Counting Partitions of Sets and Bell Numbers | Combinatorics

[@djrkm9281]

props to ur enthusiasm. If all teachers were as enthusiastic as you know knows maybe we would actually attend the lectures. Thx so much

[@springvibes5344]

المُنقذ شكرًا جزيلًا.. I said in Arabic that you are Savior, so Thank you very much.

[@tomascremaschi1008]

Great explanation thank you! I can also see the passion you have for the subject which is amazing, keep the great work.

[@WrathofMath]

Thanks a lot, I do my best! Let me know if you have any questions, and if you're looking for more on partitions and Bell numbers - I have a few more related videos... Recurrence Relation for Bell Numbers: kzbin.info/www/bejne/qYGqppevgcafo6c Recurrence proof: kzbin.info/www/bejne/l5PJdKOMdriZgq8

[@harshporwal8479]

Explanation is crystal clear

[@solitary6002]

I was introduced to this bell triangle as a way to count the number of possible equivalence relations on a set of n elements.... Back then I didn't know that every possible way to partition a set can be associated with an equivalence relation.

[@pradeepmondal4943]

Just osssm ❤️❤️❤️❤️loved it .. Great explaination .. Guys watch this , without any time waste...

[@WrathofMath]

Thanks so much, I am glad it helped!

[@ftherogamer1073]

Thank you it helped a lot i really like your way of teaching please keep it up i appreciate your work 😊

[@vikasavasthi8346]

Thanx it help me alot in public service exam for teaching. ❤️Love from INDIA 🇮🇳

[@WrathofMath]

So glad to hear it, thanks for watching and much love back from the east coast of the USA!

[@AManOfMusic]

I have a question about these Bell numbers. I was messing around with the infinite factorial sum for e. 1/n! Then , I decided to see what would happen if I replaced 1 with n, so I wrote n/n!, and the answer was e. Then, I squared the top n, and the answer I got was 2e. Then, I cubed the n, and the answer I got was 5e. I kept going with this, and I only got multiples of e: 2, 5, 15, 52, 203, 877, 4140... Even with the first two sums I did, 1 is just n^0, and n is n^1, so I get the first two 1's of the sequence. Why do these Bell numbers show up with e?

[@mayurtummewar3312]

its mathemagic 🤩

[@mamaligakimchi]

It was an amazing explanation, thank you so much!

[@WrathofMath]

You're very welcome!

[@mayurtummewar3312]

ooho 🤩 the outro is fire 🔥🔥🔥

[@AnkitKumar-ur2gq]

Understood in just one go, thank you sir 😁

[@WrathofMath]

Glad to hear it! Thanks a lot for watching and let me know if you ever have any video requests!

[@chamudisewmini3421]

I was trying to find this by myself. But now I know I was wrong. Thank you very much for the video 😍

[@WrathofMath]

Glad it helped, thanks for watching! Being wrong is one of the most interesting parts of math, always satisfying to realize what you're missing when you can't quite crack a problem!

[@illusion7687]

Great explanation sir❤😇

[@WrathofMath]

Thank you!

[@pasqualedippolito3135]

Great explanation

[@WrathofMath]

Thank you!

[@farukahmed3179]

Great Explanatio level is on fire🔥🔥

[@WrathofMath]

Thank you! If you want some real fire, check out my math songs! kzbin.info/aero/PLztBpqftvzxW7a66b0dJPgknWsfbFQP-c

[@valor36az]

Awesome video thanks !

[@WrathofMath]

Thanks for watching!

[@shreshthdimri6412]

Killer Explanation.

[@utkarshtripathi2349]

Great Explanation! Thank you so much

[@WrathofMath]

Thank you, so glad it helped! I don't know if you saw my other two lessons on this topic, here they are if not! Bell Numbers and their Recurrence Relation: kzbin.info/www/bejne/l5PJdKOMdriZgq8 Proof of the Recurrence: kzbin.info/www/bejne/qYGqppevgcafo6c

[@hibaamu7234]

Awesome sir u teach awesome 👌 👏 👍 😎 😀

[@WrathofMath]

Thank you, I do my best! If you're looking for more on partitions and bell numbers, check out my two related videos... kzbin.info/www/bejne/qYGqppevgcafo6c kzbin.info/www/bejne/l5PJdKOMdriZgq8

[@mokoepa]

This is gold... Holy Molly...

[@WrathofMath]

Thanks for watching! I made a couple other videos on this topic if you're interested. kzbin.info/www/bejne/qYGqppevgcafo6c kzbin.info/www/bejne/l5PJdKOMdriZgq8

[@ceerie7487]

10:14 I get confused on this part for the last 2 elements why not add {3},{4} but he then immediately jumps to 3 elements which is 1,2,3? Edit: Okay nvm, he added it later on

[@avinashagrahari7106]

I liked your video...it's very help for us sir...👌👌

[@WrathofMath]

Thanks for watching, glad it was helpful! Check out the other two lessons I did on this topic if you're interested! kzbin.info/www/bejne/qYGqppevgcafo6c kzbin.info/www/bejne/l5PJdKOMdriZgq8

[@naanungamulla6528]

Amazing trick and teaching is very good attractive

[@WrathofMath]

Thanks a lot, glad you liked it!

[@divyadharshini1648]

Very Very useful

[@WrathofMath]

Glad to hear it, thanks for watching!

[@iitianrupa4513]

Please make full vedios and more for all combinatorics topics,thankyou!!😊

[@WrathofMath]

You're very welcome and thank you for watching! More combinatorics videos are on the way!

[@tirthpatel20]

Amazing Explanation! ...Thank you ❤️

[@WrathofMath]

Glad it helped! Thanks for watching!

[@mathwizards6785]

😍😍😍😍sir amazing explanation

[@WrathofMath]

Thank you! I am glad it was clear and let me know if you ever have any questions!

[@johndoe9659]

Please provide a geometric and animated proof of WHY adding Stirling numbers of the second kind add up to Bell numbers. Also: please provide a non-recursive, closed formula for the Bell number and make a video that explains the formula in an intuitive way.

[@MIKL]

Thank you ❤️

[@WrathofMath]

You’re welcome 😊

[@КЫРЫМСДЫШНМЕРЕКЗИШН]

What does n choose k mean?

[@bradleyshepard]

thanks- well done!

[@WrathofMath]

My pleasure, thanks for watching!

[@jidebranco5837]

Thank you!

[@WrathofMath]

No problem - thanks for watching!

[@matejcataric2259]

Where is your combinatorics playlist?

[@griffinbur1118]

Well-earned sub from me! Great video

[@WrathofMath]

Thanks Griffin!

[@mathsokparmeshwargurjar5291]

Awesome

[@shanedymaevallejos2400]

thanks

[@WrathofMath]

No problem, thanks for watching!

[@gmjammin4367]

Awesome video :)

[@WrathofMath]

Thank you!

[@neelabhabanerjee8247]

Hi man, I am really struggling with problems of the binomial theorem and pigeon hole principle from this book "A walk through combinatorics, Bona", if possible can you suggest a few good books to start these topics off with? Thank you!

[@WrathofMath]

I haven't read much straight combinatorics, so I can't say much about that (I have been wanting that particular book though). Proofs by Jay Cummings is a wonderful modern intro to proofs book that devotes some time to the Pigeonhole Principle. But you may not find it any more thorough or useful than what's in Bona's. I am a big fan of Book of Proof, which is a free proofs book you can find online, but I honestly can't recall whether or not it has pigeonhole principle in it. I'd think it would, but I can't actually remember seeing it. I always sing the praises of A First Course in Graph Theory by Chartrand and Zhang, but that's all for Graph Theory, which comes later in the Bona text. I of course have over a hundred videos on graph theory.

[@neelabhabanerjee8247]

@@WrathofMath yes yes your graph theory proofs help a lot bro. Are you in linkedIn btw? We can connect maybe if you're interested.

[@neelabhabanerjee8247]

@@WrathofMath Also, you can make a Video on Ferrers shapes if possible they 're pretty interesting thoo

[@KkPluto]

broooooooooo thank uuuuuuuuuuuu

[@WrathofMath]

Glad to help!

[@manuxoxo6399]

Niccceeee!! 👑👑👑

[@WrathofMath]

Thanks for watching!

[@shielamaecaballes8913]

Hi to my new crush 🥰.please notice me💙 i just love how you simplify things..

[@WrathofMath]

Thank you for watching! 😊 Let me know if you ever have any video requests! Elegant simplicity and beauty, math is filled with it!

[@МихаилСмирнов-ь6у]

Отлично. Лайк.

[@Subhajit_Paul123]

You didn't explain the recurrence relation.

[@WrathofMath]

kzbin.info/www/bejne/qYGqppevgcafo6c

[@ritam_arya]

you just showed that the recurrence relation works and all the possibilities of parting a set. i expected an explanation on why is it the way it is. so overall, it's a stupid video.