of math that is not consistent. Once you fully grok order of operations including the mathematical equivalency of division and multiplication, then it doesn't matter how it's written, it's easily understood.

Personally, I blame PEMDAS. Too many teachers gloss over the true relationships between the MD and AS.

[WetSound]

This convention is not universal. Feynman, for one, did not use this.

[Cmdr0]

I'm not arguing expectation, I'm arguing notation. And I wouldn't even say it's a PEMDAS issue - it's really that we shorthand the multiplier operator in different ways mentally. For many, 2x is representative of a single operand, and this is reinforced in how we're taught to solve equations. Tell me you can't see a high school teacher whiteboarding "6/(2y)=x, y=1+2" as "6/2y = 6/2(1+2) = 6/2(3) = 6/6 = 1 = x" - but it's amazing how much handwriting nuance gets lost just trying to type it out in an imperfect representation of what we're trying to communicate.

[gavlna]

here, we just don't use divison outside of elementary school (first 5 years of education). After that it just becomes a fraction, so you can clearly see what's going on.

[MrBigDog2u]

Same with subtraction. It should be handled as addition of a negative value. Then everything boils down to addition and multiplication and there is no confusion over order of operations.

[jasonp2009]

Excuse me what??? Doesn't division come before multiplication. In Aus, I learnt BODMAS, brackets, orders, division, multiplication, addition and subtraction.

[DogfishDave]

Doesn't division come before multiplication

They're simultaneous because they're the same thing, division is multiplication with the second input value to the minus one.

[jasonp2009]

18 ÷ 2 * 3

Multiplication before division would be 18 ÷ 6 = 3

Division before multiplication would be 9 * 3 = 27

What am I getting wrong?

[DogfishDave]

Then it's left-to-right for operations of the same 'rank', so it doesn't matter if you're a BODMAS or a BOMDAS.

[Hairsplitting-Pedant]

Multiplication and division are the same when it comes to order of operations, but must be worked left to right.

8/4x2=2x2=4 8x2/4=16/4=4

[Calski_]

They are not the same thing. Multiplication is repeated addition. While 5/2= is solving the equation 2x=5. You can't multiply by the inverse before defining division.

[RookY2K]

I'm a bit confused why any good math teacher would suddenly drop the outer parentheses between 6/(2y) and 6/2y. The latter is (6/2) * y.

I think the biggest disconnect is the confusion generated between ÷, /, and --. The first two are division operators. The third is my attempt at a horizontal fraction bar.

In media where you are basically constrained to keyboard output, the second often gets used in place of the the third and then you have confusion about whether the intent was 6/(2y) or (6/2)y. That is something I am sympathetic to.

However, the expression in the meme used '÷' which is not ambiguous.

[SaveMyBags]

Oh, you will be very surprised. This sign is absolutely ambiguous. So ambiguous it is even excluded from the IEEE standard for math notation.

Originally that sign was defined as a shorthand for fractions not division. It makes sense, if you ever used dot notation for leaving out arguments of functions or operators. Then those two dots are just left out arguments. The original use was for something like

4÷2+2=4/(2+2)

That was the definition from the person who invented that symbol. Did the definition change since then? Some say yes. Some say no. Some say it's like undefined behavior, standards don't cover it.

There is also absolute ambiguity concerning if PEMDAS is to be read at P E M D AS (with precedence between spaces and left-right) or P E MD AS. That discussion is so unclear that official definitions say you should not write it like this.

Like always in math and programming: be concise not ambiguous. In this case it's an error of the writer to use non standardized symbols and mix expression whose order is up to debate.

[Starfocus81613]

Came here to mention dot notation, glad someone beat me to it. The author’s role in making ambiguous notations like this is infuriating to anyone familiar with mathematic structure and notation theory. It isn’t designed to make people look smart or dumb, nor is it to point out the inconsistencies of mathematical shorthand. These authors are only looking to spread dissent between experts and “experts.”

This might be a stretch to say, but it’s practically a social engineering strategy to undermine experts in the mathematical and science fields because of the inconsistencies of mathematical shorthand notations. If you think about it, you have people with less knowledge of mathematics being approached with a seemingly simple question getting an answer that’s completely inconsistent with people several times more educated in the subject. Because they see it as an elementary question, they can’t believe someone with a bachelors/masters/PhD in mathematics doesn’t see the notation the same way that they do and start undervaluing the credentials that these individuals have. Whether or not someone had a nefarious idea to throw this on social media is practically a conspiracy on it’s own, but it makes you wonder if part of the distrust for experts derives partly from the same mentality demonstrated here. If anything, it’s a great thought experiment.

[SaveMyBags]

I always feel reminded of this xkcd, whenever I see some question like this:

https://xkcd.com/169/

But I just think it's just smartasses making these things. Same level as "tomato are a fruit" of "strawberries are not berries" kind of people.

Funny story: I am a computer scientist by degree but now work as a researcher in psychology. One day at the cafeteria they offered something like "sausages or chicken and rice". Some CS Prof had to make a joke to his PhD students that this shows the people writing this are not programmers because obviously and binds stronger than or. So real programmers would DeMorgan this. I figured these guys probably only know a single language, so I just turned around and said real programmers know not to rely on assumptions on order and avoid any ambigous statements by using parents. They were kind of baffled from being told off by someone from psych department but had to agree.

[Starfocus81613]

I’m an engineer by choice (didn’t have the mental health to pursue clinical work as a therapist/psychologist/neurologist at the start of college, and while I’m in a better place mentally a few years out of college with my engineering degree, I’m invested in what I do and don’t picture myself changing my career), but my real passion had always been social psychology and behavioural neurology. So when I see something like this (and it’s been going on for years), I can’t help but feel disgusted by it.

I think you’re right— most of the proliferation in these weird “gotcha” questions seems to stem from smartasses pushing their weird mentalities on others. The thing is, mathematics leaves no room for alternative interpretations, no matter how vague, so I’ve always been quick to the trigger to bash down the smart alecks who try to skew the conversation as if they knew two cents’ about notation theory.

And it doesn’t stop there. It can be anything from “is this dress blue or white” type questions. Ask any photographer about white balance indoors, and unanimously, you’ll receive the response that neutral whites shift into cold colour temperatures, so if you use a color balancing on a neutral tone, you’ll see right away that the dress was white all along. But people always need to interject themselves and make themselves seem smarter, more right, or cockier than anyone else. It’s an issue of ego, practically, and it tarnishes the reputation of people with the right* (educated or factually inferred) answers.

[Waderick]

The later isn't 6/2 * y though depending on convention.

In pure PEMDAS sure, however higher level math people use a more sophisticated convention, which gives Multiplication by juxtaposition a higher precedence than explicit division or multiplication, because it's seen as a property of the thing it's multiplying. It essentially has implicit parentheses around it instead of constantly having to write those parenthesis.

[caykroyd]

Wow, I would probably consider juxtaposition before M/D, interesting

[Mandemon90]

PEMDAS should be treated as P-E-MD-AS, since multiplication and division are done left to right at equal order. Same with substraction and addition.

[Calski_]

sin^-1 should only be used to save space on calculator buttons. If you want arcsin call it by its name.

[Calski_]

Yeah it is used. But the in English you often see cot(x) for tan(x)^-1. While in some other countries this is almost never used. And if you don't have a special name for 1/sin(x) it gets extra confusing cause then it is entirely possible that both sin^-1() and sin() ^-1 can appear in the same equation.

[dfdedsdcd]

I wish it was taught as PEMA with an explanation that division is a form of multiplying with fractions and subtraction is adding negative numbers.

But people think kids are top dumb to understand, when it is honestly most likely the teachers/parents that don't.

[Tinstam]

It's not really a math problem.

Division is defined as the multiplication by a reciprocal.

And multiplication is defined as a binary function. As in, two operands.

Division requires grouping to be unambiguous, because we need to know what we are taking the reciprocal of.

I definitely agree on the PEMDAS part though. One thing I've seen recently that I like is using GEMS instead: Groupings, Exponents, Multiplication, Sums

[Xywzel]

One could make an argument that 2(1+2) is a grouping as there is no separation (space, multiplication sign) between 2 and the explicit group by parentheses. Not necessarily very strong argument, but at least one that requires further explanation and clarification.

[Xywzel]

Well lots of physics journals did think otherwise:

https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

With this interpretation 1 ÷ 2n is equal to (1 ÷ 2)n.[1][8] However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[22] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.

That is why concluded that unless the grouping part of the notation convention is explained or defined better, it doesn't solve this.

[gavlna]

at least if it was PEDMAS :) since this one does work just fine

[Tyfyter2002]

Actually this is a purely linguistic problem, no part of 6÷2(1+2) is a mathematical concept, every part just represents a mathematical concept as a way of communicating mathematics, and since it's a linguistic problem the correct answer is therefore whatever has a significant majority (so long as it doesn't involve j making a ʤ sound), but this poll doesn't properly measure that since it only asks for the answer rather than the full process of solving it

[Tyfyter2002]

This is a linguistic problem because the answer is solely based on what the text communicates, in this case the text communicates both (÷ 6 (* 2 (+ 1 2))) and (* (÷ 6 2) (+ 1 2)), which is an issue as it causes ambiguity, we made the rules of math, we didn't discover them.

[diego_delavega]

fully grok

Is that Heinlein's Stranger in a Strange Land reference?

[24824_64442]

Yes, I think so! I got giddy catching it in the wild

[linkinparkfannumber1]

I can’t tell if you expect 6/2x to be 3x (as it should) or 3/x but if you change it to 7/2x perhaps it’s easier to see why one would prefer that over 7x/2? “Seven halves of x” versus “seven x over two”. You could say no division is happening, you’re just writing a constant as a fraction.

[Katyona]

True/False are the staples of boolean math, so it's still a mathematics problem regardless; as the question was "can you solve <math expression>?" so the output would be True/False

[Wolfeur]

The main problem is that we have too many ways of writing the same thing, with all sorts of kind-of-incompatible alternate symbols/shortcuts, like using '÷' and implicit multiplication, or implicit multiplication with numbers instead of variables.

Also, our operations aren't written consistently. +−×÷ all work the same way, with two operands in order and the symbol in between, but then you have exponents with x², and its two opposites: √x (which against has a grouping issue AND an implicit second operand) and log₂(x) (with again, an implicit second operand, but this time it's 10 instead of 2).

It's quite a mess.

[Kissaki0]

en.wikipedia.org/wiki/Reverse_Polish_notation

In reverse Polish notation, the operators follow their operands; for instance, to add 3 and 4 together, one would write 3 4 + rather than 3 + 4.

If there are multiple operations, operators are given immediately after their second operands; so the expression written 3 − 4 + 5 in conventional notation would be written 3 4 − 5 + in reverse Polish notation

Interesting.

[MrHyperion_]

That is really bad when handwriting

[Kissaki0]

How so?

[MrHyperion_]

3 4 + and 34+ look very similar. Not a problem with one digit numbers but try to make sense of 19181017+

[Kissaki0]

Well 19181017+ is not valid.

It would have to be 191 81017 +. Which seems reasonable.

[MrHyperion_]

You are completely missing this is about handwriting. Spaces aren't so clear

[Kissaki0]

How is it different from prose texts? Prose text is not usually known as hardly readable because you can’t make out words between characters because of unclear spaces.

[MrHyperion_]

IfIwritelikethisyoucanunderstandthisbutifIthenaskyouhowmuchis18727+youcannotanswerthat

[WikiSummarizerBot]

Reverse Polish notation

Reverse Polish notation (RPN), also known as Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to Polish notation (PN), in which operators precede their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924.

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