I understand why this is wrong (order of operations dictates the division happens first, so it's really 25 - 1 = 24), but why is it funny? I don't mean "This isn't funny," I think I'm just missing the joke.
Just a small correction in case you didn't know, but your answer shows as 432*1 because Lemmy formats text wrapped by * as italic, so it thinks you want to italicize the 3. You meant to write 4*3*2*1 (written as 4\*3\*2\*1). This is because \ is an escape character that tells lemmy not to take the * as a formatting character.
Factorial means n! = (n)(n-1)(n-2)... etc. down to 1, where n is a positive integer. It's used to calculate the different number of configurations of a set of elements, mainly in combinatorics.
Like if you have four different objects and you want to know how many different configurations you can order them in, you have four choices for the first object, then three for the second, then two for the third, then one for the final slot. So the answer is 4 x 3 x 2 x 1 = 24 = 4!.
They're used in permutations and combinations a lot. Combinations is pretty obvious based on the name. Given X things, how many ways are there to choose Y. Permutations are the same but where order matters.
For example, if you shuffle a deck of cards properly randomly there will be 52! possible orderings (permutations).
the most tangible and direct application is how many different ways you can order x many items.
eg. how many different ways can you order 3 items?
let's say you have these 3 items: 🍏🫐🍒
the first one can be any one of the three, so you have 3 options. that's 3 different ways to start your order. let's write that down:
3
now for the second one. whichever one you picked for first position will be unavailable, so you'll have 2 options this time. this is true for each first pick separately, so you multiply the possible number of first picks by the possible number of second picks:
3 x 2
now for the third item, since two of the three are already picked, you only have one left, which means not much to choose. you just multiply the 1:
3 x 2 x 1
of course multiplying by 1 doesn't change anything but as we mentioned there was no option this time, once you pick the second fruit the third is also auto-picked, so the third item doesn't add to our number.
so the final answer seems to be:
3 x 2 x 1 = 6
is that true? might feel like there should be more ways but let's test it; can't be that complicated:
🍏🫐🍒
🍏🍒🫐
🫐🍏🍒
🫐🍒🍏
🍒🍏🫐
🍒🫐🍏
here you go. you can extrapolate this logic to any number. four items would've followed the same sequence starting with 4 and have 1 less option with each pick, so 4 x 3 x 2 x 1. and that's also 4!
There are lots of applications, so I’ll give you three
Factorials are used in the Taylor Series to approximate trigonometric (sine, cosine, etc) and the exponential function. This can help speed up calculations.
In probability and statistics, if you want to find how many different ways a deck of cards can be shuffled, the answer is 52! Because the first card can be any of the 52, the second can be any of the remaining 51, and so on until the last card. Building upon this concept results in ways to model data like the binomial distribution , which is simply “how many successes will i get if i do this trial a certain number of times”. E.g. If I flip a coin 100 times, how many times will it be heads?
In computer science, the complexity of a program is compared to functions like the factorial, exponential, quadratic, etc. to visualize it’s performance given the size of the input, n. E.g. a program of linear time complexity is denoted as O(n), and as n increases, we expect the time for the program to finish to increase linearly. For a factorial time complexity, O(n!), we expect the time to complete to increase a lot compared to O(n)
In the applications mentioned by other people, you run into calculations that would look really messy and confusing. Things like 5•4•3•2•1 can be shorted to just 5! Imagine writing the full version of 123!
In High School education, Factorials are generally part of the curriculum, but they're one of those things you get one section on, it shows up on one test, then in common usage, you never see it again. In many schools, someone could have been out for a day, gotten two answers wrong on a test, and never have known it. Then in my school, unless you were heading on a math track, you'd hardly even touch Calculus to see it actually used anywhere.
I usually shun talking to other Kings, while I appreciate your explanation, the <3 and the 4!and 4 is not less than 3, let alone 4! sent me on a mild mental breakdown.
Anyway, I’ll just relax by beheading some peasants and imm sure I’ll be fine.
The exclamation point makes it right. The formula, when worked with proper order of operations, equals 24, which is equal to 4 factorial (4!)
1 * 2 * 3 * 4=24
ASCII hack failure of language. Even in mathematics, ! has multiple meanings like with Boolean NOT. We need a science, math, and language reformation to remove non intuitive narcissistic names, and implied contextual meanings.
.i la lojban cu mutce lo ka smuske tinsa .i ku'i ly. na logji prane pe'i .i loi jbopre cu piso'iroi da'asnu lo ka prane nitcu .i ru'a lo klamburi cu na'e lojbo ka'u .i jy. xebni lo malgli .iseju lo nu lojbo klamburi zbasu cu nandu ba'a jeku'i cumki
Lojban is very semantically rigid, but not perfectly logical IMO. Lojbanists often argue about the necessity of logical perfection. I suspect that puns might not be seen as culturally Lojbanic. Lojbanists hate Anglicisms or bits of English leaking into the way they speak Lojban. Regardless, making Lojbanic puns might be difficult but it's possible.
I've never seen ! used for boolean NOT in maths, just ¬. I think ! is something programming languages went for because it's easier to type. That said, screw (a, b). Is that a (coordinate) pair, an interval, an inner product, some secret fourth thing? Who knows!
On the flipside we have other symbols for things like Delta and Epsilon, Summation, cross-product, dot-product, curvature, tau, etc and most people would probably not memorize all of these or go through the effort to type them.
Plus it needing context to discern makes it harder for AI, too, so win-win.
The answer in the comic is correct. It's just written in a way to make you as the reader think he's got it wrong for a second.
The ! operator in mathematics indicates a function called a factorial. Four factorial, or 4! = 4 × 3 × 2 × 1 = 24. Which is the correct answer if you follow the proper order of operations.
So with people who do order of operations incorrectly, you have 25-5 =20 and then divide it by 5 and you get 4.
However the correct answer is 24 since you do the division first.
Where the joke comes in is he states “4!”, which sounds like he is emphatic about the wrong answer. However an exclamation mark is “factorial” which translates to 4x3x2x1… which happens to equal the correct answer of 24.
Jokes and tricks that hinge on unclear communication (eg: not using parenthesis or other notation to make intent clear), and then are smug when people are tricked, remind me of the old xkcd https://xkcd.com/169/
I just saw some jokes about factorials so at least I got this one, heh.
25 - 5 ÷ 5 when read naively left to right looks like it would be "25 - 5 = 20. Then take that and divide by 5, for an answer of 4". It would be clearer to write it as (25 - 5) ÷ 5 or 25 - (5 ÷ 5) depending on what's intended.
You see those kind of "gotcha!" posts online sometimes, where someone posts a problem that tempts you into doing order of operations wrong.
Someone who sees how to do it correctly immediately and thinks everyone knows that is invited to view https://xkcd.com/2501/ as well.
Naively, not natively. Someone who wasn't a good math student, or just doesn't remember, might read it left to right and come to the wrong conclusion. The rules for order-of-operations are, so far as I know, arbitrary, and different people coming at it without instruction (ie: naively) could arrive at different conclusions. Knowing that you're supposed to do division first isn't obvious.
You could read 25 - 5 ÷ 5 as "25 - 5 is 20. 20 divided by 5 is 4" or you could read it (correct, per the standard rules) as "25 minus.. hold on.. 5 divided by 5 is one. Now 25 subtract that from the 25 sitting over there, and get 24." This isn't the same kind of error as, like, "5 divided by 5 is 0"
On the extremely rare occasion when I have the misfortune to be performing a mathematical calculation, I take enormous pleasure in carrying out the operations exclusively left to right unless indicated otherwise by brackets, which is the correct way to indicate this. If you want me to do a calculation separately, put brackets around it or bugger off. It’s your choice, really
Many of the things we believe about ourselves and our experiences turn out to be false. Sometimes this is due to innocent memory failures or to the lack of needed information.
Suppose that Charles believes that he failed his biology test because the professor asked obscure and ambiguous questions.
Charles believes this because he doesn’t realize that he got the lowest score out of the 100 students who took the test, and that most people did quite well.
If Charles had this information, he would realize that he failed the test because he didn’t study hard enough, or because he’s not very good at biology.
On the other hand, if Charles continues to believe that the test was unfair after seeing the grade distribution, he is either severely challenged in his capacity for rational calculation or he is the perpetrator of willful ignorance.
unless indicated otherwise by brackets, which is the correct way to indicate this
No it isn't. The order of operations rules are at least 200 years older than the use of Brackets in Maths. Not sure how you think Maths was done before we started using Brackets.
put brackets around it or bugger off.
Bugger off with your disinformation. There are no Maths textbooks which use Brackets for such a basic expression. Students are expected to know the order of operations rules
Most people know the symbols for addition subtraction multiplication and division. Far fewer people know the established order of operations. That's what powers those "only 3% of people solve this problem correctly!" math memes.
But okay. Communicate badly (ie: by failing to acknowledge your audience's context) and be smug if you want.
Don't expect me to pander to willful ignorance. If you're going to act like an idiot, expect to be treated like one.
Also, what's with the passive aggressiveness? I understand that my confrontational approach there can make some people uncomfortable, but it's my prerogative.
Isnt that the entire point? There is suggested ambiguity (to those who don't know how operators work) due to how the equation is written, it could seem to be 24 or 4. But the answer is 4! which could be read as 4 being exclaimed wrongly or 4! (4 factorial) exclaimed correctly which is 24.
It's not a gotcha, it's a clever play on a classic argued mathematical ambiguity with a deliberately ambiguous answer to ram home the point.
How would this work out in a rtl language? Because the reader would be used to parsing language in the opposite direction. Does that mean the same equation has two objectively correct answers?
Hey, Munroe is a rather cool and very intelligent engineer. Very witty writer, and awful at drawing. But his philosophy is mid at best. He is not an authority, and is often wrong or common place when it comes to social topics and human affairs. He understands communication in a very techy engineering dimension. There's no need to take his comics as anything but what they are. One white dude's anecdotic commentary on his own very limited experience of the human condition. He knows squat about human communication, sociology, psychology or postmodernism.
I dont get it... why is 4! Funny. I understand it equals 24. But those two equations are not equivalent... am i being pedantic? Yes, am i going to stop being pedantic. Probably not.
4! is funny because there’s a common pitfall with math, which is just going from the left to right, instead of the order of operations. The former, pitfall answer is 20/5 which equals 4. The correct answer from using PEMDAS is 25-1 which 24.
Since the math is presented pretty simply, and She is asking for the solution to her problem, our first assumption is that the response is an enthusiastic 4, where this boy is confident, but very incorrect. We see he fell for the common blunder. (In a situation like this, without any other context, it’s safe to assume she’s looking for an integer, not a function. That would be like going to a store, and when the cashier gives you change, they say, “here’s 3 factorial dollars”).
But, this is clever, as his answer can be read in a second way, that still makes sense as a solution to the problem. 4 factorial is 24, the real solution. So, this boy could also be correct, that he’s telling her the right answer, albeit not outright, if we were to believe she’s looking for a simple “24” response, so he’s kind of being a dick.
Now that we’ve fully dissected this joke and killed any of the humor, thank you for coming to my Ted Talk!
I’m only going to say this once but if I’m doing a sum and you want me to do it in a specific order, use brackets. That’s what brackets are for. Don’t expect me to do things in a predetermined order because I literally can’t be bothered and I will never care enough to do that. I’m already doing a sum so don’t push it, okay bud
But that's a bit like saying "If you're going to talk to me, put the adjectives before the nouns," even in Spanish where they come after. Mathematical notation is a language and it has a syntax. Sure, you can decide to ignore that syntax, or insist that people modify their use of it for you, but it's not really a reasonable expectation.
I think this is very stupid for a number of reasons. Why is there an order of operations that supersedes the direction the operations are written in? That’s at best dim witted and at worst deliberately misleading. Grog write left to right. Grog read left to right. Grog do sum left to right.
There is absolutely no reason in the world why anybody should have to know that division comes before subtraction. That’s fucking insane, man. What is the point of writing things down if you’re only going to do them in a set order anyway? May as well have a big jumble of letters and numbers and symbols on the page at that point, like who cares. The whole point of writing things down is to express concepts. Can’t do that with any kind of nuance if you’re going to read it one way anyway, no matter how you write it down. That would be like saying you always pronounce certain letters at the start of words even if they’re in the middle. Completely nuts.
If all people did was simple equations like the one in the OP, you'd probably be right, but math syntax has to deal with all kinds of equations. Your way, I can't write 3x^2–4x+5. Instead, I'd have to write ((((3x)^2)−4)x)+5. That's WAY more obnoxious. It's better to have an unambiguous syntax that covers all the cases and lets me write equations in an more simple form.
No no, they're saying "4!" literally is the answer. The joke is that you say 4!, the other person who presumably knows the order of operations assumes you got it wrong and did 25 - 5 = 20 ÷ 5 = 4 when really you do division first so the real answer is 24. The punchline is that "4!" is how you write 4 factorial or 1 × 2 × 3 × 4 which is 24.
Yes, I understand that 4! is the correct answer. That is not my point. Without the misconception that the answer is 4, there is no punchline. This comic strongly implies that the natural assumption should be that the answer is 4, and that the secret, hidden answer is 24. In other words, in a world where people understand order of operations, the comic is not funny, because you wouldn't look at that and think 4 is a reasonable answer.
The joke relies on, as you put it, the assumption you did it wrong.
Your explanation of the joke would suggest that it would be equally funny if the question were "what's 21 + 3?" But obviously that isn't true -- the joke is meant to be that both 4 and 4! are equally valid answers to the question. However, in reality, 4 is not a valid answer; I just feel the same disappointment any prescriptivist feels when they see a word misused.
What are you even talking about? In what world is the assumption supposed to be that the actual answer is 4 and that 24 is some kind of secret hidden answer?
The assumption being made by the comic is that the reader knows the order of operations and will think that the person answering 4! is the one that did it wrong and mistakes the ! operator for them being enthusiastically wrong.
Imma be weird and argue that the answer actually should be 4.
Dear Aunt Sally is great or whatever, but syntax also fuckin matters. We can all probably agree that the faster, more intuitive answer is obviously 4. Most of those in the western world (meme's largest audience) read left-to-right and there is nothing the delineate that division must actually come before inverse addition until one has carefully examined the entire the problem (which you should definitely be doing, dumb-dumb) and slapped on another layer of thinking (inefficient waste of time when doing quick mafs). Use the damn parenthesis, ffs!
I find it far more efficient to parse. I also put superfluous parenthesis in my code where I feel it helps readability.
It's something to judge on a per-case basis, it'd also work very well to use whitespace (i.e. 25 - 5/5 instead of 25 - 5 / 5). Of course you don't want to parenthesis everything but it can help a lot.
Simple rules are only simple if they are intuitive and consistently applicable. Otherwise, they are nothing more than yet another thing to remember and think about, yet another source of error, and yet another possible point of confusion. With enough time/ effort, one can brute force the intuitiveness, but that doesn't automatically make the rule good or universally useful.
As a math teacher, I can assure you that not everyone has the same level of understanding or knowledge when it comes to order of operations. Some people struggle to remember the specific order, and mnemonics are worthless. Others struggle to read or visually process problems written with unclear or inconsistent symbology. Hell, most people don't even learn exactly the same fucking rules. Tell me, where is the simplicity in all of that?
When I teach order of operations, the glass eyes and exasperated sighs of frustration come out. But when I teach just the parenthesis and exponent stuff, lightbulbs and understanding. Suddenly, people "too dumb" to do 2+2 are doing algebra and getting excited about math for the first time ever. Some of this is certainly a failing of our collective education system, but we can't just forget that everyone has their own flavor of learning disability, neuro-diversity, and life experience. Simple rules quickly fail to be simple in the face of complex people.
I find this to be unironically both easier to read (by an incredibly wide, dyslexic margin) and faster to write and type.
Parenthesis consists of only two symbols that only require two keyboard keys and a single stroke of a pen to write compared to the four keys and varying strokes of the standard operators (aka. more efficient). But, far more importantly for me anyway, "+", "×", "*", "÷", all look nearly identical unless I stare the keyboard or problem for an agonizing century (waste of time, perhaps?) and even then it's a mystery whether my brain processed the symbology correctly or put the numbers in the right spot to do math (yep, waste of time). The humble ( ), however, is very easy to see, and it creates neat little windows that don't leave much room for misinterpretation.
2*7²+5*3³ = accessibility nightmare
(2(7²))+(5(3³)) = readable with clearly defined order of operations
Parenthesis consists of only two symbols that only require two keyboard keys and a single stroke of a pen to write compared to the four keys and varying strokes of the standard operators
The humble ( ), however, is very easy to see, and it creates neat little windows that don't leave much room for misinterpretation.
2*7²+5*3³ = accessibility nightmare
(2(7²))+(5(3³)) = readable with clearly defined order of operations
I mean, I guess I have no reason to doubt your word so I'll just believe you were being serious and respond in kind.
Time savings you might gain from parentheses being easier to write and requiring less keystrokes is lost on you needing to use twice as many since they come in pairs.
Furthermore, with the exception of *, which we don't even write most of the time, you still need to use all of the other operators even with parentheses, so using them everywhere isn't even a trade off, it's a net loss. This also means that parentheses will not help you differentiate between the operators because you'll still be using them.
Finally, the only reason you find the example I gave easier to read with parentheses is because I used a lot of multiplication, but you have multiplication to thank for that, not parentheses. In most cases, it would have fairly simple expressions like this:
1+2+3+4+5+6+7+8
turned into this:
1+(2+(3+(4+(5+(6+(7+(8))))))
If you truly want to eliminate ambiguity, have a look at reverse polish notation. I find it confusing as hell but some people like it.
Ok, now I'm curious, why is it only after I call you out that you decide to read what I wrote with any criticality? What about my argument (which I happily acknowledged was based purly on personal experience, and therefore not all parts are universally applicable to everyone) makes you think I'm nothing more than a dumb internet troll with no meaningful opinions or thoughts worth sharing or discussing like adults?
Sure, parenthesis need a buddy, but I still find them a lot faster to type simply because it is always the exact same two keys. No stopping to hunt for operators and symbols that seem to move or disappear every, single, fucking, time. When handwriting, parenthesis only takes one single, quick stroke that stays in line with what you are writing (maybe a small thing, but I find it important if my hands hurt, aka. always).
At no point have I argued the elimination of the operators, only that using them exclusively determine order of operations presents an accessibility issue and is largely unintuitive for many individuals.
The actual reason I find the parenthesis easier to read is because it isolates the problem into distinct, physically easier to read sections that eliminates a hard to distinguish operator and creates a clear step-by-step process to solving the problem that doesn't really on any rule beyond working from the inside out.
Single operator problems can be solved in any sequence, no parenthesis or order of operations needed. In your example, it's literally no different than combining like terms. But beyond basic cases like that, parenthesis always create a more comprehensible problem. Tell me, which is more clear and has less room for error:
1+2+3×4+5+6
1+2+3÷4+5+6
1+2×3÷4*5-6
OR
(1+2+3)(4+5+6)
(1+2+3)/(4+5+6)
1+((2×3)/(4×5))-6
Literally, all I'm arguing is that parenthesis make math easier to read and less prone to error or unintentional misinterpretation and should therefore replace the potential amigousness of order of operations. On top of that, I find them to be dramatically more efficient. Not everyone feels the same, fair enough, not really trying to paint with broad strokes on that front.
makes you think I'm nothing more than a dumb internet troll with no meaningful opinions or thoughts worth sharing or discussing like adults
Holy fuck. I called you one out of all of those and it was the one who isn't even a pejorative. I thought you were joking, because your comment sounded like you were joking. There's really no deeper meaning to that.
No stopping to hunt for operators and symbols
That's what I'm saying, using parentheses won't make the operators and symbols go away. You'll still have to stop and hunt for them, you're just adding parentheses in addition to that.
because it isolates the problem into distinct, physically easier to read sections
That's only true for simple expressions, though. Once you try to type something more complicated, parentheses get very confusing very fast. Anyone who's ever had WolframAlpha refuse to evaluate an expression because of a missing parentheses knows what I mean.
As for your examples,
1+2+3×4+5+6
1+2+3÷4+5+6
In these, the version with parentheses is different from the one without because you want the operations to be done in a certain order that isn't indicated anywhere.
1+2×3÷4*5-6
And in this one, you're mixing several operators with equal priority on the same line while not indicating which one you want to be done first.
What I'm getting at is that you've provided the exact examples where you have to use parentheses so it makes no sense to ask which one is clearer because only one version is correctly written. It would be like me asking you if (24)+1 is clearer than 2*4+1 and concluding parentheses are confusing because you didn't divine I wasn't typing twenty four but instead wanted you to multiply the 2 and 4.
Finally, the order of operations isn't just some arbitrary convention, it might seem that way when we limit ourselves to only numbers but its intuitiveness really shows in algebra. Take the polynomial:
2x²+1
Even if you've never heard of the order of operations, there's absolutely zero confusion about which order you're meant to do the operations. It would take a madman to decide that "+1" is part of the exponent or that you're supposed to add the 1 to the x² and then multiply it by 2.
In this case, adding parentheses here would turn it into
2(x(²))+1
which is unnecessary and it gets annoying very fast. For example:
(2(x))+(3(x(²)))+(5(x(³)))+(8(x(⁴)))
vs
2x+3x²+5x³+8x⁴
You might say that's not fair because this expression clearly needs no parentheses so I just added them to make it seem more confusing and you'd be right but that's the point: there has to be an arbitrary line where we decide parentheses are no longer necessary and that's the order of operations. We settled on that because that's what works in algebra. When it comes to what's intuitive in arithmetic, left to right is obviously the best (for westerners). Unfortunately for arithmetic, we've decided that intuitiveness in algebra is more important than intuitiveness in arithmetic.
I understand why this is wrong (order of operations dictates the division happens first, so it's really 25 - 1 = 24), but why is it funny? I don't mean "This isn't funny," I think I'm just missing the joke.
4! Is meant to be 4 factorial. 4! = 4 x 3 x 2 x 1 = 24
Aha! Got it, thank you so much.
And here I was thinking I was still decent at math. I got bamboozled...
Everybody forgets the factorial...
[email protected]
I always get a chuckle every time someone posted this in an unrelated comment.
Especially when we have never seen that shit before
Or if you don’t know order of operations, then you probably also don’t know factorials, so 20 / 5 = 4
The fuck is a "factorial"? They didn't teach me that one in high school math and I couldn't afford college.
Im sorry your highschool curriculum failed to teach you. I learned factorals in jr highschool
4 factorial (written as 4!) is 4•3•2•1
I think this example explains it perfectly lol
Edit: using • instead of * to avoid markdown
Just a small correction in case you didn't know, but your answer shows as 432*1 because Lemmy formats text wrapped by * as italic, so it thinks you want to italicize the 3. You meant to write 4*3*2*1 (written as 4\*3\*2\*1). This is because \ is an escape character that tells lemmy not to take the * as a formatting character.
Right, i sometimes forget about markdown lol. Yeah, it obviously is 4•3•2•1
Is a factoral just 1^X^ Because yeah i don't think I learned that either, but I was taught exponentiation. Whats the value of factorals?
Factorial means n! = (n)(n-1)(n-2)... etc. down to 1, where n is a positive integer. It's used to calculate the different number of configurations of a set of elements, mainly in combinatorics.
Like if you have four different objects and you want to know how many different configurations you can order them in, you have four choices for the first object, then three for the second, then two for the third, then one for the final slot. So the answer is 4 x 3 x 2 x 1 = 24 = 4!.
What's the point of factorials?
They're used in permutations and combinations a lot. Combinations is pretty obvious based on the name. Given X things, how many ways are there to choose Y. Permutations are the same but where order matters.
For example, if you shuffle a deck of cards properly randomly there will be 52! possible orderings (permutations).
the most tangible and direct application is how many different ways you can order x many items.
eg. how many different ways can you order 3 items?
let's say you have these 3 items: 🍏🫐🍒
the first one can be any one of the three, so you have 3 options. that's 3 different ways to start your order. let's write that down:
now for the second one. whichever one you picked for first position will be unavailable, so you'll have 2 options this time. this is true for each first pick separately, so you multiply the possible number of first picks by the possible number of second picks:
now for the third item, since two of the three are already picked, you only have one left, which means not much to choose. you just multiply the 1:
of course multiplying by 1 doesn't change anything but as we mentioned there was no option this time, once you pick the second fruit the third is also auto-picked, so the third item doesn't add to our number.
so the final answer seems to be:
is that true? might feel like there should be more ways but let's test it; can't be that complicated:
here you go. you can extrapolate this logic to any number. four items would've followed the same sequence starting with 4 and have 1 less option with each pick, so 4 x 3 x 2 x 1. and that's also 4!
There are lots of applications, so I’ll give you three
Factorials are used in the Taylor Series to approximate trigonometric (sine, cosine, etc) and the exponential function. This can help speed up calculations.
In probability and statistics, if you want to find how many different ways a deck of cards can be shuffled, the answer is 52! Because the first card can be any of the 52, the second can be any of the remaining 51, and so on until the last card. Building upon this concept results in ways to model data like the binomial distribution , which is simply “how many successes will i get if i do this trial a certain number of times”. E.g. If I flip a coin 100 times, how many times will it be heads?
In computer science, the complexity of a program is compared to functions like the factorial, exponential, quadratic, etc. to visualize it’s performance given the size of the input, n. E.g. a program of linear time complexity is denoted as O(n), and as n increases, we expect the time for the program to finish to increase linearly. For a factorial time complexity, O(n!), we expect the time to complete to increase a lot compared to O(n)
Makes things shorter.
In the applications mentioned by other people, you run into calculations that would look really messy and confusing. Things like 5•4•3•2•1 can be shorted to just 5! Imagine writing the full version of 123!
You didn't learn factorials in high school?
In High School education, Factorials are generally part of the curriculum, but they're one of those things you get one section on, it shows up on one test, then in common usage, you never see it again. In many schools, someone could have been out for a day, gotten two answers wrong on a test, and never have known it. Then in my school, unless you were heading on a math track, you'd hardly even touch Calculus to see it actually used anywhere.
I usually shun talking to other Kings, while I appreciate your explanation, the <3 and the 4! and 4 is not less than 3, let alone 4! sent me on a mild mental breakdown.
Anyway, I’ll just relax by beheading some peasants and imm sure I’ll be fine.
4! Is a factorial which means it's 4 x 3 x 2 x 1 = 24
Totally missed that. Thank you.
4 factorial
The exclamation point denotes the factorial function. 4! = 4 ⋅ 3 ⋅ 2 ⋅ 1
I see no one has explained yet, so I'll give it a shot. He is excited about math, and that needs to be encouraged.
The exclamation point makes it right. The formula, when worked with proper order of operations, equals 24, which is equal to 4 factorial (4!) 1 * 2 * 3 * 4=24
Cause math people has a weird humor?
The exclamation point in the answer, from a math perspective, makes it 4 factorial: 4 x 3 x 2 x 1 = 24, which is the correct answer.
Could it be you’re responding to the wrong person?
Indeed, it could.
Sorry to said that, but you made my guess quite real.
They all said the same thing.
Maybe the dumb guy is yelling 4 and the smart guy is saying factorial 🤔
Yeah but I'm a consequentialist.
they're all correct in their own way
Best math meme so far.
Unexpected expected factorial
Except it is correct. 4!=24
ASCII hack failure of language. Even in mathematics, ! has multiple meanings like with Boolean NOT. We need a science, math, and language reformation to remove non intuitive narcissistic names, and implied contextual meanings.
You might find Lojban interesting if you are not already aware. (I haven't tried to learn it myself, I just know it exists)
Relevant xkcd
https://xkcd.com/191/
If someone wants to start a Lojban pun community, I would definitely subscribe just to learn about Lojban.
Although, if no one posted in the community, I wouldn't be sure if it was a perfectly logical language or the community was just dead.
.i la lojban cu mutce lo ka smuske tinsa .i ku'i ly. na logji prane pe'i .i loi jbopre cu piso'iroi da'asnu lo ka prane nitcu .i ru'a lo klamburi cu na'e lojbo ka'u .i jy. xebni lo malgli .iseju lo nu lojbo klamburi zbasu cu nandu ba'a jeku'i cumki
I believe you mean, "nice pun!"
I've never seen ! used for boolean NOT in maths, just ¬. I think ! is something programming languages went for because it's easier to type. That said, screw (a, b). Is that a (coordinate) pair, an interval, an inner product, some secret fourth thing? Who knows!
Inner products are written as ⟨a,b⟩, no? Fair point on the interval, tho
On the flipside we have other symbols for things like Delta and Epsilon, Summation, cross-product, dot-product, curvature, tau, etc and most people would probably not memorize all of these or go through the effort to type them.
Plus it needing context to discern makes it harder for AI, too, so win-win.
Greek is a hack too. There is no reason a standard should be obtuse or memorized. Symbolic notation can be intuitive without gatekeeping nonsense
™ © £ € ¥ $ @ #.Ok this is funny
Comment section full of people looking for an opportunity to argue
No it isn't
Yes it is
Wait, will this be the 5-minute or the half hour?
You're not arguing, you're just being contrary!
Hah, joke's on you, I just need 4!
WHAT!
You got the wrong symbol in the headline, it should be >3
This is quite possibly the best maths joke I've ever seen.
[edit] I guess it still can't beat the 'be rational' / 'get real' one.
Clever! lol
for those that didn't get it: clever factorial = brilliant
Thank God this meme is muted
Promptly Evacuate Manure Drain And Septic
The answer in the comic is correct. It's just written in a way to make you as the reader think he's got it wrong for a second.
The ! operator in mathematics indicates a function called a factorial. Four factorial, or 4! = 4 × 3 × 2 × 1 = 24. Which is the correct answer if you follow the proper order of operations.
Can someone explain to me why this is funny?
So with people who do order of operations incorrectly, you have 25-5 =20 and then divide it by 5 and you get 4.
However the correct answer is 24 since you do the division first.
Where the joke comes in is he states “4!”, which sounds like he is emphatic about the wrong answer. However an exclamation mark is “factorial” which translates to 4x3x2x1… which happens to equal the correct answer of 24.
Ah! :D I like it.
007 will never get this wrong, it's 4, 24.
5-5/5 != 4
4 != 24 but also
4! = 24
4! = 5-5/5
5-5/5 != Sandwich
>3
25 - ⁵/₅ = 25 - 1 = 24
If you wrote it vertically:
25 - 5
————— = 4
5
But once you lay it out on one line, you have to use prins to prioritize addition / subtraction:
(25 - 5) / 5 = 20 / 5 = 4
Some YouTube mathematicians deep-dive into this.
ETA: Nothing goes over my head! My reflexes are too fast, I would catch it.
The joke is 4! (Factorial) Is 24 so it looks right even if you do order of operations incorrectly.
Ok so I'm not dumb! Usually I am with math but I got this one. Go me!
Yeah and 24 = 4 factorial = 4!
My favourite kind of nerd.
#DAMN YOU MATHEMATICIANS! YOU GOT ME AGAIN!!!
It's about time there was a real argument in here
Jokes and tricks that hinge on unclear communication (eg: not using parenthesis or other notation to make intent clear), and then are smug when people are tricked, remind me of the old xkcd https://xkcd.com/169/
I just saw some jokes about factorials so at least I got this one, heh.
Sorry but what is unclear in OPs image?
25 - 5 ÷ 5when read naively left to right looks like it would be "25 - 5 = 20. Then take that and divide by 5, for an answer of 4". It would be clearer to write it as(25 - 5) ÷ 5or25 - (5 ÷ 5)depending on what's intended.You see those kind of "gotcha!" posts online sometimes, where someone posts a problem that tempts you into doing order of operations wrong.
Someone who sees how to do it correctly immediately and thinks everyone knows that is invited to view https://xkcd.com/2501/ as well.
Natively? It's a math equation there is only one way to read it as far as I am aware.
Hear hear
Reread
Naively, not natively. Someone who wasn't a good math student, or just doesn't remember, might read it left to right and come to the wrong conclusion. The rules for order-of-operations are, so far as I know, arbitrary, and different people coming at it without instruction (ie: naively) could arrive at different conclusions. Knowing that you're supposed to do division first isn't obvious.
You could read
25 - 5 ÷ 5as "25 - 5 is 20. 20 divided by 5 is 4" or you could read it (correct, per the standard rules) as "25 minus.. hold on.. 5 divided by 5 is one. Now 25 subtract that from the 25 sitting over there, and get 24." This isn't the same kind of error as, like, "5 divided by 5 is 0"You could. You could also lower your pants and drop a massive turd and call that the answer. Both answers would be equally wrong.
PEMDAS isn't a suggestion that you follow when it suits you, like religion. It's how math is communicated, unambiguously.
In any case, if that's where we lost you, then I've calculated the chance of you catching the factorial as √-1.
On the extremely rare occasion when I have the misfortune to be performing a mathematical calculation, I take enormous pleasure in carrying out the operations exclusively left to right unless indicated otherwise by brackets, which is the correct way to indicate this. If you want me to do a calculation separately, put brackets around it or bugger off. It’s your choice, really
Many of the things we believe about ourselves and our experiences turn out to be false. Sometimes this is due to innocent memory failures or to the lack of needed information.
Suppose that Charles believes that he failed his biology test because the professor asked obscure and ambiguous questions.
Charles believes this because he doesn’t realize that he got the lowest score out of the 100 students who took the test, and that most people did quite well.
If Charles had this information, he would realize that he failed the test because he didn’t study hard enough, or because he’s not very good at biology.
On the other hand, if Charles continues to believe that the test was unfair after seeing the grade distribution, he is either severely challenged in his capacity for rational calculation or he is the perpetrator of willful ignorance.
Which is it?
No it isn't. The order of operations rules are at least 200 years older than the use of Brackets in Maths. Not sure how you think Maths was done before we started using Brackets.
Bugger off with your disinformation. There are no Maths textbooks which use Brackets for such a basic expression. Students are expected to know the order of operations rules
You're being weirdly aggressive, but okay.
Most people know the symbols for addition subtraction multiplication and division. Far fewer people know the established order of operations. That's what powers those "only 3% of people solve this problem correctly!" math memes.
But okay. Communicate badly (ie: by failing to acknowledge your audience's context) and be smug if you want.
You do realize your "You're communicating badly" attitude is the only smugness happening here, right?
Oh you're gonna love my other reply then.
Don't expect me to pander to willful ignorance. If you're going to act like an idiot, expect to be treated like one.
Also, what's with the passive aggressiveness? I understand that my confrontational approach there can make some people uncomfortable, but it's my prerogative.
No, they're not.
It is if you've been to school or read a Maths textbook
The only rules
Isnt that the entire point? There is suggested ambiguity (to those who don't know how operators work) due to how the equation is written, it could seem to be 24 or 4. But the answer is 4! which could be read as 4 being exclaimed wrongly or 4! (4 factorial) exclaimed correctly which is 24.
It's not a gotcha, it's a clever play on a classic argued mathematical ambiguity with a deliberately ambiguous answer to ram home the point.
How would this work out in a rtl language? Because the reader would be used to parsing language in the opposite direction. Does that mean the same equation has two objectively correct answers?
People don't read math like that tho, as you learn the order of operations in year 2. Also, the original post is correct,
25 - 5/5 = 4!Hey, Munroe is a rather cool and very intelligent engineer. Very witty writer, and awful at drawing. But his philosophy is mid at best. He is not an authority, and is often wrong or common place when it comes to social topics and human affairs. He understands communication in a very techy engineering dimension. There's no need to take his comics as anything but what they are. One white dude's anecdotic commentary on his own very limited experience of the human condition. He knows squat about human communication, sociology, psychology or postmodernism.
user has left the channel
I dont get it... why is 4! Funny. I understand it equals 24. But those two equations are not equivalent... am i being pedantic? Yes, am i going to stop being pedantic. Probably not.
4! is funny because there’s a common pitfall with math, which is just going from the left to right, instead of the order of operations. The former, pitfall answer is 20/5 which equals 4. The correct answer from using PEMDAS is 25-1 which 24.
Since the math is presented pretty simply, and She is asking for the solution to her problem, our first assumption is that the response is an enthusiastic 4, where this boy is confident, but very incorrect. We see he fell for the common blunder. (In a situation like this, without any other context, it’s safe to assume she’s looking for an integer, not a function. That would be like going to a store, and when the cashier gives you change, they say, “here’s 3 factorial dollars”).
But, this is clever, as his answer can be read in a second way, that still makes sense as a solution to the problem. 4 factorial is 24, the real solution. So, this boy could also be correct, that he’s telling her the right answer, albeit not outright, if we were to believe she’s looking for a simple “24” response, so he’s kind of being a dick.
Now that we’ve fully dissected this joke and killed any of the humor, thank you for coming to my Ted Talk!
I appreciate the clarifications. I now find the joke funny, beep boop beep! I am not a robot, for the record, I just like R2D2. Hes my spirit animal!
I’m only going to say this once but if I’m doing a sum and you want me to do it in a specific order, use brackets. That’s what brackets are for. Don’t expect me to do things in a predetermined order because I literally can’t be bothered and I will never care enough to do that. I’m already doing a sum so don’t push it, okay bud
But that's a bit like saying "If you're going to talk to me, put the adjectives before the nouns," even in Spanish where they come after. Mathematical notation is a language and it has a syntax. Sure, you can decide to ignore that syntax, or insist that people modify their use of it for you, but it's not really a reasonable expectation.
I think this is very stupid for a number of reasons. Why is there an order of operations that supersedes the direction the operations are written in? That’s at best dim witted and at worst deliberately misleading. Grog write left to right. Grog read left to right. Grog do sum left to right.
There is absolutely no reason in the world why anybody should have to know that division comes before subtraction. That’s fucking insane, man. What is the point of writing things down if you’re only going to do them in a set order anyway? May as well have a big jumble of letters and numbers and symbols on the page at that point, like who cares. The whole point of writing things down is to express concepts. Can’t do that with any kind of nuance if you’re going to read it one way anyway, no matter how you write it down. That would be like saying you always pronounce certain letters at the start of words even if they’re in the middle. Completely nuts.
If all people did was simple equations like the one in the OP, you'd probably be right, but math syntax has to deal with all kinds of equations. Your way, I can't write 3x^2–4x+5. Instead, I'd have to write ((((3x)^2)−4)x)+5. That's WAY more obnoxious. It's better to have an unambiguous syntax that covers all the cases and lets me write equations in an more simple form.
Gorg is from another country and writes right to left.
Gorg reads right to left
Gorg does sums right to left
well then you should stop doing math cuz you're doing it wrong
Thanks I take enormous pleasure in never doing any maths at all ever, largely for reasons like this 😌
Very funny joke, but I don't agree with the division sign. Its supposed to be either a / or \ depending on which way you want to divide.
never in my life have I seen a
\division sign.Well it was a joke, but it seems like a lot of people did not get it.
Did nobody learn order of operations?
The meme is correct. It is 4!.
Yeah but it's playing on the idea that the reader would think 25-5÷5 is 4. That's the joke. Without it there's no punchline.
No no, they're saying "4!" literally is the answer. The joke is that you say 4!, the other person who presumably knows the order of operations assumes you got it wrong and did 25 - 5 = 20 ÷ 5 = 4 when really you do division first so the real answer is 24. The punchline is that "4!" is how you write 4 factorial or 1 × 2 × 3 × 4 which is 24.
Nothing goes over my head! My reflexes are too fast; I would catch it.
Yes, I understand that 4! is the correct answer. That is not my point. Without the misconception that the answer is 4, there is no punchline. This comic strongly implies that the natural assumption should be that the answer is 4, and that the secret, hidden answer is 24. In other words, in a world where people understand order of operations, the comic is not funny, because you wouldn't look at that and think 4 is a reasonable answer.
The joke relies on, as you put it, the assumption you did it wrong.
No the joke is that first think they got wrong, then realize it's a factorial so they got it right (the a-ha moment!).
Then we realize that they might not have gotten it because the wrong answer is 4 and they may not know of factorials.
The ambiguity is very clever. Some other commenters call it a pun.
that commenter was me. Try ctrl+f.
Your explanation of the joke would suggest that it would be equally funny if the question were "what's 21 + 3?" But obviously that isn't true -- the joke is meant to be that both 4 and 4! are equally valid answers to the question. However, in reality, 4 is not a valid answer; I just feel the same disappointment any prescriptivist feels when they see a word misused.
No because 4 is the obvious wrong answer. 21+3 my isses idea completely.
4(exclamation) is wrong while 4(factorial) is right.
I think the smugness of someone who knows factorials is also part of what makes it fun.
What are you even talking about? In what world is the assumption supposed to be that the actual answer is 4 and that 24 is some kind of secret hidden answer?
The assumption being made by the comic is that the reader knows the order of operations and will think that the person answering 4! is the one that did it wrong and mistakes the ! operator for them being enthusiastically wrong.
Imma be weird and argue that the answer actually should be 4.
Dear Aunt Sally is great or whatever, but syntax also fuckin matters. We can all probably agree that the faster, more intuitive answer is obviously 4. Most of those in the western world (meme's largest audience) read left-to-right and there is nothing the delineate that division must actually come before inverse addition until one has carefully examined the entire the problem (which you should definitely be doing, dumb-dumb) and slapped on another layer of thinking (inefficient waste of time when doing quick mafs). Use the damn parenthesis, ffs!
Using parentheses where a few simple rules will do seems awfully inefficient. Both to write and to read.
Textbook authors be like:
sintx^2 + cosπx^3 - 3
I find it far more efficient to parse. I also put superfluous parenthesis in my code where I feel it helps readability.
It's something to judge on a per-case basis, it'd also work very well to use whitespace (i.e. 25 - 5/5 instead of 25 - 5 / 5). Of course you don't want to parenthesis everything but it can help a lot.
Simple rules are only simple if they are intuitive and consistently applicable. Otherwise, they are nothing more than yet another thing to remember and think about, yet another source of error, and yet another possible point of confusion. With enough time/ effort, one can brute force the intuitiveness, but that doesn't automatically make the rule good or universally useful.
As a math teacher, I can assure you that not everyone has the same level of understanding or knowledge when it comes to order of operations. Some people struggle to remember the specific order, and mnemonics are worthless. Others struggle to read or visually process problems written with unclear or inconsistent symbology. Hell, most people don't even learn exactly the same fucking rules. Tell me, where is the simplicity in all of that?
When I teach order of operations, the glass eyes and exasperated sighs of frustration come out. But when I teach just the parenthesis and exponent stuff, lightbulbs and understanding. Suddenly, people "too dumb" to do 2+2 are doing algebra and getting excited about math for the first time ever. Some of this is certainly a failing of our collective education system, but we can't just forget that everyone has their own flavor of learning disability, neuro-diversity, and life experience. Simple rules quickly fail to be simple in the face of complex people.
Yes they do, but sure, go ahead and produce a Maths textbook which teaches different rules to all the others (I've never seen one yet) - I'll wait 😂
Following your logic,
2*7²+5*3³ becomes (2(7²))+(5(3³))
Talk about inefficient waste of time.
I find this to be unironically both easier to read (by an incredibly wide, dyslexic margin) and faster to write and type.
Parenthesis consists of only two symbols that only require two keyboard keys and a single stroke of a pen to write compared to the four keys and varying strokes of the standard operators (aka. more efficient). But, far more importantly for me anyway, "+", "×", "*", "÷", all look nearly identical unless I stare the keyboard or problem for an agonizing century (waste of time, perhaps?) and even then it's a mystery whether my brain processed the symbology correctly or put the numbers in the right spot to do math (yep, waste of time). The humble ( ), however, is very easy to see, and it creates neat little windows that don't leave much room for misinterpretation.
2*7²+5*3³ = accessibility nightmare
(2(7²))+(5(3³)) = readable with clearly defined order of operations
I did preface this by pointing out I'm weird.
Oh, you're trolling. Carry on, then.
Oh, you don't know how to read, carry on then.
lol are legitimately saying this was not a joke?
I mean, I guess I have no reason to doubt your word so I'll just believe you were being serious and respond in kind.
Time savings you might gain from parentheses being easier to write and requiring less keystrokes is lost on you needing to use twice as many since they come in pairs.
Furthermore, with the exception of *, which we don't even write most of the time, you still need to use all of the other operators even with parentheses, so using them everywhere isn't even a trade off, it's a net loss. This also means that parentheses will not help you differentiate between the operators because you'll still be using them.
Finally, the only reason you find the example I gave easier to read with parentheses is because I used a lot of multiplication, but you have multiplication to thank for that, not parentheses. In most cases, it would have fairly simple expressions like this:
1+2+3+4+5+6+7+8
turned into this:
1+(2+(3+(4+(5+(6+(7+(8))))))
If you truly want to eliminate ambiguity, have a look at reverse polish notation. I find it confusing as hell but some people like it.
Ok, now I'm curious, why is it only after I call you out that you decide to read what I wrote with any criticality? What about my argument (which I happily acknowledged was based purly on personal experience, and therefore not all parts are universally applicable to everyone) makes you think I'm nothing more than a dumb internet troll with no meaningful opinions or thoughts worth sharing or discussing like adults?
Sure, parenthesis need a buddy, but I still find them a lot faster to type simply because it is always the exact same two keys. No stopping to hunt for operators and symbols that seem to move or disappear every, single, fucking, time. When handwriting, parenthesis only takes one single, quick stroke that stays in line with what you are writing (maybe a small thing, but I find it important if my hands hurt, aka. always).
At no point have I argued the elimination of the operators, only that using them exclusively determine order of operations presents an accessibility issue and is largely unintuitive for many individuals.
The actual reason I find the parenthesis easier to read is because it isolates the problem into distinct, physically easier to read sections that eliminates a hard to distinguish operator and creates a clear step-by-step process to solving the problem that doesn't really on any rule beyond working from the inside out.
Single operator problems can be solved in any sequence, no parenthesis or order of operations needed. In your example, it's literally no different than combining like terms. But beyond basic cases like that, parenthesis always create a more comprehensible problem. Tell me, which is more clear and has less room for error:
1+2+3×4+5+6
1+2+3÷4+5+6
1+2×3÷4*5-6
OR
(1+2+3)(4+5+6)
(1+2+3)/(4+5+6)
1+((2×3)/(4×5))-6
Literally, all I'm arguing is that parenthesis make math easier to read and less prone to error or unintentional misinterpretation and should therefore replace the potential amigousness of order of operations. On top of that, I find them to be dramatically more efficient. Not everyone feels the same, fair enough, not really trying to paint with broad strokes on that front.
Holy fuck. I called you one out of all of those and it was the one who isn't even a pejorative. I thought you were joking, because your comment sounded like you were joking. There's really no deeper meaning to that.
That's what I'm saying, using parentheses won't make the operators and symbols go away. You'll still have to stop and hunt for them, you're just adding parentheses in addition to that.
That's only true for simple expressions, though. Once you try to type something more complicated, parentheses get very confusing very fast. Anyone who's ever had WolframAlpha refuse to evaluate an expression because of a missing parentheses knows what I mean.
As for your examples,
In these, the version with parentheses is different from the one without because you want the operations to be done in a certain order that isn't indicated anywhere.
And in this one, you're mixing several operators with equal priority on the same line while not indicating which one you want to be done first.
What I'm getting at is that you've provided the exact examples where you have to use parentheses so it makes no sense to ask which one is clearer because only one version is correctly written. It would be like me asking you if (24)+1 is clearer than 2*4+1 and concluding parentheses are confusing because you didn't divine I wasn't typing twenty four but instead wanted you to multiply the 2 and 4.
Finally, the order of operations isn't just some arbitrary convention, it might seem that way when we limit ourselves to only numbers but its intuitiveness really shows in algebra. Take the polynomial:
2x²+1
Even if you've never heard of the order of operations, there's absolutely zero confusion about which order you're meant to do the operations. It would take a madman to decide that "+1" is part of the exponent or that you're supposed to add the 1 to the x² and then multiply it by 2.
In this case, adding parentheses here would turn it into
2(x(²))+1
which is unnecessary and it gets annoying very fast. For example:
(2(x))+(3(x(²)))+(5(x(³)))+(8(x(⁴)))
vs
2x+3x²+5x³+8x⁴
You might say that's not fair because this expression clearly needs no parentheses so I just added them to make it seem more confusing and you'd be right but that's the point: there has to be an arbitrary line where we decide parentheses are no longer necessary and that's the order of operations. We settled on that because that's what works in algebra. When it comes to what's intuitive in arithmetic, left to right is obviously the best (for westerners). Unfortunately for arithmetic, we've decided that intuitiveness in algebra is more important than intuitiveness in arithmetic.