Factorial Fact Frenzy (!)

[@ComboClass]

Ok here's the Patreon that people requested, which I just launched (with various cool rewards for different tiers) www.patreon.com/comboclass

[@alexpotts6520]

Deserves a like just for "welcome to the factorial factory for a factorial fact tutorial"

[@HipsterShiningArmor]

fun fact: factorials don't actually exist, your math teacher was just very excited about the number 6

[@cycrothelargeplanet]

Lmao

[@NoActuallyGo-KCUF-Yourself]

We math teachers are excited about every number. Every number factorial!

[@AdfasSSBM]

@@NoActuallyGo-KCUF-Yourself but dislikes 1 and 2 more than any other numbers bigger than it, or 0

[@x0cx102]

@@AdfasSSBM wdym

[@anaisromero744]

6! It’s a six!

[@peppermann]

Your channel is highly addictive, great maths facts and problems spinning from easy to mind-bending. You clearly know a lot of maths but your modest and chaotic back yard approach is refreshingly enjoyable. One of the best maths channels I’ve seen. Keep the videos coming! 👍❤️😎

[@bjorntorlarsson]

His choice of maths topics is as practical as he himself is.

[@galaga16]

2:00 The clock on the far right is 4:24 4! = 24 clever

[@ComboClass]

Thanks for watching ! Leave a comment that’s ambiguous whether you’re yelling or using factorial symbols ! Also, to everyone who asked if I have a Patreon: I’ll be launching one at the start of December, with cool behind-the-scenes videos and other rewards, which I’ll link in next week’s “snack break” episode here ! Also check out my Bonus Channel for more videos: www.youtube.com/@Domotro

[@smartsmellafartfella1922]

How many eyes do most people have? 2!

[@Pr1sk1]

I really love ur videos but I cannot understand why these arent more popular, but I have suspicion why, thing is u keep telling same thing over and over again as if viewers were 8 years old. I want u to be more popular but I think u should "tighten up" a bit, so many videos u essentially saying same thing over and over again as if people have difficulty understand what u are saying. This is just my personal opinion and I think u deserve to be more popular than u are. (youtube algorithm is bitch) mr beast is best source of how to make videos "viral". There is science behind it :) btw keep the stupid comedy, its great :D

[@0homes]

In the letter video, you said you would remove c, but what about the ch noise?

[@cashtaylor9804]

@@Pr1sk1Your talking about him repeating himself?? Have you even read your own comment🙄 Seriously, I bet he's thankful for your help telling him what he's doing wrong with his channel. Especially coming from someone with such a huge, and successful Utube channel like the one you have...... RIGHT??🙄🙄🙄

[@cheekibreeki904]

The simplest way to distinguish a mathematician from a programmer is to ask them the meaning of!

[@kitten6317]

Double factorial is actually part of an infinite family of factorials, as things like a triple, Quaduple, and Pentuple factorials also exist, each giving even smaller results than the last

[@ComboClass]

Yeah that family is the "multifactorials" I mentioned :)

[@kitten6317]

Didn't see you mention that Also curious to see if something like a "Double Primorial" can exist

[@trudyandgeorge]

I love this guy so much. I missed out on maths having quit school in year 9 (because reasons). When I turned 30 I wanted to try and learn something before I was dead and enrolled in a "get-your-dumbarse-into-uni"-course for adults. A year later I got into computer science. After so. many. late nights after work doing the very basics of algebra, then trig, then calculus (god bless Khan Academy), I kept my head above water enough to graduate. Halfway through I realised that maths is not a calculation thing like I always thought, it's a creative thing! A deeply imaginative thing and it's chock full of fascination. This guy embodies that realisation so perfectly. "And look! There's pi and e lurking in there!! *wide-eyed stare* I wish I had a teacher like him when I was a boy.

[@ker0356]

damn man, a lot of people learn this stuff just because they were told to, but you have made a conscious decision and followed it through which I think is way harder. That's impressive, you should be proud of yourself

[@trudyandgeorge]

@@ker0356 Hey thanks man. To be honest, my missus deserves a medal because she picked up my slack due to lost time. Stuff like cooking, shopping, and forcing exercise breaks. God daaaaamn it's important who you marry, and I got mad-lucky 🍀. We have a kid now and "her time" is still yet to come, and I fear it never will, revealing an unfortunate statistic for many women. I am now sloggin' it out, trying to earn a motza in an attempt to provide some freedom for her, but so far it hasn't paid off 😄🔫. The work/husband/father balance is bloody tricky.

[@bjorntorlarsson]

Modern elementary school maths is sooo bad, it is as if made to deter kids from it. Since the 2nd century until European governments introduced mandatory schools in the 19th century, everyone learned maths from Euclides. And he basically just put together what was already ancient common knowledge. Do have a look at his book Elements! And construct maths with a compass and a straight edge. For example, construct the square root of the product of the lengths of two line segments. That is: given a rectangle, construct a square that has the same area. It is so irrefutably tangible that one can't protest. It has to be this way. An illiterate has no handicap when it comes to understanding mathematics. It is instinctive how physical objects fit together. That's why one can go through doors and do stuff. When one understands how maths actually works like this, then one can put numbers on it and go from there on, confident that this undeniably represents our everyday reality.

[@trudyandgeorge]

@@bjorntorlarsson that is so brilliantly said. I have a daughter now and have bought the book in preparation for when she is older. Thank you for your comment, stranger

[@bjorntorlarsson]

​@@trudyandgeorge Great, now you only need to teach her ancient Greek! (No, that's the very stuff that is cut out from the subject of how stuff logically fits together). Domotro is all about "bases", he likes 6 rather than 10. But what "base" did the ancient Greeks use? Does it even matter in geometry? Of course, geometry isn't everything. But it is and historically it actually was, a good beginning.

[@JarmezGD]

The absolute insanity and chaotic nature of these videos just gets me hooked every time, along with the interesting random number facts! Awesome work, keep it up!

[@dovesr0478]

Bro are you a real teacher? You're one of the most passionate educators I've ever seen, definitely the kind of person a kid would remember for the rest of their life.

[@reecec626]

Is anyone else loving the length time of this video? The sum of two cubes, twice!

[@smbs47]

Please explain

[@bilkishchowdhury8318]

​@@smbs471729 famous Ramanujan taxicab number, is the smallest number that can be expressed as sum of two cubes in two different ways

[@dustindoesstuff374]

You’re killing it, bro 👍🏼

[@Eoraph]

My coworker once reminded us that we needed some parts: "we need 170!"

[@matthijshebly]

I love this channel so much

[@Momotaroization]

That's one way to keep students attentive : at any moment, either I will learn something mind-blowing or chaos will explode on screen.

[@ww4830]

Your videos continue to blow me away! Absolutely love the content

[@JoeBorrello]

Old geezers like me will remember the old Texas Instruments calculators from the 70s would do factorials, and since the biggest number it could display was 10^100-1, the biggest factorial it could do was 69. And it took several seconds to calculate that, which was a novelty, so it was fun to do 69!

[@Inspirator_AG112]

These are the official names of the following factorial variants. Subfactorial: The number of arrangements of n elements where all n elements are out of order. Superfactorial: Πₖ₌₁ⁿ(k!) Hyperfactorial: Πₖ₌₁ⁿ(kᵏ) Ultrafactorial: Πₖ₌₁ⁿ((k!)^(k!))

[@1234567zeek]

I can't express how much I appreciate your hard work to present your unique perspective. Its enlightening hearing unique content. Thank you!

[@berni_schmorg]

Goddam! Mister Domotro, you had me totally bamboozled there! I really thought i was getting myself into a factorial factory for a factorial fact tutorial but luckily it was Combo Class afterall...

[@RedRamDRA]

Glad you brought up playing cards, one of my most favorite math-in-action examples. 52! is a number so huge, it's like holding a small universe in your hands.

[@cheeseburgermonkey7104]

you honestly deserve more subs than 17.4k with this type of content in my opinion, 2 things i love are math and (occasionally) watching things collapse and crash and stuff, so mixing those together makes the perfect video for me. keep up the good work Can't wait for comment bots to attack your comment sections though because that's definitely good and wont cause any harm whatsoever /j

[@XxCrystalPhoenix]

This entire channel is phenomenal.

[@berni_schmorg]

HAHAHAHA at 15:49 I think domotro and I were making the EXACT same face at each other AAAAAAAHHHHHH what

[@kenhaley4]

Easier way to explain why 0! = 1: Notice that 5!/5 = 4! and 4!/4 = 3, etc. In general, n!/n = (n-1)! So 1! / 1 should be 0!. Thus 0! = 1

[@dyhnen8977]

He is like the Explosion & Fire dude but with math

[@StoveLad]

Ha I said that a few videos ago.

[@mondfuchs_]

I love this guy, he teaches math while destroying thousands of clocks and all his scenery.

[@wandrespupilo8046]

this is so underrated!!!!

[@jameelmaki]

Thanks a million! Your channel is one of my favorites. I love it. Fantastic job! Keep up the great work. God bless you.

[@samjarvis9745]

This man may be the greatest teacher of all time he’s so passionate and charismatic

[@MrKockabilly]

I think the most practical use of knowing factorials is about the lotteries, knowing what the chance of our bet's winning to know if it's worth it.

[@mousaey]

I like your use of set pieces to demonstrate the universe's tendency toward entropy.

[@aksela6912]

Factorials grow really quickly, and some computer systems have a hard time calculating big ones, but if you're only interested in knowing how many digits you'd need to write a factorial, there is a much less computationally intensive way to do it. If you remember how to use logarithms you can maybe figure it out. Hint: log(A) + log(B) = log(A*B)

[@monhi64]

I remember messing around on a calculator and noticing 2^2^2 is only 16 but just 3^3^3 is already in the trillions which was kind of wild to me

[@aksela6912]

@@monhi64 I was about to say that doesn't seem right, but then I remembered you can associate both left and right. (3^3)^3 is only moderately large, but 3^(3^3) is, as you say, in the trillions.

[@alexicon2006]

My three favourite topics in maths are Permutations Combinations, Probability, and Statistics. So let's just say I'm a huge fan and leave it at that.

[@guyedwards22]

That intro hit my funny bone out of left field man; keep making videos, your personality is simply splendid and your content thoroughly interesting ❤️

[@e3lord856]

Dear god this channel is chaotic and I’m all for it

[@jatniel3297]

Such an underrated gem of a channel!!

[@matthewlennon6289]

Been watching a lot of your videos, great stuff. Fascinated by the primes, and I never realized the importance of the number 4!

[@Nikola_M]

This is like Breaking Bad but they cook math instead.

[@hkayakh]

So there’s this kid in my math class that always sleeps One day the teacher decides to call him out by asking him “Hey! What’s 5!” Pretty simple. The guy woke up and said “uhh 120” And then fell back asleep

[@lexinwonderland5741]

Once again, you never fail to amaze with your unique interpretations. Factorials being highly divisible relating to common intervals of time being made from multiple small prime numbers? 8! minutes in February? That's absolutely brilliant! I'm absolutely stealing that for future use. Keep up the great work m8!

[@nicholaswilson1310]

Oh man, I love it when pi and e hang out together!

[@MiniEquine]

Alright this is a fun channel. Keep it up, I can't wait to hear more!

[@katakana1]

9:35 Although, 432 is a cool first number for that pattern to break given that it's 4! * 3! * 3. More factorials...

[@geekwhoeatsrice]

You can even count the number of trailing zeros with these factorials. There's a REALLY CUTE way that uses the floor function.

[@Risperdali]

Your channel keeps coming up in my recommended. i finally officially subscribed. Nice work!

[@bongo50_]

Good video. I like the ending!

[@a2g555]

Hey dimitri and carlo, I really enjoy your videos about math. I'm always getting my mind blown by how complex but beautiful math is (even though I'm in grade 11 and still haven't mastered what I'm being taught lol). Keep up the good work and I'm 100% sure you'll make it big one day and get the attention you deserve. Love you, from an avid combo class student ❤️🫶

[@mralexxx4400]

You are absolutely 💯 awesome! Interesting! Knowledgeable, Diffrent! And More!

[@ceulgai2817]

Alright, this is my third or so video of yours I've watched, and the fact you used the actual definition of factorial instead of leaving it at "1x2x...xn" means that you're worth your salt. Glad to be a new subscriber, and I can't wait to watch your channel grow!

[@simonwillover4175]

In complex analytics, we define it with just 2 rules: * factorial(0) = 1 * factorial(z) = z * factorial(z - 1) * factorial is continuous and it's 1st derivative is continuous too * or is the rule that all derivates must be? * some rules on complex derivatitves, based on the real derivatives of functions defined by the 1st 3 rules

[@tomt5745]

as always brilliant, and very well thought through

[@Kaztalek]

my favorite factorial fact is that the product of (n) consecutive integers is always divisible by (n!). for example, 58*59*60*61*62 (5 consecutive integers) is divisible by 120 (5!)

[@nottaibo]

Man I loved this video, I'll watch it a weird number of times, like 7! Maybe more!

[@TD-er]

Those clocks in your yard are really great! It makes you realize, it is time for some fun :) Or time for math, depending on your perception.

[@TigruArdavi]

fun and maths are not mutually exclusive.

[@TD-er]

@@TigruArdavi neither is "or" :)

[@maynardtrendle820]

I almost never make it through a whole video because I get so many ideas along the way! A really great channel! 🐢

[@seize2581]

"Pi and e hanging out in there !" made me laugh 😄Gotta admit that's pretty crazy !

[@Chewychaca]

I actually love that he keeps dropping shit.

[@TalsBadKidney]

TO THE MOOOOOON

[@doriannlegrande5048]

It is helping my daughter and brushing me up.🎉 I enjoy it.

[@thecarman3693]

Funny thing about that last curve for fractional factorials ... it actually dips down between 0 and 1 before taking off again, meaning there is a minimum value less than one. Yes, a value less than 1 given that both 0! and 1! equal 1.

[@laz001]

Love it, that was so fun and clearly explained!

[@jamez6398]

Is there a symbol for adding up all of the numbers between 1 and a certain number, or exponentiating all of the numbers between 1 and a certain number?

[@SuperYoonHo]

fantastic factorial factory for a fun free factorial fact frenzy f-uhh_video 😂 f-thanks

[@bigbeans202]

God I love this channel I'm so sad it's not any bigger

[@archeacnos]

Your channel is gold, hope it'll grow soon

[@jonahunderhill]

I'm surprised at how good that approximation is already when you do 2! It seems really good except for 0!

[@nbooth]

I see Stirling's Approximation scores another point for tau against pi.

[@philipoakley5498]

Those cards: one deal per second, every billion years, one 1cm step along the equator, each time you pass the pacific empty out a medicine spoon (5mL) of water, every time it empties add a sheet of A4 paper to the pile, every time you reach the moon start actually counting, when you get to the millionth visit, realise you are not even 90% of the way to having completed the exercise (Oh, the universe ended aeons ago)!

[@elephantdinosaur2284]

For tetrationial factorials: 1 = 1 2 ↑↑ 1 = 2 3 ↑↑ 2 ↑↑ 1 = 27 4 ↑↑ 3 ↑↑ 2 ↑↑ 1 = 4 ↑↑ 27 is really big For context 4 ↑↑ 2 = 256 4 ↑↑ 3 = 4 ↑ 256 = 1.3 * 10^154 4 ↑↑ 4 = 4 ↑ 1.3 * 10^154 has 8.0 * 10^153 digits ... 4 ↑↑ 27 is unimaginably large. The fact about 432! and the primality for the alternating factorials is very surprising and counter-intuitive.

[@erdmannelchen8829]

A way to get a lower bounds on how many digits a certain factorial has is thinking about how many times the number with n digits is multiplied with another up to your factorial, then multiply that result with n to get a number, lets call it Z (for Zeroes) and then just add how many n-1 digit numbers there are and multiply that by n-1, repeat until you reach 2-digit numbers. I know what I've written is a bit convuluted, but I don't know a better way to describe it. So here's an example. 432! has at least how many digits? There are 432-100 3 digit numbers. So 332 3-digit numbers. 332*3 is 996. There are 89 2-digit numbers. So 89*2 is 178. | 996+178 = 1174 So by this example, 432! has at the very minimum 1174 digits.

[@hallucinogender]

When this reached the part about how 432! does something special, my initial thought was along the lines of "if a large number is going to introduce something special to a pattern, of course it'd be something like 432, that's twice the cube of 6, it has a lot of factors and comes up often". And then it turns out that the special thing it does is _breaking_ a divisibility pattern? Bizarre.

[@MarloTheBlueberry]

"Welcome to the factorial factory for factorial fact tutorial, unfractured edition!"

[@RafaelAAMerlo]

Excellent video as hinted on the Discord channel! What this video made me curious was about Permutations / Combinations: what if the things I'm ordering have some kind of characteristics to them that would sub-group them? Like in a deck of cards some numbers are printed in different colors (like Spades, Cups, etc), or when something have more than one sub-grouping characristic in uneven quantities? How to model this on mathematical terms?

[@steelegagnon5273]

great class professor!

[@atrsarst7158]

My favorite number is 5!

[@babygirl_lunaa9096]

Combo Class: keeping me excited for the math portion of my CS degree and tempting me to switch one video at a time

[@navjotsingh2251]

If you have the option, do numerical methods module, discrete mathematics (sometimes called algebraic structures) and also automata theory. All are really interesting theories that have applications to both computer science and mathematics as a whole.

[@chazzbunn7811]

Great video, I'm a mathematician too, and I was wondering if you would mention non-whole-number factorials and the gamma function. You kind of did at the end. What I like about your channel is that you present things in an interesting way that can be understood by a general audience. I was wondering "how is he going to talk about the gamma function, which requires all this complicated integral calculus?"

[@ComboClass]

Yeah the gamma function will be tricky to explain in an easily understandable way, and didn’t fit in this episode more than that brief mention, but I’ll try making an episode about it at some point :)

[@Xnoob545]

@@ComboClass oh by the way, the pi function exists, which isn't offset by 1 and also the integral for it looks even slightly simpler

[@navjotsingh2251]

@@ComboClass not everything has to be simplified, even if you approached it with all its complexities but made it easy to digest I'd still say you were successful.

[@kenj4136]

You kinda feel like the 'beakmans world' of mathematics. Just need a guy In giant rat costume :) Love it

[@Deeer69420]

If u put factorials in the calculator the limit would be 69! before math error

[@Gunbudder]

5:07 Statistically, 7 shuffles is considered a good shuffle, and a wash shuffle is the most fair. a skilled card player can riffle shuffle in such a way that the cards never actually change position by more than 1, and an even number of these perfect riffle shuffles will result in the deck not having changed its order at all. there are handful of seemingly impossible magic tricks that rely on a perfect riffle shuffle to be done at least twice

[@ComboClass]

Most of that is true but since you split the deck in half when doing shuffles, it takes more than 2 perfect riffle shuffles to reset a deck. Can be done with 8 “out-shuffle” riffle shuffles though. I’ll make an episode about that sometime :)

[@finlordlegendarygamer7014]

Ooh, fire. I'm going to try that at home because I didn't see a warning.

[@Xnoob545]

Great video! wasn't the stunt at the end dangerous though? also I've mean meaning to talk to you about some areas in math I've explored, but haven't gotten around to it, I'll do it eventually though

[@dyhnen8977]

Could you go through the general solution of Navier Stockes next class ? Need this for fluid dynamics

[@SpecTwo]

i feel the urgent need to play factorio now .. the factory must !

[@codatheseus5060]

Talking about noninteger factorials reminds me of that video I watched on 1/2 derivatives and antiderivatives I'd like to know if gaussian primorials are useful

[@cryptobogdan]

Awesome. One small tip I have would be maybe always speak towards the mic, because the sound gets distorted.

[@sobertillnoon]

Who wouldn't have clocks to arrange? That's crazy talk.

[@NoOffenseAnimation]

factorials are one of my favorite parts of math

[@BatzelChaos]

a pyromaniac obsessed with clocks teaching weird math on his backyard? never knew anything better.

[@TMNIARB3A]

harb lk alferda hh , nadi!

[@ausaramun]

Nothing beats TREE(3)

[@Bovineprogrammer]

I like swinging factorials the most ~

[@kikivoorburg]

I would personally write “multifactorials” as ‘x !_n’ (subscript n), and reserve ‘x!!’ for ‘(x!)!’. I also generally support the use of superscripts for function composition so that f^2 (x) = f(f(x)), but that’s thrown off by the very strange notation sin^2(x) = (sin(x))^2.

[@antonbashkin6706]

This one is a lot of fun and very funny 😂

[@ajaxflaskaarbra9915]

Thank you

[@shreyjain3197]

the lengths he goes to make his videos interesting..

[@KingYejob]

I find it so funny that I can hear birds in the background

[@livedandletdie]

25-5/5=4! Whether you understand math or not.

[@JuliusUnique]

wtf I never knew our time-system is so related to factorials, cool fun fact