subfactorial & derangement, an explicit approach

Check out a recursive way for subfactorial here: • Subfactorial, a recurs...
Check out Best Friend 1/(1-x), • BEST FRIEND
Check out the "giftaway" for the best friend t-shirt, / 1066456224361672706
#XmasIsReal #derangement
⭐️Please subscribe for more math content!
☀️support bprp on Patreon: / blackpenredpen
Guess what my first job was! • My First Job Story ,
My simple setup: 😃 • My Simple KZbin Setu... ,
Check out my site & social media
😃 blackpenredpen...
😃 / blackpenredpen
😃 / blackpenredpen
Thank you for supporting! You're awesome and I know it!
blackpenredpen | 曹老師

[@ThAlEdison]

kzbin.info/www/bejne/qZzMhGSMprSUec0 Venn higher than 3

[@blackpenredpen]

OMG!

[@blackpenredpen]

simply amazinggggg!!!

[@AndDiracisHisProphet]

wow, cool

[@GourangaPL]

you said "but unfortunately i need more space", combining it with the sentence you always say, it would be "i don't like to be on the bottom, i like to be on the top, but unfortunately i need more space"... hmmmmm.......

[@i_am_anxious0247]

GourangaPL ^

[@gouravmadhwal5548]

Plz integrate ln(ln(ln(lnx)))

[@blackpenredpen]

Gourav Madhwal More ln please.

[@gouravmadhwal5548]

@@blackpenredpen blackpenredpen btw.. I really have one😅😅 Plz integrate 1 ------------------------------- ln(. 1 --------------------------- ln(. 1 ---------------------- ln(. 1 ------------------ ln(x)))

[@blackpenredpen]

Gourav Madhwal That's it? That's too easy. When I was your age, I was able to integral x$^x$, where $ is a version of the superfacorial. I am currently working on #x^#x for my ph.D.

[@gouravmadhwal5548]

@@blackpenredpen I know that's easy for you.....but not for me...we have limited mathematical learning here till 12th standard....but I love maths...specially calculus...therefore I watch your videos....gain something from them...that's why I keep asking questions from you using the comment section....you remember that question?...0 to 2π cos(sinx)•e^cosx...that question was asked by me only...from another youtube account😅😅....therefore plz integrate ln(ln(ln(lnx))) and 1 ------------------------------- ln(. 1 --------------------------- ln(. 1 ---------------------- ln(. 1 ------------------ ln(x)))

[@jessehammer123]

blackpenredpen Primorials? I love primorials!

[@Goku17yen]

holy crap, that intro looks surreal

[@blackpenredpen]

Thanks to a subscriber!

[@ChrisAsHell]

But is impossible that just two out of three get their gifts back... If they did, the third one also did

[@quantumcity6679]

The new intro🔎 looks awesome!! 😘👌🤘

[@jay_sensz]

The Taylor series for e^-1 converges very quickly. That means that n doesn't have to be very large at all for it to be a good approximation. It seems that the following expression holds for all n>0: !n = floor(n!/e + 0.5)

[@crazy4hitman755]

Epic

[@goliathcleric]

The new intro looks great!

[@blackpenredpen]

Meliodas The Sin of Wrath thanks!!!! A subscriber did it for me.

[@i_am_anxious0247]

Oh my gosh, you are making such unique intros and thumbnails, u r being so creative

[@blackpenredpen]

Thanks to my subscribers for the intros. I do the thumbnails myself : )

[@i_am_anxious0247]

blackpenredpen your an awesome guy with an awesome community :)

[@codyhintz7866]

Toward the end you mention for big enough n you can use !n(about)=n!e^(-1) so how big does n have to be for this to apply?

[@CarmenLC]

i know im late but for n = 5 its already only 1% off from 1/e (≈37%) !5 ≈ 5!/e to 3rd s.f. so big values are n > 4

[@davidrheault7896]

I just received my copy of the T-shirt, 3 weeks for delivery in canada. A note for the video, !n is EXACTLY n!/e when you use the round function, I mean instead of doing 'sup factoreo of 4 by recursive formula, we can do !4 = round (4!/e) = 9, |3 = round(3!/e) = 2 !2 = round(2!/e) = 1 !1 = round(1!/e) = round(0.37) = 0 we can compute the digits of e by going high enough with the recursive formula, I did it high enough to compute 1000 digits of e :) Basically, you just need to divide the factoreo by the derangements

[@blackpenredpen]

Oh yea. I am actually aware of that. Thanks for letting me know and hope you like the t shirt.

[@chinmayasahu5577]

I feel so dumb and so smart at the same time

[@Nick-hc2cs]

that means that e is equal to n!/!n

[@blackpenredpen]

take n to inf, then yes

[@nicolassamanez6590]

yo, i actually know how to do this if you look at a three-way venn diagram, you can draw it by starting your way inside-out; draw a reuleaux triangle, then complete the 2-way intersections, then finally the circles. you can generalize this for any n-gon. start out with a reuleaux (for odd n) or reuleaux-esque (in case of even n-just make the sides circle arcs) polygon, and work your way up from there, drawing in the intersections in increasing order, finishing with the circles. so many years of doodling in math class finally paid off, it seems

[@bjarnivalur6330]

Hay! Do you make your videos for your students or just for fun? Or is there some other secret purpose behind them?

[@blackpenredpen]

Bjarni Valur both!

[@johnbohnenstiel605]

shouldn't it be 2 (choose) 1? @@blackpenredpen

[@yrcmurthy8323]

@@johnbohnenstiel605 yep dude, it's correct

[@Apollorion]

@@blackpenredpenIs that "both" an answer to Bjarni Valur's first question or the second?

[@SylComplexDimensional]

The explicit approach is 🔥🔥🔥🎅🏾

[@blackpenredpen]

Sylvester Cleveland thank you!!!!

[@HerbertLandei]

How about a "deranged" version of the choose operator? dechoose(3,2) would mean "all possibilities for two people to choose from 3 gifts without getting their own"

[@NuptialFailures]

I really love your factorial family videos. I think that it would be interesting to see videos on the factorial (and the other types) of the imaginary number.

[@yrcmurthy8323]

Sir, what is the relationship between subfactorial with hyperfactorial and Double factorial.

[@yrcmurthy8323]

Sir, even I had some limit questions I mailed you...

[@blue_blue-1]

I am looking like the octopus in the thumbnail. Yes, I admit not having understood the explanation about the sample space. Edit: In my previous note I mixed up the n‘s at the end.

[@angelmendez-rivera351]

This is good stuff! Now to generalize this using the Incomplete Gamma function, or just good old Gamma function?

[@zubmit700]

Love your videos and I'm not even studying math.

[@btdpro752]

Hi

[@NonTwinBrothers]

Christmassssss math time

[@clubstepdj]

I still don't get it Is it ok if the 3rd person gets his own gift (gift C) as a gift? Is it "all 3 of us cannot get the same gift" or "only i can't get my own gift, screw with others"?

[@przemysawkwiatkowski2674]

Actually how good is the approximation n!/e ?

[@quantumsoul3495]

A 4 person Venn diagram is impossible because 4 is not prime

[@sugarfrosted2005]

I was wondering if this divided factorial and it does.

[@kedarsalunkhe1142]

R u using inclusion exclusion principle?

[@blackpenredpen]

Yes. I forgot if I mentioned in the video or not.

[@kedarsalunkhe1142]

blackpenredpen thank you sir

[@ThePharphis]

you did mention it in the video, btw

[@choltiabdenour8326]

Plz..... I Need How To Be Cool In InteGrale

[@ffggddss]

Except for n = 0, you can write !n = {n!/e} where {x} is the *nearest* integer to x. In fact, the difference goes as !n - {n!/e} ~ (-1)ⁿ/(n+2) in the sense that the ratio of those two sides 1 as n ∞; and that it converges to 1 faster than any other term of the form a/(n+b). Fred PS. Somehow I missed this when it came out over a year & a half ago, but I'm glad I found it now. Next, I will check out its predecessor - the recursive approach.

[@yunfeichen9255]

Wow even linus is sponsered by honey huh??

[@apta9931]

Cool new intro

[@Ridwan-wm3is]

Poor octopus went into toxic shock...

[@proggenius2024]

this is a very nice video. thanks

[@lucazara9137]

So the limit x->infinity of x! / !x is e

[@kiiometric]

I love your videos! I think you're underrated in youtube, you should get much more likes for that amazing stuff

[@askyle]

At the last bit i thought you were also gonna plug the Stirling approximation ._.

[@rodbhar6522]

So "Isn't it?" is gone, but "Well well" is here. Can't we have both?

[@rmela4501]

Can !n! Be defined?

[@origamikatakana]

(!n)! or !(n!)? And both should work just fine.

[@stevethecatcouch6532]

Yes. But we have to decide whether !n! = !(n!) or !n! = (!n)!? Using a left to right convention, !n! would equal (!n)!.

[@i_am_anxious0247]

Steve the Cat Couch but the thing is, by that logic, !n=1(!n)=1!n=1n=n. This could be an entirely new notation instead...

[@stevethecatcouch6532]

@@i_am_anxious0247 Huh? How do you go from 1(!n) to 1!n? The whole point of the parentheses is to show that the ! goes with the n, not the 1.

[@i_am_anxious0247]

Steve the Cat Couch I’m being serious when I say that was a test, I wanted you to say this

[@OneEyedJacker]

Now I get it!

[@owem6511]

1C2= 1/2 confirmed

[@blacker4404]

Nope. 1C2 = 2.

[@blacker4404]

Oh, nvm. I thought you meant 2C1.

[@benwiley6512]

INTRO

[@AndDiracisHisProphet]

11:25 that's why my wishes never come true -.-

[@OtiumAbscondita]

who made the intro?

[@blackpenredpen]

a subscriber

[@OtiumAbscondita]

blackpenredpen ok but look at my comment on your 2 latest videos...

[@blackpenredpen]

Mathedidasko I did and I replied.

[@i_am_anxious0247]

Black Pen Red Pen-> Someone asked this and I wanna know, but ima put my own spin on it; Could !n! Be H(n) (hyperfactorial)?

[@yrcmurthy8323]

No, my friend

[@yrcmurthy8323]

I checked

[@i_am_anxious0247]

Yrc Murthy oh I see how it is... I mean, we always say Sin^-1(x) for inverse sin(x), but that should mean 1/(Sin(x)), you can use notation in other ways, but fine...

[@yrcmurthy8323]

@@i_am_anxious0247 Yes exactly !, my friend. Arcsine function cannot be written as In the denominator. i.e.lets assume we don't know if it is true. if it is true what you said, then let us take theta = 45 deg. Let's assume we don't know theta. sin(45 degrees) = 1/√2 and theta = x arcsin(1/√2) = x 1/sin(1/√2) = x Then sinx = 1/√2 Then again it continues. But finally x = theta = 45 degrees.

[@i_am_anxious0247]

Yrc Murthy we know, it’s just the notation. Not all notation follows your exact expectations all the time. You saying it can’t be written in the denominator only helps Emmy case, because the notations works a little different, so why not apply this here and say !n! = H(n)? I might sound idiotic, and correct me if I’m wrong, but arcsin(x) = Sin^(-1)(x), but this isn’t equal to the typical -1 power, sometimes notation doesn’t work like you think.

[@10_01-i6b]

what is i! in complex world?

[@pituitlechat3807]

yeah! a prove that Christmas is real!

[@brooksgunn5235]

_Peep that intro!_

[@CalamityInAction]

I like the new intro. :)

[@Methylshift]

cool intro!

[@Patapom3]

Amazing!

[@hamsterdam1942]

I see in ur intro discontinuous montage ;о

[@blackpenredpen]

?

[@maginobionrequiem9167]

Find x in x = 3+x

[@BabaFroga]

I see two of them...

[@SanjeevKumar-js4mu]

Infinity

[@zaidsalameh1]

Dude can you do a series about Wheels theory

[@blackpenredpen]

ZAID SALAMEH that looks really cool. I will look into it.

[@zaidsalameh1]

Thanks dude!!

[@Blue-jk4fw]

!4=9 thank me later

[@angelmendez-rivera351]

Aden Tate The incomplete Gamma function is more rigorous.

[@angelmendez-rivera351]

Aden Tate The incomplete Gamma function should still work

[@yoavcarmel1245]

for any real number x* 13:35

[@blackpenredpen]

Yes, thanks.

[@rockapedra1130]

This is cool. Never heard of !n before