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The Subfactorial is Hilarious 

Wrath of Math
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30 окт 2024

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Комментарии : 252   
@WrathofMath
@WrathofMath День назад
Well, that was fun! Join Wrath of Math to get exclusive videos, lecture notes, and more: ru-vid.com/show-UCyEKvaxi8mt9FMc62MHcliwjoin More math chats: ru-vid.com/group/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
@kilgorezer
@kilgorezer 11 часов назад
i agree, that was fun
@disnecessaurorex4908
@disnecessaurorex4908 23 часа назад
I feel like "It's 1/e, isn't it?" is the "he is right behind me, isn't he?" of maths
@RickofUniverseC-137
@RickofUniverseC-137 18 часов назад
Great analogy!
@CliffSedge-nu5fv
@CliffSedge-nu5fv 9 часов назад
Euler is always there. Sometimes he's downstairs.
@enderslice8378
@enderslice8378 День назад
IT'S ALWAYS e LEAVE ME ALONE EULER
@patrickwienhoft7987
@patrickwienhoft7987 День назад
I love that even in your furious use of caps lock you still have the respect for mathematics to properly write e as lower case
@enderslice8378
@enderslice8378 День назад
My rage doesn't make me disregard how symbols work. I have standards.
@pagjimaagjinen9733
@pagjimaagjinen9733 День назад
This smaller case e makes it seem like you say e calmly, and shout the rest
@kingnoob3503
@kingnoob3503 День назад
Euler will chase you for your life
@interconnected.
@interconnected. День назад
I love this reply lmao 🤣
@deepdrag8131
@deepdrag8131 День назад
“A dark room with several men who aren’t wearing any hats.” Oh! The nightmares I’ve had about that!!
@WrathofMath
@WrathofMath День назад
😂😂
@McDonalds-Empty-Cup
@McDonalds-Empty-Cup 11 часов назад
Nightmares? I had fantasizes about that
@-danR
@-danR 10 часов назад
That's Inception level 1 The deeper nightmare is none of them getting their hats back. This is a branch of Applied Mathematics I never knew I needed.
@CliffSedge-nu5fv
@CliffSedge-nu5fv 9 часов назад
Oh, _hats_ not wearing hats, right. That's what they aren't wearing.
@davidwright8432
@davidwright8432 2 часа назад
It might not be the lack of hats in such a situation that's hazardous, but the lack of clothing well south of the hat region. Or if not hazardous, perhaps adventurous. e ...xactly!
@carly09et
@carly09et День назад
This is Weird : I was just doing some economic modelling and this result popped out. This explains the entropy of a market, as it estimates states.
@WrathofMath
@WrathofMath День назад
That sounds very interesting, will have to research
@joshuaiosevich3727
@joshuaiosevich3727 22 часа назад
You might find it useful that derrangements can be represented by an integral: int_{0}^{/infty} (e^(-x))(x-1)^ndx
@carly09et
@carly09et 16 часов назад
@@joshuaiosevich3727 That's true. But I was finding the ratio by construction - ie a fractal result. This explained why the result converged on this.
@whamer100
@whamer100 День назад
as a programmer, seeing "!n" just makes me think "logical not n" which evaluates as either 0 or 1 depending if its non-zero lmao
@cosmnik472
@cosmnik472 День назад
bitwise not also works
@dapcuber7225
@dapcuber7225 День назад
I'd be more inclined to think bitwise not as I usually write logical not as ¬ but yeah this would be confusing 😭
@kuwi1061
@kuwi1061 День назад
​@@cosmnik472 For that ~ is used like this ~n
@litfill54
@litfill54 День назад
or strict n in haskell
@JdeBP
@JdeBP День назад
Those who have programmed in some home computer BASICs will be thinking "pling n".
@James2210
@James2210 22 часа назад
Brings a whole new meaning to "Statements dreamed up by the utterly Deranged" (from the "stop doing math" meme)
@briancooke4259
@briancooke4259 20 часов назад
Your pace and depth are perfect. I would not attempt those formulas on my own, but you made perfect sense if them. Thank you so very much!
@der.Schtefan
@der.Schtefan День назад
A dark room with many men in it... Sounds like a Berlin nightclub.
@empathogen75
@empathogen75 14 часов назад
And then e showed up.
@nicholasiverson9784
@nicholasiverson9784 6 часов назад
@@empathogen75 only if it was one of Those clubs, with hatless men.
@coyets
@coyets Час назад
It does indeed sound like a Berlin nightclub, but the calculation was not gender specific, and it could therefore also be applied to any dark room where people remove their hats on entering.
@KookyPiranha
@KookyPiranha 22 часа назад
POV: average combinatorics problem mindset
@meatyman4803
@meatyman4803 17 часов назад
Finding this guy in a math video is a fever dream
@Ryanisthere
@Ryanisthere День назад
0:38 this is getting very spicy several men without hats
@WrathofMath
@WrathofMath День назад
Spicy indeed, in a world of hatless men, where do we find God?
@the_siili
@the_siili 23 часа назад
​@@WrathofMaththe God is a man without a hat
@tweer64
@tweer64 17 часов назад
Did they leave their friends behind?
@Akio-fy7ep
@Akio-fy7ep 4 часа назад
@@tweer64 If their friends don't dance, well they're ... no friends of mine.
@Frownlandia
@Frownlandia 20 часов назад
I have a feeling the men without hats are happy to be partying in a dark room. After all, they can dance if they want to, and they can leave their friends behind.
@WrathofMath
@WrathofMath 19 часов назад
True, but one has to worry about the hats going wherever they want to, a place the men may never find
@NestorCustodio
@NestorCustodio День назад
I will never write a "3" or a "2" as legibly as this man did @ 2:30. 😢
@WrathofMath
@WrathofMath 23 часа назад
I was cooking with those
@CliffSedge-nu5fv
@CliffSedge-nu5fv 9 часов назад
I did once, and then never again. 😢
@furrball
@furrball День назад
I wasn't wearing socks and my toes blew up.
@WrathofMath
@WrathofMath День назад
Sorry 😞
@VioletRM
@VioletRM 13 часов назад
a small price for science
@furrball
@furrball 4 часа назад
@@WrathofMath np, that solved having to trim toenails.
@Frahamen
@Frahamen День назад
that's quite a deranged equation.
@WrathofMath
@WrathofMath День назад
You could say that
@blacklistnr1
@blacklistnr1 15 часов назад
I appreciate the gentle transition to combinatorics via hats and Zeus's wrath :))
@dukenukem9770
@dukenukem9770 День назад
I’m excited to integrate a “deranged“ math lesson into my sons home-study curriculum!
@lollol-tt3fx
@lollol-tt3fx День назад
poor son😂
@isavenewspapers8890
@isavenewspapers8890 День назад
Oh cool. I love taking an integral of the subfactorial function.
@jonathanallan5007
@jonathanallan5007 17 часов назад
I think that if we asked 10000 people the question (for some arbitrary number of hats, like 20) to give a percentage from 0-100 that no-one gets their hat back there would be quite a peak at 37%. Yeah, there would likely be one at 73% too.
@AusTxMale
@AusTxMale День назад
That was well worth the wait. Thanks for such a fun explanation.
@ReinOfCats
@ReinOfCats 13 часов назад
I'm a game developer, and a strikingly similar scenario - and result - came up awhile back when doing a deep dive on some item drop rate adjustments. Imagine you have a monster that drops an item when defeated at a rate of 1 in 100 times and then you defeat 100 of that monster. What's the chance you've gotten at least 1 of that item? Due to the "at least 1", this is easier to count the inverted result of "how many times did you fail to get the item" and repeat 100 times. So: (1-1/100)^100. And then invert that result: 1 - (1-1/100)^100. Giving a result of approximately ~63.4% chance of getting at least once. Generalizing this as n instead of 100, and then letting an n approach infinity, we get the result: Lim n->inf [1 - (1 - 1/n)^n] = 1 - (1 / e)
@cuitaro
@cuitaro День назад
5:38 "it will blow your socks off" What a relief that it won't blow my _hat_ off 😌
@WrathofMath
@WrathofMath День назад
The hats are long gone at this point 😂
@KylerRaineP.Nangit74
@KylerRaineP.Nangit74 День назад
6:39 WHAT YOU'RE LETTING AI?!?!?!
@JuniperHatesTwitterlikeHandles
AI's taking everyone's jobs, not even the set of all permutations where i is fixed is safe....
@WrathofMath
@WrathofMath День назад
gotta do what you gotta do
@yan-amar
@yan-amar 19 часов назад
What I love about mathematicians is that they'll mention Greek gods like it's 1200 BC.
@tomkerruish2982
@tomkerruish2982 День назад
Clearly, they were not doing the Safety Dance. (Gen X earworm, activate!)
@surkh
@surkh День назад
Well, then they're no friends of mine!
@lulairenoroub3869
@lulairenoroub3869 День назад
But they were men without hats And they were dancing And they were friends The men without hats never claimed they didn't "own" hats. They just didn't have any, currently, as is the case with our dancers
@porl42
@porl42 День назад
I had exactly the same thing in my head 😂
@RandyKing314
@RandyKing314 17 часов назад
i was trying to work out a comment like this…well played!
@incription
@incription День назад
In my head I thought "its definitely something like e, or 1/e", and imagine my surprise when I saw the result! Although, not much of a surprise, whenever probability is involved, e will show up.
@WrathofMath
@WrathofMath День назад
Yeah, for the mathematically initiated, it may be far less surprising. but it’s so amusing to take a silly word problem like that regarding hats, and the answer is 1/e 😂
@Oyakinya-Izuki
@Oyakinya-Izuki День назад
It's here!
@SquidLikesTalking
@SquidLikesTalking День назад
What a fantastic video, such an enjoyable watch, the mario 64 music was just the cherry on top
@WrathofMath
@WrathofMath День назад
Thanks so much! Trying to get the music at the right volume, I think I got it just about right this time.
@MPBSODIYL
@MPBSODIYL 7 часов назад
As a fascinating exercise, consider the following: Suppose you help n people receive their own hats by randomly distributing all of them. Then, those with incorrect hats return them to you to randomly distribute again among those still missing hats. What is the expected number of iterations it will take for everyone to have their own hat? (I more or less have a proof for this, but i also have homework due today 😢)
@Jacko_hedgehog
@Jacko_hedgehog 19 часов назад
This video amazed my mom as I watched this since she never heard of subfactorials before
@Connorses
@Connorses 15 часов назад
i was scared for just a second when you started drawing that hat rack
@-danR
@-danR 10 часов назад
I was wondering how he would manage to hang the hats on it.
@stephenspackman5573
@stephenspackman5573 22 часа назад
Fixed points in this sense are cycles of length 1. The obvious generalisation is to permutations with other minimum (and indeed maximum) cycle lengths. These would be practical things to know.
@IRLtwigstan
@IRLtwigstan 14 часов назад
I remember finishing our subfactorials a year ago and I loved them so much. I made a scratch project to plug a number in to give the sub factorial of the number.
@WrathofMath
@WrathofMath 10 часов назад
Super fun!
@IRLtwigstan
@IRLtwigstan 10 часов назад
@ Hell yeah!
@monad_tcp
@monad_tcp 15 часов назад
That must be the result of "Big Grammar!" those evil Barons
@Plasticshavings
@Plasticshavings 20 часов назад
the real question is why do they care so much about their hats, like should that really the biggest of their concerns?
@deangeloenriquez1603
@deangeloenriquez1603 7 часов назад
They are really expensive hats and they won’t be seeing each other for a long while so it is pretty important to them that they get the right hat
@secondbeamship
@secondbeamship День назад
This seems like something that may be non-polynomial.
@HopeHarmony
@HopeHarmony 23 часа назад
you forgot to draw eyebrows on the men
@thesmilingbraniac4438
@thesmilingbraniac4438 18 часов назад
12:45 writing (-1)^(j-1) feels illegal
@emiliocespedes3685
@emiliocespedes3685 16 часов назад
0:30 My favourite
@MaxwellClarkeNZX
@MaxwellClarkeNZX 9 часов назад
Seems like there's an easier way to count using a recursive definition: let Ai be the set which has *exactly one* fixed point at index i. This means that index i is a fixed point, and the rest is a derangement: !(n-1). Likewise for Bij (the set which has exactly two fixed points). So the number of derangements is going to have the form !n = n! - ((n choose 1)!(n-1) + (n choose 2)!(n-2) + ... + (n choose n-1)!(n-(n-1)) + 1) Then I'm sure we can do some re-arranging.
@VAFLEG
@VAFLEG День назад
1:03 there's hawk tuah🗣️🗣️
@zaqgamingstuff
@zaqgamingstuff День назад
HAWK TU-*fucking spits*
@brickinapresent
@brickinapresent 23 часа назад
Bro
@3345dbshockwave
@3345dbshockwave 16 часов назад
You are NOT funny
@pixelatedluisyt
@pixelatedluisyt 11 часов назад
you should uncomment yourcomment now
@loomkkoom
@loomkkoom 20 часов назад
We had to prove something with derangements without the subfactorial ended up just becoming deranged 😂😂
@sander_bouwhuis
@sander_bouwhuis 17 часов назад
1/e?!? I did NOT see that coming. Amazing!
@Pengochan
@Pengochan 19 часов назад
All this complex mathematics just for the extremely rare situation of men grabbing their hats in a dark room during a storm seems a bit excessive, especially considering that hats are somewhat out of fashion nowadays. Also they could certainly distinguish some hats by feel. I mean, nobody would confuse a baseball cap with a top hat, even in complete darkness.
@719PsychLgn
@719PsychLgn День назад
heres a math hack! start with 0, then *1 + 1, then *2-1, and so on till u reach your value you want to subfactorial
@micknamens8659
@micknamens8659 3 часа назад
When you start from n=0, the first value is !0=1 (because the empty permutation has no fixpoint) or even via recusion as !0=!(-1)*0 + 1 (=1) [assuming the unknown value of !(-1) is finite], and from there: !1=!0*1 - 1 (=0), !2=!1*2 + 1 (=1), !3=!2*3 - 1 (=2), !4=!3*4 + 1 (=9), !5=!4*5 - 1 (=44), ...
@Manisphesto
@Manisphesto День назад
I now wanna question what n!n is, is it n! × n, or n × !n...
@callyral
@callyral День назад
parentheses are your friends
@matino0820
@matino0820 День назад
Id say n × !n bc you put numbers before variables like 2x
@mathguy37
@mathguy37 День назад
!n!
@tobithesergal
@tobithesergal День назад
stuff like this is why im not better at math, that’s very ambiguous
@Abdullah-uszZZ
@Abdullah-uszZZ День назад
well, clearly, the bodmas order wasn't enough 😢😂
@denischen8196
@denischen8196 23 часа назад
Is there a math symbol or function for how many permutations of n have m fixed points where 0
@cocoabutter5888
@cocoabutter5888 22 часа назад
Something like n-m choose n maybe?
@joshuaiosevich3727
@joshuaiosevich3727 22 часа назад
Here’s a fun fact, integration from 0 to infinity of (x-1)^ne^-x is equal to !n. I don’t think I’m the first to discover this, basically, expand (x-1)^n with binomial theorem, change sum and integral and you get the n-th discrete difference of n! Which is also known as the subfactorial. I’ll leave my derivation for the derrangement formula here as well. Let p(N,k) denote the number of permutations of N elements fixing k. The sum from k=0 to N of P(N,k) is N!. Now note that P(N,k)=C(N,k)P(0,N-k) since fixing k elements is the same as fixing k and NOT fixing the remaining ones. Now you have the sun from k=0 to N of C(N,k)P(0,N-k)=N!. This we know that N! Is the “binomial transform” of the the derrangements, meaning we can invert this sum of write the N-th derrangement as the N-th difference of N! With a bit of tweaking you can use an argument like this to count any permutations of fixing r elements.
@steveclark2205
@steveclark2205 15 часов назад
With 4 🎩 you Cannot have 3 fixed points, only 1, 2, or 4 fixed points 🤔 😊
@MitchBurns
@MitchBurns День назад
e is also closely related to pi. e^pi*i=-1. Also if f(x)=f^4(x), f(x) could equal both e^x, or sin(x). Also, since you mentioned rounding, both pi and e round to 3.
@josenobi3022
@josenobi3022 День назад
Or you know, cos(x) and basically any sine function of the form a*sin(x+b) or a*cos(x)+b*sin(x)
@asmithgames5926
@asmithgames5926 День назад
It's always a fun party when e shows up 🤣
@ThePsyko420
@ThePsyko420 7 часов назад
I gotta say when i read the title I was expecting the same as factorial except with division instead of multiplication
@Locus616
@Locus616 18 часов назад
lovely video bruv
@WrathofMath
@WrathofMath 18 часов назад
thank you!
@shadeblackwolf1508
@shadeblackwolf1508 День назад
Without accounting for double counting, the direct sum of all sets [A1] to [An] equals n x (n-1)!, is N! again. just thought that's a funny consequence of the math
@satsumagt5284
@satsumagt5284 14 часов назад
6:45 oh yeah, inline four firing order !
@joshr.6785
@joshr.6785 23 часа назад
Love the Zelda background music!
@Mintymenty
@Mintymenty 14 часов назад
1:04 1:49 2:10 3:07 3:19
@ErikYoungren
@ErikYoungren 18 часов назад
5:33 Now I just want to know how likely is it that none of the viewers get both their socks back?
@thetruetri5106
@thetruetri5106 День назад
Hmmm Derangements are actually exactly what I need for my experimentations on creating sudokus. Is there also a way to easily figure out what those derangements are instead of just their amount?
@buddermybacon
@buddermybacon 17 часов назад
Latin squares
@thetruetri5106
@thetruetri5106 17 часов назад
@buddermybacon well latin squares only have n derangements not every possible one though
@DontWatchWhileHigh
@DontWatchWhileHigh 18 часов назад
Me: There's no way there's an explicit formula for this Also me after watching the video: Oh right I did this in combinatorics like 7 years ago
@zacjdavis
@zacjdavis 18 часов назад
10:21 I hear faint sounds of skyward sword. Haha
@ZyloSol99
@ZyloSol99 День назад
I see someone is a fan of zelda and satoral marsh from Xenoblade.
@mihaleben6051
@mihaleben6051 День назад
Can not comprehend. No formula????
@asmithgames5926
@asmithgames5926 День назад
1/e also shows up in another famous math problem, which I'll poorly paraphrase: When dating, what % of the total pool should you check out before committing to one? The answer is 37% of the pool, 1/e.
@WrathofMath
@WrathofMath День назад
With how big dating pools are now due to modern transportation and dating apps, I still have a significant amount of work to do 🤣
@wmpowell8
@wmpowell8 8 часов назад
Explain to me why !n ≠ (n-1)×(n-1)! = n!-(n-1)! if the first item has n-1 choices for what it could be, and if you choose the spot corresponding to that item to fill in next you get n-1 choices, and if you keep going doing that again and again you get n-2, n-3, etc. guaranteed I know this is wrong since (n!-(n-1)!)/n! = 1-1/n which approaches 1 as n→∞, not 1/e
@J7Handle
@J7Handle 22 часа назад
I can't believe I didn't see 1/e coming. I just thought "ooh, Taylor series for cosh(1) minus Taylor series for sinh(1)". Of course, that _is_ 1/e, isn't it? Reason you have to round n!/e to get !n is that you're only summing the terms of the series up to n, and if you add more terms after that to approach n1?e, you'll only have shrinking, alternating fractional terms starting with n!/(n + 1)!, which at largest will be 1/2, meaning the sum of all fractional terms going to infinity will be strictly between -0.5 and +0.5, meaning you just round to eliminate all the fractional terms, and of course eliminating all the fractional terms gives you all the integer terms, which is the truncated series formula for the subfactorial.
@DishDetergent898
@DishDetergent898 16 часов назад
What happens when we put it on the left? It becomes Spanish
@jceepf
@jceepf День назад
Put n beautiful women in this room, and they will never find their hats even the lights on. Now put n-m women, and what is the probability lights off? I have not done the calculation (10PM here in Beijing tired), but I would call this function "n rejects m" !
@DaveEtchells
@DaveEtchells 11 часов назад
It’s crazy the way e just pops up everywhere. You can speculate about what the universe would be like if any of the co-called fundamental constants of physics were a little different, but there’s no way to even hypothesize a mathematics with e having some different value. (Or is it? Am I just being limited by the fact I’m living in the universe we find ourselves in? Could there be spaces governed by a completely different kind of mathematics? I don’t see how there could be, it seems that math is necessarily just math in order to be self-consistent, bit again I wonder of that’s just my limited, parochial view?)
@WrathofMath
@WrathofMath 11 часов назад
Yeah, it's difficult to comprehend the order amongst the chaos. I'm an atheist, but the one thing that regularly makes me lean more towards belief in God is mathematics.
@AmosNewcombe
@AmosNewcombe Час назад
If we are adding a new operator, what is its associativity? What for example is “!3!”? Is it 2! or !6 ?
@randyohm3445
@randyohm3445 15 часов назад
I'm not understanding why the answer to the number of derangements isn't just (n-1)! since if you assume that no element can be placed in its original location then the first one has n-1 options, and the second element has n-2 options (since we exclude whatever we picked for the first one) etc.
@WrathofMath
@WrathofMath 15 часов назад
Good question! That will fail to count them all. For example, if we have 4 hats then there are 3 people that Hat 1 can be given to, say we give it to Person 2. Now how many people can Hat 2 be given to? It is not n-2 as (n-1)! would suggest. Instead, there are still 3 options, Person 1, 3, or 4.
@randyohm3445
@randyohm3445 13 часов назад
@@WrathofMath Ohhh, okay that's a good point. Thanks!
@CYXNIGHT
@CYXNIGHT 5 часов назад
20:04 That's you, reading this comment
@Fensmiler
@Fensmiler 7 часов назад
I'm kind of disappointed because i thought it would show the triangle numbers
@secondbeamship
@secondbeamship День назад
Man? From Aslume?
@supsendchapal4679
@supsendchapal4679 19 часов назад
Containment has been breached
@steveclark2205
@steveclark2205 14 часов назад
BTW not to throw a spanner in the works but, mein tutē has got driẹ ekkon, drie ekkon hast mein tutē, if it had not drie ekkon it would not be mein tutē... put th@ in a picture of a pipe & smoke it Dada 🤪
@deltainfinium869
@deltainfinium869 15 часов назад
omg the panennkoek music
@ehtuanK
@ehtuanK День назад
I think I'm missing something. Where exactly does it take into account that you can never have exactly n-1 fixpoints?
@zoomsp91
@zoomsp91 День назад
Imagine you have 6 hats. If you already have 5 fixed points, then the last hat is also fixed.
@ehtuanK
@ehtuanK День назад
@@zoomsp91 well yeah, i know, but how exactly does the math take that into account?
@JdeBP
@JdeBP День назад
​@@ehtuanKIt is in the final 2 terms of the expansion which subtract the n overcounted n-1 fixed point possibilities and add back the 1 all-fixed possibility, or vice versa.
@douglascaskey7302
@douglascaskey7302 16 часов назад
To a C++ programmer you put a bang (!) in front of a bool variable n or expression and we're going to assume it means NOT n. IF n = false THEN !n = true. If (!(3 < 10))... = false. 😏
@interconnected.
@interconnected. День назад
This is going right on my autism list, doesn't mean it's bad. But it's just weird
@micknamens8659
@micknamens8659 18 часов назад
13:20 Is there a way to develop this formula by induction over n?
@cheetosnour.scratch-learn
@cheetosnour.scratch-learn 17 часов назад
i want a new factorial with addition instead of multiplication
@WrathofMath
@WrathofMath 17 часов назад
1+2+3+...+n is called the nth triangular number (imagine a triangle of dots, 1 at the peak, then 2, then 3, then 4...) and there is a simple way to calculate such a sum
@deangeloenriquez1603
@deangeloenriquez1603 7 часов назад
Fun fact: at zero the summation reads 1 whereas the round of 0!/e reads 0
@tolstoj_
@tolstoj_ День назад
Shouldn't the sum starting at i=0 stop at n-2? 19:10
@yatta99
@yatta99 22 часа назад
Men without hats? Who could it be now? Euler obviously 😀
@WrathofMath
@WrathofMath 19 часов назад
always is!
@tweer64
@tweer64 17 часов назад
"Who could it be now?" Were those hatless men at work?
@timbeaton5045
@timbeaton5045 22 часа назад
probably a dumb question. but is this extensible to continuous functions in a similar way to the Gamma function?
@TheMelloJelloGuy
@TheMelloJelloGuy 13 часов назад
I stopped understanding what was going on like, a quarter into the video
@KineticWentFishing
@KineticWentFishing День назад
I thought it was factorial but you divide every number before it instead of multiplying
@WrathofMath
@WrathofMath День назад
We could just represent that as 1/n! Or n/(n-1)! Depending on what you mean
@robertmaxey5406
@robertmaxey5406 20 часов назад
But what if man 3 likes hat 2 more than his hat which is actually hat 1? I guess you did not account for that, smarty pants. 😅 Great video, now a fan.
@WrathofMath
@WrathofMath 19 часов назад
It doesn't matter because he can't see the hats anyhow! Haha, thank you!
@robertmaxey5406
@robertmaxey5406 18 часов назад
@WrathofMath In that eventually, just ask Google. He knows all sizes. Cheers. I wear a grey Fedora, by the way.
@greggorr314
@greggorr314 5 часов назад
Hat two, Bruté?
@mohammedfaris7610
@mohammedfaris7610 19 часов назад
Guys have anyone seen my hats?
@juandesalgado
@juandesalgado 23 часа назад
The factorial sign has been hijacked! The thumbnail looks like a ransom note :P j/k
@kshounishbhadra-bhaduri8602
@kshounishbhadra-bhaduri8602 15 часов назад
i wonder if there’s a way to generalize this to the gamma function 👀
@OBGynKenobi
@OBGynKenobi 19 часов назад
We Can Math if We Want To
@WrathofMath
@WrathofMath 18 часов назад
we can leave our factorials behind
@suyunbek1399
@suyunbek1399 День назад
Hat two? What did you say?
@WrathofMath
@WrathofMath День назад
Yeah, hat two, fit on that thang
@suyunbek1399
@suyunbek1399 21 час назад
@WrathofMath get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class get out of my class
@AidenOcelot
@AidenOcelot 20 часов назад
Does factorial not have a 'real' equation and only has the instructions for it?
@butlazgazempropan-butan11k87
@butlazgazempropan-butan11k87 День назад
Ah yes, the "fac n-torial"
@WrathofMath
@WrathofMath День назад
That’s a hilarious name 😂
@Zerohde
@Zerohde 17 часов назад
what about if we did !3!!
@davidspaics6221
@davidspaics6221 День назад
You videos are great but, i dont quite enjoy how much foreplay you do before getting to the math
@WrathofMath
@WrathofMath День назад
Lol, I do my best to strike a good balance, but it’s hard to get it perfect. Keep in mind the vast majority of my videos are parts of lecture series on college-level topics, in those videos I’m able to assume a significant amount of prior knowledge. In these videos I am not assuming that, and I get quite worried of slinging around terms where the audience doesn’t know what I’m talking about. Suffice to say these worries slow my pace some.
@jay-tbl
@jay-tbl 14 часов назад
love zelda music
@WrathofMath
@WrathofMath 10 часов назад
same!
@donwald3436
@donwald3436 23 часа назад
So !T is...... lol.
@HansJMicheelsen
@HansJMicheelsen 22 часа назад
Cut the music. It disturbs.
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