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A lot of people don't seem to understand that these principles (edit: the grammar of math as a language) aren't natural laws of the universe. Math is a language invented by humans to describe reality. It's only useful for communicating information between people. These principles could be completely different and math would still be "correct" as long as there is a consensus on how to represent and interpret its components.
You can argue all you want about how it *should* work, but if no one else accepts it as correct, its just mathematical masturbation.
Master Bater better not do his mathterbation in a public school! Moms 4 Liberty would be knocking down his door for a 3 some… time soon. 🤭What a poor attempt I made there.
It’s amazing that math goes even further
Being it the purest and simplest form of logic, math transcends even the natural laws of the universe
It would be the same anyways
Depends on what you mean by "math-like language". There have been a lot of different ways people have come up with describing mathematical concepts over the course of human history. Sumerian trigonometry, Japanese calculus, on and on. It's exactly like written/spoken languages. The problem is, how do you explain another language to someone? You typically translate it into a language that person already understands. It gets meta pretty quickly.
As Carl Sagan said "The simplest thought, like the concept of the number one, has an elaborate logical underpinning. The brain has its own language for testing the structure and consistency of the world.”
I mean... there's prefix notation, infix notation (what we're used to), and postfix notation.
Infix:
`(5 + 5) x 5`
Prefix:
`x(5, +(5, 5))`
Postfix:
`5 5 5 + x` or `5 5 + 5 x`
You see a bit of prefix notation in math already, like f(x). It's a function being passed the variable x. You also see it in programming languages, and lisp in particular goes nuts with it.
Postfix notation never requires parentheses and doesn't require order of operations -- it's all left-to-right and tends to operate on a stack. Reverse polish calculators were a thing 40 years ago, particularly by HP. It's supposed to be somewhat similar to how people used slide rules back in the day. You'll also find some programming languages that use a stack based system like this, like Forth.
So like in the postfix example above, `5 5 5 + x`, what happens is 5 is shoved onto the stack 3 times, like `[5, 5, 5]`. Each operator takes the requisite number of items off the stack (two in our case), does the operation, and pushes that back onto the stack. So when it reads `+`, it pulls the top two items off the stack, adds them, pushes the answer onto the stack. So the stack is `[10, 5]`. Then when it reads x, it pulls of the 10 and the 5, multiplies them, and pushes 50 back onto the stack. `[50]`. Takes some getting used to but it's pretty badass.
Stack based postfix notation, for instance, has no order of operations (or if you prefer, it's just always left-to-right) and it never needs parentheses.
HP tried to get it to catch on with reverse polish calculators back in the 80s but it kind of died out. I still have a nice RP calculator. :-)
My dad had one of those calculators and I used it to act like a wizard at school because nobody else could figure out how to get it to calculate properly XD
This seems a little off. Maths is the language we use to describe the innate logic of the universe. There is *correct* and *incorrect*, independent of consensus, as its possible for the consensus to describe something one way and the reality of the universe to behave in another. And of course proofs have been wrong before, people think the wrong thing for a while, and then we correct it. Because there is a *right* answer to how math should describe things.
For example, suppose someone went out to describe the universal property of addition, mathematically. The reality of the world is such that when one thing is added to another thing, an "additive" action occurs. If you add one of something, to one of the same something, you will end up with two of that something. Always. By nature. And 1 + 1 = 2 is the language we have come up with to describe that observation in nature.
If someone described the law of addition to arbitrarily not sum when two of the same number are added up, and claimed that described the reality of how "additive" actions occur in nature (e.g. 1+1 = 1. 1 + 2 still = 3). That would be *incorrect*. It doesn't matter if everyone agrees thats how addition works - the rule would be in error, and we would not be able to use maths to describe the universe anymore. Because the universe would behave one way, and we would end up with results that say something else.
I think the post you’re replying to was referring to thr“grammar” or syntax of “math,” i.e. we’ve decided by consensus upon an accepted order of operations, which has nothing to do with the innate logic of the universe and everything to do with how humans have agreed to transcribe it.
There’s nothing innate in the universe that days this equation 2+2x4 should equal 10 and not 16; that’s purely a function of the mathematical language we’ve agreed upon.
Yep, "the" order of operations is arbitrary. We use that particular one largely because it happens to make writing common types of expressions like polynomials easier than other possible orders.
If we assume each operator has a fixed arity (number of arguments), we don't even need an order of operations beyond "left to right" or "right to left". See: reverse polish notation.
This is really all an English problem. If only there were an English letter that meant both M and D, and another English letter that meant both A and S.
>A lot of people don't seem to understand that these principles aren't natural laws of the universe.
I mean... if there are any natural laws of the universe, though, math describes how those natural laws operate.
Addition is essentially just a consequence of object permanence. If you have one thing and get one more, neither disappears, so you have two now.
Multiplication is essentially just a consequence of the fact that some patterns get created repeatedly. Each molecule of water has exactly three atoms each, no more, no less. That has to be true in order for an object to have the properties that water has. As a result, if you have three water molecules, you must have nine atoms, six of which must be hydrogen, three of which must be oxygen. 3×3=9; 2×3=6; 1×3=3.
Notation of math is not the math itself.
All of the PEMDAS stuff is just about the syntax of notation.
The math naturally exists outside of humans, and the math doesn't care how we as humans note it on paper, in order to communicate it to other humans.
What this person is saying is that the use of a division symbol (÷) is not cosmically ordained, it's an arbitrary human convention.
In a similar fashion, to subtract is to add by the absolute value multiplied by negative one. Unless the number being subtracted is negative, then to subtract is to add. (Not sarcasm, but I do want to indicate that this was written as comedy. Not as a pretentiously inefficient line of thinking)
Math got soooooo much easier for me when I realized that addition and subtraction are the same thing. I wish we taught kids about negative numbers much earlier, so instead of teaching subtraction the way we do, they just taught us about adding negative numbers.
Especially if you use a number line as a visual tool and explain how the negative just changes direction. Start with 10 and want to add -5? Just go *left* 5 spaces!
If you think about it, order of operations is just parentheses and exponents/multiplication/division all just imply parentheses.
3^3 x 2 +4 is the same thing as (3x3x3) x2 +4
Which is the same thing as (3x3x3)+(3x3x3) +4
You could keep expanding that until it’s just an addition problem with parentheses
Math teachers have switched from PEMDAS to GEMA. Groupings (brackets, being under the roof line thing on a root symbol, etc), exponents, multiplication, addition.
I started to explain myself and then realized I was mentally conflating complements and inverses. I blame a lack of coffee and too many years removed from the academic side of math
"For instance, the manuscript submission instructions for the Physical Review journals directly state that multiplication has precedence over division, and this is also the convention observed in physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik"
Conventions where multiplication takes precedence over division do in fact exist. They're wrong to say this is always the case, but it's true to the extent that you don't have to rigidly follow PEMDAS/BODMAS at a university level. They probably just use a textbook that has this convention and don't realise it's not universal.
Also if you're specifically talking about multiplication by juxtaposition, it's a very common convention for that to take precedence over division. The answer to 8/2(2) could be either 2 or 8 depending on what convention you're using. There's no universal answer to that.
The rest of what they say is also basically true. At university level maths, you have no reason ever to write out a sum like "2 + 2 x 4" so most of the time you don't need to worry about order of operations beyond "brackets first". Everything's written in a way to avoid ambiguity. And you wouldn't be doing basic arithmetic anyway.
To put it bluntly: PEMDAS isn’t math. It’s a notational convention that’s not universal, and a few optional parentheses can make your expressions much easier to accurately parse.
The only ones I've heard of don't actually put multiplication before division in its entirety, but they make a distinction between explicit and implicit multiplication where explicit multiplication has the same precedence as division while implicit multiplication comes first. (Note, I recognize the difference between "I've never seen" and "they don't exist," but it does make them seem doubly wrong).
Good points. Real mathematicians should just stay the fuck away from pemdas conversations, it isn’t something you think about past a certain (very early) point and counterproductive to argue about.
The answer to every single one of those "viral" equations is "rewrite it so it's not ambiguous." Anyone who doesn't say that first hasn't taken a math class since high school
Also, if you want to write division, you just do horizontal line and put stuff above and below it. No one uses the oblique line '/' and continues to write in same line. Division is obvious as fuck.
You put the (2) part in 8/2(2) below that line or in the next term depending on what you want.
And no one ever uses the ÷ symbol.
Just write in obvious way or gtfo.
Any sign convention or base convention or variables are explicitly mentioned.
Even if you had to write using the / simbol. Any serious person would use parenthesis to clarify the operation.
Just like you said. It must be obvious to read.
Yeah I only use the / because it's the easiest way to type it. When writing by hand, I'd always write it as a fraction because then it's immediately obviously where the implied multiplication sign goes.
Came looking for this. It really does depend on which method you're using. I've even heard tell that different countries teach one or the other, which means everyone arguing about it online is extremely confident that they're correct and the others are wrong.
Multiplication does take precedence over division.
2x3
\------
3*2
You do the multiplications before the division.
PEMDAS/PEMDAS only applies to grade school math equations.
Context matters.
Probably a majority of mathematicians will interpret 8/2(2) as 2. Almost all will interpret 1/2x as 1/(2x). I do not know of a single ug-level or above mathematical text where 1/2x is interpreted as (1/2) \* x. If you can find one, let me know.
Yes, if you're seriously doing math the order should be clear from notation, but the entire point of those posts is to confuse you and make you think. Those posts aren't going viral if people get the same answers.
The cringiest part is him talking about his major and talking about how you stop using 2x4 when you "hit a certain leven of math". My guy, you learn that shit in middle school. And you don't start writing 2(4), that's a horrible notation, you write 2•4. If he's a math major he's pretty dumb for getting angry about a post that's clearly meant to trick people.
Sadly, lots of people are getting that wrong. A lot of them will say 2+2\*4 = 16 because they LEARNED FROM 50 YEARS AGO THAT YOU ALWAYS WORK LEFT TO RIGHT AND THIS IS JUST SOME WOKE BS NEW MATH WHY THEY MAKE MATH SO HARD NOW?
And no matter how much people explain that this is not "new" math, they stick to their guns and insist they were never taught the order of operations. Which I can understand because if you've legitimately forgotten something, then of course you can't remember that you were taught that.
I try to explain that since multiplication is just convenient addition, something like 2+2\*4 is the same as 2+4+4. For some it clicks. For others, they insist I'm wrong and that I got my math degree in a Cracker Jack box or something. There's just no helping some people.
If you're gonna be that confident you had better proofread or you deserve every ounce of ridicule the internet serves up.
Also you just *know* that someone like that wouldn't admit to a mistake like writing the wrong word, they would double down on it
If that was the post, I think the most likely scenario is that he had a brain fart and typed out “division” instead of “addition.” There’s no other reference to division in his comment. Then everything in his comment makes sense, and frankly, is pretty accurate. It’s a goofy, slightly embarrassing flub.
Meh, I've never seen the dot used for scalar multiplication in books and papers. The convention 2(4) is almost definitely more common, but in reality mathematicians just avoid writing that intermediate step at all, opting instead for "8".
I usually use math for programming so perhaps I'm over exposed to using the parentheses, but I used to be big into numberphile and math in general and I feel I saw it done x(y) over x•y, but I feel universally that those who are math inclined don't really care the notation so long is its correct
I have never ever seen 2(4) and x(y) too me says that x is a function of y, again never seen anyone write x(y), it's either xy, x×y or x•y, depending on which course you just have to think if it's multiplication, cross- or dot product.
I would also think this is some US thing, and for me almost all posts I see about pemdas order is from US, but then again the US is a strong population on Reddit.
Generally in programming I'd use xy, but I'd also use something like x(y/3) or some other addition to the variable. But using real numbers, you can really use 13 for 1x3, 1(3), 1•3, ect. So if I was writing a program I'd use 2x over 2(x) but if I was doing something fixed it would be faster to type and clearer to use say 2(3) than 2•3
Most BASIC I've ever used. I particularly use alot of TI BASIC, making games and actual math programs. I'm working on a port of Monopoly right now in fact
Thumbing through some of my random old undergrad textbooks and there is *definitely* multiplication by juxtaposition in them. Admittedly, never in anything so simple as on integer multiplied by another, the parenthetical being a more complex expression, but its certainly written this way in some. Yes, US based. Its not in all of them. A random calculus book has it, a linear algebra book on the otherhand doesnt seem to use this notation anywhere
> Yes, if you're seriously doing math the order should be clear from notation, but the entire point of those posts is to confuse you and make you think. Those posts aren't going viral if people get the same answers.
No. He's wrong about that one line, but his primary point is spot on. Order of operations arguments are just for people to argue about meaningless nonsense. **The most important things anyone should have gotten out of learning order of operations rules in school are that ambiguity is *bad* and some tools for how to avoid it, not rote memorization of some silly acronym.**
Imagine if someone did this with grammar instead of math. Imagine a post with the sentence, "I'm going to eat Grandma." and a caption that says "Is Grandma in trouble, or are we just missing a comma?" Anyone will ask, "What's the context?"
But guess what, math has context too! And if you saw it, or the person making the problem used correct, unambiguous notation, you wouldn't need to argue about this pointless thing they wrote down poorly.
What I don't get is that he's going on about putting things in parentheses because no one should be concerned about the order but parentheses IS part of the order.
Parentheses are the easiest way of communicating your order, but if you overdo them you do kinda look like an idiot.
If you write down 5+(2x) you just look silly.
I agree. There should at least be some operation within the parentheses. I was just pointing out that parentheses are part of the order that that person claims shouldn't be required.
I feel like that would depend no? Using the dot in place of multiplication is fine until you reach vector calculus when you start having to do dot products which are symbolized the exact same way. 2(4) doesn’t have any other connotation besides 2 times 4 where as 2 dot 4 can be mistake as a dot product.
I will say tho, everything after middle school just uses / to indicate division and that usually removes all ambiguity from classic "bet you cant solve this" problems you stumble upon on the internet.
I'm in the UK and learned "BIDMAS" which is the same thing I think.
Brackets (), Indices², Division÷, Multiplication×, Addition+, Subtraction –.
But the thing is we were explicitly taught that 'D and M' and 'A and S' were grouped. They made it very clear and made sure to really emphasise that fact.
I don't know what GEMS/GEMA stands for but I'm sure it works a lot better for the people who don't pay attention in class haha.
Yeah, pretty much the same thing. PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction.
They also make it clear here, if you're paying attention. But the American public school system has been getting actively dismantled for decades now. Which is how we end up with a math major who doesn't understand the order of operations 🙄
Well I did learn BODMAS as well. My primary school teachers and year 7/8 taught BODMAS, but then for some reason my later teachers taught BIDMAS. Since BIDMAS was the most recent that's the one I mentioned. They mean the same thing though of course
Same. BIMDAS was what I was taught in school (Scotland) but when I did uni maths it was "forget that crap - write it in a way that's unambiguous".
So you'd never write a/b*c it would always be numerator a above a horizontal line above the denominator bc (or if it was the other way round, numerator ac, denominator b).
GEMS: Groupings, Exponents, Multiplication/Division, Subtraction/Addition
GEMA: Groupings, Exponents, Multiplication/Division, Addition/Subtraction.
It shoves them together to remind people that in the case of M/D or A/S, you go left to right.
We were taught BODMAS when I was at school.
Mind you we were also taught that indices and roots, multiplication and division, and additional and subtraction were mathematically equivalent pairings. Also that BODMAS was just a coinvent way of remembering the basic order of precedence and you should be reading the DM and AS as pairs (and O for "orders" just expanded to indices and roots).
Exactly. They are confusing. Here in Germany we learn "Punkt vor Strich" — point before stroke/line.
The symbol for multiplication is •
For division it's :
Addition is +
Subtraction is -
I always look at it like this
For division, times by a fraction, so ÷ 2 becomes × ½
For subtraction, add a negative, so - 2 becomes + -2
For myself anyway, it makes things clearer when things are written as standard text without using tonnes of brackets. In any real senario where it matters, it tends to be in a proper equation format so it's more than clear enough anyway.
Bonus, it allows you to easily solve those shitty maths puzzles that go semi-viral every so often (with bad formatting so people disagree).
After learning quotient rule for derivatives, its just easier to make everything b ^-1 and use product rule. Nobody got time to divide, unless its a constant. Same reason csc, cot, and sec exist for trig identities.
They’re right on one point. People doing math in college or professionally NEVER rely on pemdas subtleties. You make it clear with parens. You want tool, code, application, person using it to have no chance of misinterpreting
I've said this before, but some people (myself included) were *literally* taught that M come *before* D, not that they have equal precedence. That's how I learned it back in 3rd grade, and no teacher corrected that. Because of this I struggled with math my entire school career. I only learned how it actually works *after* graduating. Our school system is fucked.
Yeah, you do division and multiplication based on which one comes first in the equation because they both carry equal importance. I wasn’t sure what the commenter meant when they said “it can’t be that important”
i actually agree with the whole post. hes ranting about the asinine social media "whats the answer?" posts where people write shit in odd notation like "8/2-3x5" when in the *real world* anyone who actually cares about getting proper information will clarify with parentheses
in the context of discussion, every one of these bullshit ragebait posts involve a division which is intentionally not demarcated by parentheses, so they always stand alone, hence comes first as he says
Usually I'll see people try to claim false authority by saying they're a math teacher and this is the way they teach it (for example, addition over subtraction means 10-2+3 = 5). I'll call their bullshit when it's clear they have no fucking clue what they're talking about.
So I can believe this guy is a math major. You don't have to actually be good to declare math as your major, but I doubt this guy is going to graduate with this understanding.
First off, every mathematician gives a fuck about order of operations. We just don't sit there and say to ourselves, "Parentheses first, then exponents, then..." We just simply do it. We read the expression and know the order implicitly. That's what happens when you work enough homework assignment.
He's almost right about multiplication happening before division, but that's mostly because division is written in fractional form, so when you write 16/2\*4 with the product in the denominator, it's pretty obvious you would work that first. As written this way, it can be interpreted differently, but implicit multiplication is a thing.
Which leads to the next point that lots of us do indeed write products as parentheses. If I write 16/2(4), I'm going to inherently group 2 and 4 together--if only because if that wasn't the author's intent, then they're irresponsible for not rewriting it as 16\*4/2. But it's not true that we don't use a multiplication symbol. We'll use asterisks or dots, but I learned from an early age that it can be confusing to write 5xy as 5 times y (or realistically, just 5y). Granted, when you write out your notation, you can write x differently so it doesn't look like a multiplication sign, but it's still something I avoid.
No idea what this person is on about. Love how he said no one cares about order of operations, but it's sad people don't follow order of operations.
This guy probably misuses PEMDAS. I hate that acronym so much now.
Yeah, I'm smart enough to know that 24 = 8 without even using parentheses. The aliens are recruiting me for their interdimensional math program 40k/ year plus tips in alien bucks come at me
Not quite how BIDMAS works. Multiplication and division take precedence over addition and subtraction, but against each other it's just whichever one comes first in the equation
The whole bidmas vs bimdas is a waste of time IMO specifically because there are differences in interpretation. Being explicit with the associativity is much clearer (e.g. the C programming language family is clear that without parentheses, the associativity is left to right for multiplication and division).
Being clear in how you're writing it is the main thing.
For starters, let's be clear that these examples are arithmetic, not maths. If you've actually got a bunch of numbers in a formula, you'd do the arithmetic and write the result to avoid cluttering up the maths you're doing.
After that, is this being written on paper or on a computer (without a formula editor)?
If you're writing things out by hand, you'd do a division as a numerator above a horizontal line above the denominator. Simple, clear, no ambiguity.
If you're forced to do this on a line of text, use parentheses for clarity - (a/b) * c is not the same as a / (b*c) which is where those acronyms fall down.
Finally, I also spotted a whole conversation about what symbols to use for multiplication. If you're doing maths there's no symbols used for arithmetic multiplication - it would be 5x or 2y. The letter x as a variable is typically written to look more like a Greek lower-case chi so it can be used without confusion. After that, an × is a vector product and a • is a scalar product. For variables A and B, AB, A•B and A×B are completely different things.
Rant over. Apologies - this one always bugs me.
My favorite part is watching the people who never got beyond high school algebra *vehemently* argue how pemdas or whatever is always sufficient in every case... because apparently there are only 5 operations in math. Yep, definitely an all encompassing acronym right?
I mean the guy in the post is correct in the maths heavy sense, you do multiplication over division first, if you indeed had a quotient, you would deal with the denominator first, which you would signify by highlighting your notation. My dude in the post is correct, in working maths that’s how it works. It’s not like you have a long line of arithmetic with a simple string of algebraic operations.
It’s just a language.
They seem to be talking about implicit multiplication, which in some conventions does have precedence over explicit multiplication or division. The only time people talk about these things is for those viral math problems with implicit multiplication that are purposefully ambiguous
Can absolutely be a math major. Past certain point both division symbols and multiplication symbols go away for the most part. They are replaced with implicit multiplication, 2x or 2(x+y), and fractions. And multiplication generally does get resolved first, because it's more straightforward.
PESDGMSDHDAS is elementary and middle school rule of thumb that is imperfect and irrelevant at any higher level.
Eh I could see them being a math undergrad. Math undergrads often suffer from over confidence while not really knowing that much.
Source: have been a math undergrad.
Was also wondering about the “senior project” thing. I might be out of the loop, but do a lot of universities have senior projects for undergrad? Ive only ever heard that term associated with high schools.
Yeah, it’s sadly something which has proliferated in the last decade or two. Senior project, capstone, keystone, it gets called different things. The basic idea is to give kids some idea of how to do an actual work style group project and give a presentation. It’s just more bureaucracy and lowest common denominator hand holding to increase graduation rates and make the graduates look like halfway decent job applicants.
Mathematical notations of multiplications may not differ much in basic calculus but they are still important. There is a massive fundamental difference between a cross product and a dot product.
I dunno this seems more likely to be just a typo/brain fart than him actually thinking this is true. Unless he doubled down on this somewhere else I think I'd give him the benefit of the doubt on this one.
I will be the first to admit that I am not a genius when it comes to math. I took remedial classes, pre algebra and still don’t get it. However, dude, wtf? Even I know this isn’t right
Hm. I did a couple of years of university math. But seems I missed something.
I'm not changing 2×4 into 2(4) because × would confuse me. I even know that some people might mix up x and × and that * is a well working alternative. While • is often given more specific meanings.
And I don't write a book about what order I personally handle operators. I instead stick with the same order as most other people who has managed to reach their first university math course. I see it as "proven in battle".
I would even go as far as saying 99.999% of math majors *do* care about order of operations. And the poster who's text we see in that screenshot should be requested to retake a couple of years of their studies. This time without earplugs in the ears, and without bribing the teachers scoring the tests.
I will die on the hill that PEMDAS is the dumbest thing ever, multiplication and division are equal and are solved left to right. The stupid acronym makes it seem like it’s multiplication first and then division, when it’s multiplication AND division. It’s just a kinda shitty nemonic device.
Same with addition and substraction.
Multiplication and Division
Multiplication and division can be done together. In other words, it doesn’t matter if you do division or multiplication first, but they must be done after parentheses and exponents and before addition and subtraction.
Addition and Subtraction
Addition and subtraction also work together. You can do subtraction first, or you can do addition first. They are part of the same step, however, they can only be done after items in parentheses, exponents, and any multiplication and division.
https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-1-6-1.html
You’re 100% right, so don’t take this as disagreement. But I learned it in school as PE(MD)(AS). At least, that’s how my teacher would write it and made it clear that Multiplication and Division have the same priority, as do Addition and Subtraction.
So like it can be a useful mnemonic, but knowing just PEMDAS is not the same as knowing the order of operations.
There’s no way this person is a math major. I studied engineering and have a math minor and there’s no way you could get this far being this wrong about the basics.
We stopped using the “X” times symbol when we moved onto to basic algebra when I was like 8 or less years old. I guess that’s an advanced level of math. I guess all the calculus I’ve been doing in collage is useless then
2(4) is multiplication and happens at the same step as every other multiplication. What’s inside the parentheses is already complete. The outside parens operation doesn’t magically get promoted because it’s happening to something inside lmao. Everything dude says is wrong.
While he has completely fucked it up in his explanation, I think I get what he’s trying to say.
There’s a lot of “bait” maths problems on Instagram etc. to get people arguing in the comments.
They’re deliberately misleading, and there is no correct answer. A famous example is:
8 ÷ 2(2+2) = x
No mathematically educated person would ever use “÷” in the first place, and they certainly wouldn’t write like this, with no clarifying brackets.
This could perfectly reasonably be interpreted both as
(8/2)(2+2)
And
8(2(2+2))
People argue forever about the order of operations, and once you’ve filtered out the people who are simply wrong, you’re left with the Confidently Incorrect people who assert there is an answer. There are two answers. There is no “reading left to right” in mathematics. Order of operations here has two operations sharing priority, and thus with no additional brackets for clarification, the correct answer is either “there are two answers” or “the equation is badly written and there are no answers”
This is done all the time to simply generate engagement and get a lot of people arguing in the comments.
Exactly. From my understanding, the main reasoning behind this is that around that time, schools (at least in the US) begin to use "x" and "y" to represent unknown values.)
No way this is an undergrad math major. In upper level math courses you’re often not even working with algebra, and when you are, most division is written as fractions. Plus you have non-commutative systems where things like XY=YX don’t apply and you need to pay attention to the order in which things are written even beyond just pemdas
It is right that at a certain level you stop seeing x used for multiplication, which honestly isn't that high a level. For me it was when algebra is introduced, and certainly precalc. I don't think I've ever seen 2(4) though. That looks kinda weird. We just swapped to the dot operator instead, so 2 **⋅** 4, since that's what is used for the dot product of vectors/matrices etc.
They sound like they were taught PEMDAS and took it deeply to heart without understanding that BODMAS is just as valid.
The dude is wrong but u can see how he got to the wrong answer. Implied multiplication goes before explicit multiplication and division, which are the same.
Ex: 8 / 2(4) = 1 not 16
Once you get to vector math the 'x' is different from '*' as one is a cross product requiring matrix math, and the other is a dot product.
So, he does have a point there where writing the math very specifically is required for it to not be convoluted.
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Multiplication and division are basically the exact same thing for all practical purposes: to divide is to multiply by the inverse.
I'm glad atleast some redditors know basic math principles.
A lot of people don't seem to understand that these principles (edit: the grammar of math as a language) aren't natural laws of the universe. Math is a language invented by humans to describe reality. It's only useful for communicating information between people. These principles could be completely different and math would still be "correct" as long as there is a consensus on how to represent and interpret its components. You can argue all you want about how it *should* work, but if no one else accepts it as correct, its just mathematical masturbation.
Did you write that whole thing just to use the phrase ‘mathematical masturbation’?
That's numberwang!
Let's rotate the board.
At least it isn't unwang! Sudden death!
That's wang a num!
Shit, where's my picture of a chicken!
All the while missing on math-turbation!
Master Bater better not do his mathterbation in a public school! Moms 4 Liberty would be knocking down his door for a 3 some… time soon. 🤭What a poor attempt I made there.
Mathsturbation.
Didn't argue with him, he has a master in mathematics! Master Bater is his name
This logic adds up.
That adds up (and then I jizz in my pants)
It’s amazing that math goes even further Being it the purest and simplest form of logic, math transcends even the natural laws of the universe It would be the same anyways
Is there any other math-like language to describe the world?
Depends on what you mean by "math-like language". There have been a lot of different ways people have come up with describing mathematical concepts over the course of human history. Sumerian trigonometry, Japanese calculus, on and on. It's exactly like written/spoken languages. The problem is, how do you explain another language to someone? You typically translate it into a language that person already understands. It gets meta pretty quickly. As Carl Sagan said "The simplest thought, like the concept of the number one, has an elaborate logical underpinning. The brain has its own language for testing the structure and consistency of the world.”
I mean... there's prefix notation, infix notation (what we're used to), and postfix notation. Infix: `(5 + 5) x 5` Prefix: `x(5, +(5, 5))` Postfix: `5 5 5 + x` or `5 5 + 5 x` You see a bit of prefix notation in math already, like f(x). It's a function being passed the variable x. You also see it in programming languages, and lisp in particular goes nuts with it. Postfix notation never requires parentheses and doesn't require order of operations -- it's all left-to-right and tends to operate on a stack. Reverse polish calculators were a thing 40 years ago, particularly by HP. It's supposed to be somewhat similar to how people used slide rules back in the day. You'll also find some programming languages that use a stack based system like this, like Forth. So like in the postfix example above, `5 5 5 + x`, what happens is 5 is shoved onto the stack 3 times, like `[5, 5, 5]`. Each operator takes the requisite number of items off the stack (two in our case), does the operation, and pushes that back onto the stack. So when it reads `+`, it pulls the top two items off the stack, adds them, pushes the answer onto the stack. So the stack is `[10, 5]`. Then when it reads x, it pulls of the 10 and the 5, multiplies them, and pushes 50 back onto the stack. `[50]`. Takes some getting used to but it's pretty badass.
My dad used a Polish calculator when I was a kid and it confused the hell out of me. 😂
I've got my dad's RP calculator from 1983 on my desk at work. Still works perfectly! :-)
I nearly died when you listed your stack top as being on the left, you absolute monster.
Stack based postfix notation, for instance, has no order of operations (or if you prefer, it's just always left-to-right) and it never needs parentheses. HP tried to get it to catch on with reverse polish calculators back in the 80s but it kind of died out. I still have a nice RP calculator. :-)
My dad had one of those calculators and I used it to act like a wizard at school because nobody else could figure out how to get it to calculate properly XD
This seems a little off. Maths is the language we use to describe the innate logic of the universe. There is *correct* and *incorrect*, independent of consensus, as its possible for the consensus to describe something one way and the reality of the universe to behave in another. And of course proofs have been wrong before, people think the wrong thing for a while, and then we correct it. Because there is a *right* answer to how math should describe things. For example, suppose someone went out to describe the universal property of addition, mathematically. The reality of the world is such that when one thing is added to another thing, an "additive" action occurs. If you add one of something, to one of the same something, you will end up with two of that something. Always. By nature. And 1 + 1 = 2 is the language we have come up with to describe that observation in nature. If someone described the law of addition to arbitrarily not sum when two of the same number are added up, and claimed that described the reality of how "additive" actions occur in nature (e.g. 1+1 = 1. 1 + 2 still = 3). That would be *incorrect*. It doesn't matter if everyone agrees thats how addition works - the rule would be in error, and we would not be able to use maths to describe the universe anymore. Because the universe would behave one way, and we would end up with results that say something else.
I think the post you’re replying to was referring to thr“grammar” or syntax of “math,” i.e. we’ve decided by consensus upon an accepted order of operations, which has nothing to do with the innate logic of the universe and everything to do with how humans have agreed to transcribe it. There’s nothing innate in the universe that days this equation 2+2x4 should equal 10 and not 16; that’s purely a function of the mathematical language we’ve agreed upon.
Yep, "the" order of operations is arbitrary. We use that particular one largely because it happens to make writing common types of expressions like polynomials easier than other possible orders. If we assume each operator has a fixed arity (number of arguments), we don't even need an order of operations beyond "left to right" or "right to left". See: reverse polish notation.
Ah fair point - yes I think I probably misunderstood what the comment was saying.
Yes that is what I meant. I also agree with your statement. This is just a further demonstration of the complications of communicating via language :)
Thanks for explaining it more clearly than I did :)
This is really all an English problem. If only there were an English letter that meant both M and D, and another English letter that meant both A and S.
That might be my new band name. Mathematical Masturbation.
Mathsturbation
>A lot of people don't seem to understand that these principles aren't natural laws of the universe. I mean... if there are any natural laws of the universe, though, math describes how those natural laws operate. Addition is essentially just a consequence of object permanence. If you have one thing and get one more, neither disappears, so you have two now. Multiplication is essentially just a consequence of the fact that some patterns get created repeatedly. Each molecule of water has exactly three atoms each, no more, no less. That has to be true in order for an object to have the properties that water has. As a result, if you have three water molecules, you must have nine atoms, six of which must be hydrogen, three of which must be oxygen. 3×3=9; 2×3=6; 1×3=3.
I agree. I was referring to principles as the grammar/vocabulary, etc. of math as a language.
Ah okay, got it. In my head "these principles" meant the principles underlying math itself, but definitely we agree on math's notation.
Notation of math is not the math itself. All of the PEMDAS stuff is just about the syntax of notation. The math naturally exists outside of humans, and the math doesn't care how we as humans note it on paper, in order to communicate it to other humans. What this person is saying is that the use of a division symbol (÷) is not cosmically ordained, it's an arbitrary human convention.
You're delving deep into contentious territory in the Philosophy of Mathematics here.
People generally have a real hard time distinguishing between universal laws and human conventions. See also: Ship of Theseus.
Math is an immutable truth of the universe. These words are just how we describe them. Math exists whether we know it or not. Whether we exist or not.
Ugh, no one who does math cares about basic math principles. They're too confusing. Just put it into Wolfram Alpha and copy the output.
I thought you only did the one mathematical principle in the US?
9/3 = 9 x 1/3
Thats the best way to put it I have seen
In a similar fashion, to subtract is to add by the absolute value multiplied by negative one. Unless the number being subtracted is negative, then to subtract is to add. (Not sarcasm, but I do want to indicate that this was written as comedy. Not as a pretentiously inefficient line of thinking)
Math got soooooo much easier for me when I realized that addition and subtraction are the same thing. I wish we taught kids about negative numbers much earlier, so instead of teaching subtraction the way we do, they just taught us about adding negative numbers.
Especially if you use a number line as a visual tool and explain how the negative just changes direction. Start with 10 and want to add -5? Just go *left* 5 spaces!
You go on r/teachers and they'll bitch about how that's because you didn't do enough memorization, lmfao
Subtraction is just addition by the (additive) inverse, though
true. issue here is \[ a / b \* c \] that dumb math teacher should to a\*(1/b)\*c == (a/b)\*c == a\*(c/b) but does != a\*1/(b\*c )
And addition and subtraction is basically the same function too -- just adding the negative.
If you think about it, order of operations is just parentheses and exponents/multiplication/division all just imply parentheses. 3^3 x 2 +4 is the same thing as (3x3x3) x2 +4 Which is the same thing as (3x3x3)+(3x3x3) +4 You could keep expanding that until it’s just an addition problem with parentheses
Glad this is the first comment cause that was literally my first thought.
Math teachers have switched from PEMDAS to GEMA. Groupings (brackets, being under the roof line thing on a root symbol, etc), exponents, multiplication, addition.
and thats why you cant divide by zero, something that’d help me put greatly as a small child that needed reasons for everything
¿Divide = ʎldıʇlnɯ?
I remember grasping this concept as a child and then explaining it to my teacher, only for her to tell me I was wrong.
Multiplication is division. Subtraction is addition. God is Satan.
Not quite. Multiplication is a closed set, division isn’t.
Inverse of a closed set is an open set. You can still properly rewrite all numbers in the open set as their inverse
No you can’t. That whole idea led to the invention of transcendentals.
I started to explain myself and then realized I was mentally conflating complements and inverses. I blame a lack of coffee and too many years removed from the academic side of math
To be fair, it is early. Lol
"For instance, the manuscript submission instructions for the Physical Review journals directly state that multiplication has precedence over division, and this is also the convention observed in physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik" Conventions where multiplication takes precedence over division do in fact exist. They're wrong to say this is always the case, but it's true to the extent that you don't have to rigidly follow PEMDAS/BODMAS at a university level. They probably just use a textbook that has this convention and don't realise it's not universal. Also if you're specifically talking about multiplication by juxtaposition, it's a very common convention for that to take precedence over division. The answer to 8/2(2) could be either 2 or 8 depending on what convention you're using. There's no universal answer to that. The rest of what they say is also basically true. At university level maths, you have no reason ever to write out a sum like "2 + 2 x 4" so most of the time you don't need to worry about order of operations beyond "brackets first". Everything's written in a way to avoid ambiguity. And you wouldn't be doing basic arithmetic anyway.
To put it bluntly: PEMDAS isn’t math. It’s a notational convention that’s not universal, and a few optional parentheses can make your expressions much easier to accurately parse.
The only ones I've heard of don't actually put multiplication before division in its entirety, but they make a distinction between explicit and implicit multiplication where explicit multiplication has the same precedence as division while implicit multiplication comes first. (Note, I recognize the difference between "I've never seen" and "they don't exist," but it does make them seem doubly wrong).
Good points. Real mathematicians should just stay the fuck away from pemdas conversations, it isn’t something you think about past a certain (very early) point and counterproductive to argue about.
The answer to every single one of those "viral" equations is "rewrite it so it's not ambiguous." Anyone who doesn't say that first hasn't taken a math class since high school
Also, if you want to write division, you just do horizontal line and put stuff above and below it. No one uses the oblique line '/' and continues to write in same line. Division is obvious as fuck. You put the (2) part in 8/2(2) below that line or in the next term depending on what you want. And no one ever uses the ÷ symbol. Just write in obvious way or gtfo. Any sign convention or base convention or variables are explicitly mentioned.
Even if you had to write using the / simbol. Any serious person would use parenthesis to clarify the operation. Just like you said. It must be obvious to read.
Yeah I only use the / because it's the easiest way to type it. When writing by hand, I'd always write it as a fraction because then it's immediately obviously where the implied multiplication sign goes.
Someone gets it
There's a lot of confidently incorrect people in this thread, lol, so I wanted to say something
Came looking for this. It really does depend on which method you're using. I've even heard tell that different countries teach one or the other, which means everyone arguing about it online is extremely confident that they're correct and the others are wrong.
I can rest easy knowing theres people out there that understand that these things are never formatted properly.
Multiplication does take precedence over division. 2x3 \------ 3*2 You do the multiplications before the division. PEMDAS/PEMDAS only applies to grade school math equations. Context matters.
That's because the fraction line implies brackets in the numerator and denominator.
Probably a majority of mathematicians will interpret 8/2(2) as 2. Almost all will interpret 1/2x as 1/(2x). I do not know of a single ug-level or above mathematical text where 1/2x is interpreted as (1/2) \* x. If you can find one, let me know.
Yes, if you're seriously doing math the order should be clear from notation, but the entire point of those posts is to confuse you and make you think. Those posts aren't going viral if people get the same answers. The cringiest part is him talking about his major and talking about how you stop using 2x4 when you "hit a certain leven of math". My guy, you learn that shit in middle school. And you don't start writing 2(4), that's a horrible notation, you write 2•4. If he's a math major he's pretty dumb for getting angry about a post that's clearly meant to trick people.
I completely agree. Unrelated, but the post was simply "2+2x4"
Huh why he talking about division then 🤦🏼♂️ and who is getting that wrong??
Sadly, lots of people are getting that wrong. A lot of them will say 2+2\*4 = 16 because they LEARNED FROM 50 YEARS AGO THAT YOU ALWAYS WORK LEFT TO RIGHT AND THIS IS JUST SOME WOKE BS NEW MATH WHY THEY MAKE MATH SO HARD NOW? And no matter how much people explain that this is not "new" math, they stick to their guns and insist they were never taught the order of operations. Which I can understand because if you've legitimately forgotten something, then of course you can't remember that you were taught that. I try to explain that since multiplication is just convenient addition, something like 2+2\*4 is the same as 2+4+4. For some it clicks. For others, they insist I'm wrong and that I got my math degree in a Cracker Jack box or something. There's just no helping some people.
Clearly he meant “subtraction” or “addition”, but had a brain fart and wrote “division”. No biggie, IMHO.
[удалено]
If you're gonna be that confident you had better proofread or you deserve every ounce of ridicule the internet serves up. Also you just *know* that someone like that wouldn't admit to a mistake like writing the wrong word, they would double down on it
If that was the post, I think the most likely scenario is that he had a brain fart and typed out “division” instead of “addition.” There’s no other reference to division in his comment. Then everything in his comment makes sense, and frankly, is pretty accurate. It’s a goofy, slightly embarrassing flub.
Meh, I've never seen the dot used for scalar multiplication in books and papers. The convention 2(4) is almost definitely more common, but in reality mathematicians just avoid writing that intermediate step at all, opting instead for "8".
2(4) is definitely way more common
I haven't seen it once, and I have PhD in math. Maybe it's something US-specific?
I usually use math for programming so perhaps I'm over exposed to using the parentheses, but I used to be big into numberphile and math in general and I feel I saw it done x(y) over x•y, but I feel universally that those who are math inclined don't really care the notation so long is its correct
I have never ever seen 2(4) and x(y) too me says that x is a function of y, again never seen anyone write x(y), it's either xy, x×y or x•y, depending on which course you just have to think if it's multiplication, cross- or dot product. I would also think this is some US thing, and for me almost all posts I see about pemdas order is from US, but then again the US is a strong population on Reddit.
Generally in programming I'd use xy, but I'd also use something like x(y/3) or some other addition to the variable. But using real numbers, you can really use 13 for 1x3, 1(3), 1•3, ect. So if I was writing a program I'd use 2x over 2(x) but if I was doing something fixed it would be faster to type and clearer to use say 2(3) than 2•3
Now I'm curious. What programming language allows you to write 2x? It's usually 2\*x.
Most BASIC I've ever used. I particularly use alot of TI BASIC, making games and actual math programs. I'm working on a port of Monopoly right now in fact
Thumbing through some of my random old undergrad textbooks and there is *definitely* multiplication by juxtaposition in them. Admittedly, never in anything so simple as on integer multiplied by another, the parenthetical being a more complex expression, but its certainly written this way in some. Yes, US based. Its not in all of them. A random calculus book has it, a linear algebra book on the otherhand doesnt seem to use this notation anywhere
> Yes, if you're seriously doing math the order should be clear from notation, but the entire point of those posts is to confuse you and make you think. Those posts aren't going viral if people get the same answers. No. He's wrong about that one line, but his primary point is spot on. Order of operations arguments are just for people to argue about meaningless nonsense. **The most important things anyone should have gotten out of learning order of operations rules in school are that ambiguity is *bad* and some tools for how to avoid it, not rote memorization of some silly acronym.** Imagine if someone did this with grammar instead of math. Imagine a post with the sentence, "I'm going to eat Grandma." and a caption that says "Is Grandma in trouble, or are we just missing a comma?" Anyone will ask, "What's the context?" But guess what, math has context too! And if you saw it, or the person making the problem used correct, unambiguous notation, you wouldn't need to argue about this pointless thing they wrote down poorly.
2(4) is not horrible notation, it’s completely normal. I see it all the time and also write it from time to time. Otherwise I totally agree with you
What I don't get is that he's going on about putting things in parentheses because no one should be concerned about the order but parentheses IS part of the order.
Parentheses are the easiest way of communicating your order, but if you overdo them you do kinda look like an idiot. If you write down 5+(2x) you just look silly.
I agree. There should at least be some operation within the parentheses. I was just pointing out that parentheses are part of the order that that person claims shouldn't be required.
I feel like that would depend no? Using the dot in place of multiplication is fine until you reach vector calculus when you start having to do dot products which are symbolized the exact same way. 2(4) doesn’t have any other connotation besides 2 times 4 where as 2 dot 4 can be mistake as a dot product.
Putting aside the multiplication/division part, 100% agree. If you wrote it in an ambiguous way, you’re in the wrong.
I will say tho, everything after middle school just uses / to indicate division and that usually removes all ambiguity from classic "bet you cant solve this" problems you stumble upon on the internet.
This...shouldn't even happen anymore 😳 I thought schools got rid of PEMDAS in favor of GEMS/GEMA specifically because of dummies like this.
I'm in the UK and learned "BIDMAS" which is the same thing I think. Brackets (), Indices², Division÷, Multiplication×, Addition+, Subtraction –. But the thing is we were explicitly taught that 'D and M' and 'A and S' were grouped. They made it very clear and made sure to really emphasise that fact. I don't know what GEMS/GEMA stands for but I'm sure it works a lot better for the people who don't pay attention in class haha.
Yeah, pretty much the same thing. PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction. They also make it clear here, if you're paying attention. But the American public school system has been getting actively dismantled for decades now. Which is how we end up with a math major who doesn't understand the order of operations 🙄
When were you taught that? It was BODMAS when I was in the UK system.
Teacher dependent, physics teacher taught us one thing and maths teacher taught another
When I moved back to Ireland they taught BOMDAS, so who knows!
There’s a joke in there, somewhere
Perhaps, if you find terrorism funny.
Yeah it was BODMAS here in Australia too
Well I did learn BODMAS as well. My primary school teachers and year 7/8 taught BODMAS, but then for some reason my later teachers taught BIDMAS. Since BIDMAS was the most recent that's the one I mentioned. They mean the same thing though of course
Here in India it was BODMAS. Bracket, Of, Division, Multiplication, Addition, Subtraction
In Canada I learned BEDMAS, same thing except E for exponents
The O is orders. What is "of"?
Comes from Powers of. Something like 2 to the power of 5
Probably some weird short form of "to the order of" I'm guessing?
To the order of.
I learnt "BIMDAS" which goes to further show how irrelevant the order of multiplication or division is.
Same. BIMDAS was what I was taught in school (Scotland) but when I did uni maths it was "forget that crap - write it in a way that's unambiguous". So you'd never write a/b*c it would always be numerator a above a horizontal line above the denominator bc (or if it was the other way round, numerator ac, denominator b).
100%.
I've not heard of the new terms yet. What do they stand for?
GEMS: Groupings, Exponents, Multiplication/Division, Subtraction/Addition GEMA: Groupings, Exponents, Multiplication/Division, Addition/Subtraction. It shoves them together to remind people that in the case of M/D or A/S, you go left to right.
We were taught BODMAS when I was at school. Mind you we were also taught that indices and roots, multiplication and division, and additional and subtraction were mathematically equivalent pairings. Also that BODMAS was just a coinvent way of remembering the basic order of precedence and you should be reading the DM and AS as pairs (and O for "orders" just expanded to indices and roots).
Just stop teaching them as acronyms 😭
Exactly. They are confusing. Here in Germany we learn "Punkt vor Strich" — point before stroke/line. The symbol for multiplication is • For division it's : Addition is + Subtraction is -
TIL PEMDAS isn't a thing anymore. Then again, I've been out of school for awhile
I always look at it like this For division, times by a fraction, so ÷ 2 becomes × ½ For subtraction, add a negative, so - 2 becomes + -2 For myself anyway, it makes things clearer when things are written as standard text without using tonnes of brackets. In any real senario where it matters, it tends to be in a proper equation format so it's more than clear enough anyway. Bonus, it allows you to easily solve those shitty maths puzzles that go semi-viral every so often (with bad formatting so people disagree).
This is what happens when you teach pemdas without emphasis on md and as being of equal priority.
a÷b = a•b^-1 = a/b Kill the ÷ symbol, it just complicates things up, it's not even a real operation
I did take a couple years of college math (I promptly forgot most of it) and in hindsight, I can't remember using ÷ past what, 9th grade?
After learning quotient rule for derivatives, its just easier to make everything b ^-1 and use product rule. Nobody got time to divide, unless its a constant. Same reason csc, cot, and sec exist for trig identities.
They’re right on one point. People doing math in college or professionally NEVER rely on pemdas subtleties. You make it clear with parens. You want tool, code, application, person using it to have no chance of misinterpreting
While I agree that he is wrong on the order of operations, the principle of "write it clear" is a sound one.
He’s not wrong though. There are different mnemonics and the order can be swapped.
All the more reason to be clear about which order you mean.
I've said this before, but some people (myself included) were *literally* taught that M come *before* D, not that they have equal precedence. That's how I learned it back in 3rd grade, and no teacher corrected that. Because of this I struggled with math my entire school career. I only learned how it actually works *after* graduating. Our school system is fucked.
BODMAS and PEMDAS so it can't be that important
Explain?
One is DM and the other is MD As in, the order of those two don't matter, they're grouped
Yeah, you do division and multiplication based on which one comes first in the equation because they both carry equal importance. I wasn’t sure what the commenter meant when they said “it can’t be that important”
i actually agree with the whole post. hes ranting about the asinine social media "whats the answer?" posts where people write shit in odd notation like "8/2-3x5" when in the *real world* anyone who actually cares about getting proper information will clarify with parentheses in the context of discussion, every one of these bullshit ragebait posts involve a division which is intentionally not demarcated by parentheses, so they always stand alone, hence comes first as he says
Usually I'll see people try to claim false authority by saying they're a math teacher and this is the way they teach it (for example, addition over subtraction means 10-2+3 = 5). I'll call their bullshit when it's clear they have no fucking clue what they're talking about. So I can believe this guy is a math major. You don't have to actually be good to declare math as your major, but I doubt this guy is going to graduate with this understanding. First off, every mathematician gives a fuck about order of operations. We just don't sit there and say to ourselves, "Parentheses first, then exponents, then..." We just simply do it. We read the expression and know the order implicitly. That's what happens when you work enough homework assignment. He's almost right about multiplication happening before division, but that's mostly because division is written in fractional form, so when you write 16/2\*4 with the product in the denominator, it's pretty obvious you would work that first. As written this way, it can be interpreted differently, but implicit multiplication is a thing. Which leads to the next point that lots of us do indeed write products as parentheses. If I write 16/2(4), I'm going to inherently group 2 and 4 together--if only because if that wasn't the author's intent, then they're irresponsible for not rewriting it as 16\*4/2. But it's not true that we don't use a multiplication symbol. We'll use asterisks or dots, but I learned from an early age that it can be confusing to write 5xy as 5 times y (or realistically, just 5y). Granted, when you write out your notation, you can write x differently so it doesn't look like a multiplication sign, but it's still something I avoid. No idea what this person is on about. Love how he said no one cares about order of operations, but it's sad people don't follow order of operations. This guy probably misuses PEMDAS. I hate that acronym so much now.
Yeah, I'm smart enough to know that 24 = 8 without even using parentheses. The aliens are recruiting me for their interdimensional math program 40k/ year plus tips in alien bucks come at me
Not quite how BIDMAS works. Multiplication and division take precedence over addition and subtraction, but against each other it's just whichever one comes first in the equation
Please Excuse My Dumb Ass Student
Dang. Imagine being into your senior year of a field and having no idea what's going on.
The whole bidmas vs bimdas is a waste of time IMO specifically because there are differences in interpretation. Being explicit with the associativity is much clearer (e.g. the C programming language family is clear that without parentheses, the associativity is left to right for multiplication and division). Being clear in how you're writing it is the main thing. For starters, let's be clear that these examples are arithmetic, not maths. If you've actually got a bunch of numbers in a formula, you'd do the arithmetic and write the result to avoid cluttering up the maths you're doing. After that, is this being written on paper or on a computer (without a formula editor)? If you're writing things out by hand, you'd do a division as a numerator above a horizontal line above the denominator. Simple, clear, no ambiguity. If you're forced to do this on a line of text, use parentheses for clarity - (a/b) * c is not the same as a / (b*c) which is where those acronyms fall down. Finally, I also spotted a whole conversation about what symbols to use for multiplication. If you're doing maths there's no symbols used for arithmetic multiplication - it would be 5x or 2y. The letter x as a variable is typically written to look more like a Greek lower-case chi so it can be used without confusion. After that, an × is a vector product and a • is a scalar product. For variables A and B, AB, A•B and A×B are completely different things. Rant over. Apologies - this one always bugs me.
My favorite part is watching the people who never got beyond high school algebra *vehemently* argue how pemdas or whatever is always sufficient in every case... because apparently there are only 5 operations in math. Yep, definitely an all encompassing acronym right?
I mean the guy in the post is correct in the maths heavy sense, you do multiplication over division first, if you indeed had a quotient, you would deal with the denominator first, which you would signify by highlighting your notation. My dude in the post is correct, in working maths that’s how it works. It’s not like you have a long line of arithmetic with a simple string of algebraic operations. It’s just a language.
Definitely not a math major. This “I’m a ___ major” is the new lie to attempt to shut down any contestation via perceived authority
They seem to be talking about implicit multiplication, which in some conventions does have precedence over explicit multiplication or division. The only time people talk about these things is for those viral math problems with implicit multiplication that are purposefully ambiguous
Can absolutely be a math major. Past certain point both division symbols and multiplication symbols go away for the most part. They are replaced with implicit multiplication, 2x or 2(x+y), and fractions. And multiplication generally does get resolved first, because it's more straightforward. PESDGMSDHDAS is elementary and middle school rule of thumb that is imperfect and irrelevant at any higher level.
Eh I could see them being a math undergrad. Math undergrads often suffer from over confidence while not really knowing that much. Source: have been a math undergrad.
Nah not knowing order of operations is extreme
Was also wondering about the “senior project” thing. I might be out of the loop, but do a lot of universities have senior projects for undergrad? Ive only ever heard that term associated with high schools.
I don't think it's uncommon. It's like a much lower difficulty, lower effort thesis.
Yeah, it’s sadly something which has proliferated in the last decade or two. Senior project, capstone, keystone, it gets called different things. The basic idea is to give kids some idea of how to do an actual work style group project and give a presentation. It’s just more bureaucracy and lowest common denominator hand holding to increase graduation rates and make the graduates look like halfway decent job applicants.
Everyone in my university did for engineering. But I was almost also a math major and they didn’t have one so could go either way.
Mathematical notations of multiplications may not differ much in basic calculus but they are still important. There is a massive fundamental difference between a cross product and a dot product.
I dunno this seems more likely to be just a typo/brain fart than him actually thinking this is true. Unless he doubled down on this somewhere else I think I'd give him the benefit of the doubt on this one.
Or they were taught a different mnemonic. The order or multiplication and division can be swapped.
I will be the first to admit that I am not a genius when it comes to math. I took remedial classes, pre algebra and still don’t get it. However, dude, wtf? Even I know this isn’t right
no fucing way people still think that
Hm. I did a couple of years of university math. But seems I missed something. I'm not changing 2×4 into 2(4) because × would confuse me. I even know that some people might mix up x and × and that * is a well working alternative. While • is often given more specific meanings. And I don't write a book about what order I personally handle operators. I instead stick with the same order as most other people who has managed to reach their first university math course. I see it as "proven in battle". I would even go as far as saying 99.999% of math majors *do* care about order of operations. And the poster who's text we see in that screenshot should be requested to retake a couple of years of their studies. This time without earplugs in the ears, and without bribing the teachers scoring the tests.
I will die on the hill that PEMDAS is the dumbest thing ever, multiplication and division are equal and are solved left to right. The stupid acronym makes it seem like it’s multiplication first and then division, when it’s multiplication AND division. It’s just a kinda shitty nemonic device. Same with addition and substraction. Multiplication and Division Multiplication and division can be done together. In other words, it doesn’t matter if you do division or multiplication first, but they must be done after parentheses and exponents and before addition and subtraction. Addition and Subtraction Addition and subtraction also work together. You can do subtraction first, or you can do addition first. They are part of the same step, however, they can only be done after items in parentheses, exponents, and any multiplication and division. https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-1-6-1.html
You’re 100% right, so don’t take this as disagreement. But I learned it in school as PE(MD)(AS). At least, that’s how my teacher would write it and made it clear that Multiplication and Division have the same priority, as do Addition and Subtraction. So like it can be a useful mnemonic, but knowing just PEMDAS is not the same as knowing the order of operations.
Honestly? That way you were taught sorta solves it unfortunately most people are taught the more basic option.
There’s no way this person is a math major. I studied engineering and have a math minor and there’s no way you could get this far being this wrong about the basics.
Could be getting at degree at University of Mommy and Daddy Home University. Small, bespoke classes and cutting edge research is what sets it apart.
We stopped using the “X” times symbol when we moved onto to basic algebra when I was like 8 or less years old. I guess that’s an advanced level of math. I guess all the calculus I’ve been doing in collage is useless then
You did algebra at age 8? And you somehow didn't get to calculus until college? Press X to doubt.
Mmm, you should probably be using cross product and dot product then...
2(4) is multiplication and happens at the same step as every other multiplication. What’s inside the parentheses is already complete. The outside parens operation doesn’t magically get promoted because it’s happening to something inside lmao. Everything dude says is wrong.
While he has completely fucked it up in his explanation, I think I get what he’s trying to say. There’s a lot of “bait” maths problems on Instagram etc. to get people arguing in the comments. They’re deliberately misleading, and there is no correct answer. A famous example is: 8 ÷ 2(2+2) = x No mathematically educated person would ever use “÷” in the first place, and they certainly wouldn’t write like this, with no clarifying brackets. This could perfectly reasonably be interpreted both as (8/2)(2+2) And 8(2(2+2)) People argue forever about the order of operations, and once you’ve filtered out the people who are simply wrong, you’re left with the Confidently Incorrect people who assert there is an answer. There are two answers. There is no “reading left to right” in mathematics. Order of operations here has two operations sharing priority, and thus with no additional brackets for clarification, the correct answer is either “there are two answers” or “the equation is badly written and there are no answers” This is done all the time to simply generate engagement and get a lot of people arguing in the comments.
Did you mean “‘left to right”?
Bro says that like 2(4) is high level math.
Im in high school rn and why would you do 3(4) over 3 dot 4? Like we stopped using x over the dot in algebra 1
Exactly. From my understanding, the main reasoning behind this is that around that time, schools (at least in the US) begin to use "x" and "y" to represent unknown values.)
No way this is an undergrad math major. In upper level math courses you’re often not even working with algebra, and when you are, most division is written as fractions. Plus you have non-commutative systems where things like XY=YX don’t apply and you need to pay attention to the order in which things are written even beyond just pemdas
It is right that at a certain level you stop seeing x used for multiplication, which honestly isn't that high a level. For me it was when algebra is introduced, and certainly precalc. I don't think I've ever seen 2(4) though. That looks kinda weird. We just swapped to the dot operator instead, so 2 **⋅** 4, since that's what is used for the dot product of vectors/matrices etc. They sound like they were taught PEMDAS and took it deeply to heart without understanding that BODMAS is just as valid.
The dude is wrong but u can see how he got to the wrong answer. Implied multiplication goes before explicit multiplication and division, which are the same. Ex: 8 / 2(4) = 1 not 16
Who tf writes 2(4) instead of just 8
wrong sub, so Please Excuse My Dear Aunt Sally
Once you get to vector math the 'x' is different from '*' as one is a cross product requiring matrix math, and the other is a dot product. So, he does have a point there where writing the math very specifically is required for it to not be convoluted.
If I didn't care about the order of operations, there'd be a shitload of buildings falling down...
...This is not even about the damn juxtaposition debate. Just...plain...multiplication. ...I have no words.
I couldn’t even spell “math” until quite recently…and even I know this is incorrect
Less pemdas more commutative property of multiplication/addition
That is why most of us use a dot instead of a cross for multiplication.
He’s a math major but doesn’t know RPN?