What is a Power Set? | Set Theory, Subsets, Cardinality

[@WrathofMath]

Check out my new math rap channel for more math education in a rhythmic package! kzbin.info/www/bejne/gmebp5KNaZWGj9E

[@PepinoMusonda]

What is the song's title that plays at the end of this tutorial

[@SubeerRashiid-w4g]

Vaginal

[@benjaminframe2533]

Dude. The ability to explain a topic simply that would first appear complex is the trait of one who understands it well. Thank you for explaining.

[@WrathofMath]

Thanks for watching!

[@radiotv624]

My favorite part is when he said “set”

[@WrathofMath]

That was a pretty exciting part, I figured the viewer wouldn’t see it coming! Thanks for watching!

[@marlonremondejr8288]

Huh? :)

[@user-qn8lh7ej9g]

@@WrathofMath the sarcasm 💀

[@thelilpippin]

He set you up for that one

[@Phoenix-nh9kt]

@@user-qn8lh7ej9g lmao.. this man do be liking a reply of a reply of a comment 1.2 years later

[@kingknaz6809]

This is awesome. A topic I didn't understand throughout my first year. You took minutes to explain and I understood. Thanks so much.

[@WrathofMath]

So glad it helped, thanks for watching!

[@bhavnasingh1217]

Understood in just one go. Thanks!

[@WrathofMath]

No problem, glad it helped!

[@OsheanBro]

Sarcasm?

[@ismaildad9727]

Most people making KZbin videos "teaching" have many flaws; poor explanations, unclear examples, strong accents etc... this video was so clear I only needed to watch once and as a result, I’m now a subscriber! Thank you and keep the videos coming. They are needed...

[@WrathofMath]

Thanks so much for the kind words and for subscribing, I am glad the video was clear! More on the way and let me know if you ever have any questions!

[@riversiderocks]

This guy cuts the crap and gets straight to the point, thank you

[@GamingwithAsh221B]

Thanks man!You saved my life today in 4 min and 4 seconds !

[@WrathofMath]

So glad it helped, Ash! Thanks for watching and let me know if you ever have any questions!

[@Terrifyingtech]

You are really a good teacher love your teaching style to directly come on point of the topic not wasting the time of students like other teachers keep it up

[@WrathofMath]

Thanks a lot, glad it helped!

[@existentialrap521]

When I was reading the definition I was like SET WHAT SET WHO, SET UP?! Thanks for helpin a brotha out we out here.

[@pranshisrivastava8576]

Okay so i have been finding a vid for power set and couldn't find one.. But when i saw ur vid on this topic.. I understood this so well. U teach better then my teacher...

[@tumors1670]

Plain, Simple, Understandable

[@BlueandRedASMR]

Thats unusual! Wow! I’m so glad I found your channel, I’ve been finding so many wonderful ASMR channels recently! Looking forward for your new videos!

[@WrathofMath]

Thank you, but this is not an ASMR channel, so I am a bit confused. Do you mean that you are using these videos as ASMR? That’s quite interesting to me if so.

[@BlueandRedASMR]

Exactly! It is unintentional ASMR... I watching without thinking...magic of digital...just relaxing...actually in my scull and university I was perfect in math and high math....always worry how to pass exams...but now interesting just to watching...:)

[@WrathofMath]

Very interesting, thank you for sharing that. I have considered doing ASMR-focused math lessons before as I know a lot of people would like that, I’m just not sure it’s something I’d be particularly good at, especially as someone who doesn’t feel anything from ASMR videos. I’m glad you find ASMR value in the lessons I have already done!

[@BlueandRedASMR]

Yes it is work! Specially some people relaxing from writing, sounds and visual... so if you starting your asmr channel it is would be unique...also like in your other video writing on computer math with different colours of ink...looks soft...little bit lower sound level of talking...and it is perfect asmr...

[@WrathofMath]

Yes one of my thoughts has been that with the digital writing, which I much prefer, we lose the sound of writing, which is a nice sound. But despite that, it might be worth trying for a few videos to see how it goes. Thanks for the pointers and the comments, I’m keeping the idea near the front of my mind.

[@TusharDeb]

So briefly and precisely explained. Thank you!

[@WrathofMath]

My pleasure - thanks for watching!

[@ksh_u]

AHHHHHH THIS HELPED ME UNDERSTAND POWER SETS SO MUCH BETTER THANK YOU SMMMMM

[@sa_0515]

Magnificient video, greetings from Turkey

[@WrathofMath]

Thank you! Much love from here in the US!

[@aftabakhtar7747]

thank you so much sir - tomorrow is my maths exam at school and you really save my skin, the video was very helpful 😊

[@WrathofMath]

Glad to help!

[@chocolatetaco1376]

Thank you very much! I tried learning about power sets on Wikipedia for 26 minutes and learned here in about 3 (:

[@WrathofMath]

So glad it helped! Sometimes a quick video is just what you need, thanks for watching and let me know if you ever have any lesson requests!

[@chryzandermenezes4073]

Very good explanation I was learning for my test and found your video it helped me❤️from🇮🇳🇮🇳

[@akazbor]

Set SetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSet

[@WrathofMath]

setsetsetsetsetsetsetsetset

[@throplagm]

SetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSetSet

[@moodff8334]

setsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetsetset​@@WrathofMath

[@AdrikaSaraswat7]

@@WrathofMath💀💀🤣🤣🤣🤣

[@thunderboy3897]

In just one video, my fundamentals about power set and subset got cleared. Thank you Sir 🙏.

[@Scott-zb6eo]

Showed up in my morning feed, was nice to see you deal with the empty set, but my OCD is going off because you didn't finish it of with 2^0 = 1, which is the cardinality of the empty set, containing just the empty set itself.

[@mahenurrr]

Your way of teaching is really amazing Greeting from UK

[@WrathofMath]

Thank you, glad to help!

[@dilsaajan6447]

You are saving me in my university maths degree. THANKS.

[@WrathofMath]

Glad to help, and thank you for watching! I’m always creating new math lessons to try to be as helpful as I can both for my audience, and for those who may find the channel in the future. So, please let me know if you have any lessons you’d like to see on the channel! Sometimes I get requested lessons out as quickly as a day or two later, though it is certainly not a guarantee, haha. All depends on my schedule!

[@willardmakinishi6980]

Thank you so much for this brief and precise explanation. Stay blessed

[@vashistharts374]

The way uu teach is really ........... Fabulous 🤩🤩

[@WrathofMath]

Thank you, Saniya!

[@CVswhndja]

Your teaching is on par with MathAntics!

[@WrathofMath]

Thanks so much!

[@revanthnrajan2705]

Beautifully explained! Thanks a ton!

[@WrathofMath]

No problem, I am glad it helped! Thank you for watching, and be sure to let me know if there are any other lessons you'd like to see on the channel!

[@GabrielTobing]

Thanks, this helped me understand the power set better. I've never done this before so its helped.

[@WrathofMath]

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

[@DA-tt7kf]

Very easy explanation and straight forward to understand . Thanks a lot !

[@WrathofMath]

You're very welcome and thank you for watching! Let me know if you ever have any video requests!

[@basantatongbram9219]

Sir, thank you so much 😍😍

[@WrathofMath]

No problem! Thanks for watching!

[@SalmaAisha]

Beautiful hands 😂❤! Students shouldn't be like me😂😂. Thank you soooooooooo muchhhhhhhhhhhhh sir.

[@jaivardhan585]

Thanks man.... I can now finally understand power sets...

[@WrathofMath]

You're welcome, I'm glad to hear it helped!

[@vishwanjeyank6405]

Why we are using 2

[@Daniel.Jimenez]

this helped me so much! thank you!

[@WrathofMath]

I’m glad it helped, thanks for watching!

[@dayanazayas-bc5do]

LMAOAOOOAOAO I LOVE THIS VIDEO ITS FUNNYYYY YET EDUCATIONAL 😭😭😭

[@rhainalbertinojales8317]

OMG I GOT 50/50 ON MY PERIODICAL TEST BECAUSE OF YOUUUUU THANSKSKSKSKSKSKABAJJA

[@WrathofMath]

It's your hard work paying off - good job!

[@mriduladeka3263]

Nice 😄 explanation..... ☺☺ . You made me understand in one go... Keep it up sir

[@WrathofMath]

Thanks for watching and I'm glad it helped! I'm keeping it up as best I can - new lessons every 2 days :)

[@sportsplayer1827]

if set A contained {2,4} and the set was squared ( A^2) do you just multiply the set by itself which comes out to (4,16) ?

[@djdanzo206]

Came here for cardinality of a power set,got what i came here for🎉❤

[@muhammedalthafc.a8625]

This method is so easy!! thanku for this video👍

[@WrathofMath]

You’re very welcome, I’m glad it helped! Thank you for watching and let me know if you have any video requests!

[@sakshamsinha7304]

Thanks, man! U were a great help for me to revise this in one go. :)

[@WrathofMath]

Glad to hear it, thanks for watching!

[@coolcatboi8344]

Helped alot that's why I get bored in school not on KZbin

[@디파인-v1x]

This is a very clear explanation. Thanks.

[@WrathofMath]

Glad you found it clear, thanks for watching!

[@yahavgal7470]

You are the man.

[@WrathofMath]

Thank you!

[@anything_I_want]

Is power set and power relation different ?

[@randommail3877]

Watching From India 🇮🇳🇮🇳🇮🇳

[@WrathofMath]

Thanks for your support!

[@randommail3877]

@@WrathofMath welcome

[@yveltalgaming4169]

Expectation: me: i did not skip ads for u Reallity: me: i did not skip ads cuase the ad said video well be played after ad Very true

[@Nettle01]

You're the best. This helped a lot for my intro to programming math course.

[@WrathofMath]

Glad to hear it! Thanks for watching!

[@littlemiss9706]

ok let me first start by saying how helpful this video lesson is😭❤, but in minute 3:19 you put the empty set inside the brace. I was taught in school that you shouldn't put empty set in the braces. Anyways, THANK YOU A LOT!☺👍

[@WrathofMath]

Thank you for watching and for your comment, I am glad it was helpful for you! The empty set is just a set, and sets are allowed to contain sets, so there is nothing wrong with making the empty set an element of another set (or putting it inside the braces, so to speak). I suspect what you were taught is to not put the empty set inside the braces as a way of writing the empty set, which people sometimes do by accident. By that I mean, that 0 with a line through it is a way of writing the empty set, it is a set all on its own. If you then put it inside braces, the whole thing is no longer the empty set, it is the set containing the empty set. So if you were learning about the empty set, your teacher may have said to not put it in the braces if you're trying to write the empty set, because that isn't the empty set. But I was trying to write the set containing the empty set, which is why I put it inside the braces. Does that make sense? Thanks again and be sure to let me know if you have any video requests, I am always down to do set theory lessons, and any other requests are great too!

[@littlemiss9706]

@@WrathofMath Wow! thank you so much! So, can I pick whichever I want? I have to tell my math teacher about this. He cuts marks when we put the empty set in the braces ;( For a math video, can you please make one about graphs (as many types of graphs 😅 cuz I'm horrible at graphs)? and maybe show more methods in your math lessons😮? Do you make physics videos? btw I have another question🙈 is there a difference between { } and an empty set (a 0 with a line through)? Thank you so much sir, you save students' marks!!😭💕💕... I go to hell (school🌋🔥) to learn math for 45-60 mins from Mon-Fri and learn more from a quick and easy 5 minute video😩 P.S. sorry this was long lol😆

[@WrathofMath]

I’m not sure what you mean. You asked “Can I pick whichever I want?” so I think you might have misunderstood me. The empty set can only be written as { } or as the 0 with a line through it. What I was saying is that there is nothing wrong with the empty set being placed in another set, but if you do that, the object as a whole is no longer the empty set. So to try to clarify what I am saying, this: { } is the empty set. We can put it into another set, and have something like { { } }. But this: { { } } is not the empty set, it is the set containing the empty set. There is nothing wrong with putting the empty set into another set, but when you do that, what you have is no longer the empty set, it is a set that contains the empty set. You ask about graphs, do you mean plots, like graphs of functions? Or do you mean graph theory graphs that have vertices and edges? By show more methods do you mean something like showing different ways of solving the same problem? I try to include/mention different ways of solving problems when I think it is relevant, but I also like to keep my lessons as short and focused as possible. If I ever do a lesson on something that you would like to see done a different way, let me know and I might be able to discuss the method you are interested in! I have not made any physics videos but I plan to eventually! If you have any specific requests in that area, let me know and I might do one. No worries about the long comment, I appreciate all comments and I myself have a habit of writing very long comments. I appreciate your kind words and I am glad to be able to help! It is often the case that short online videos are far more helpful for students than classes in school, which is very frustrating for students. In many ways, I think the current form of public education is gravely flawed, which creates quite a market for alternative education methods, like all of those here on KZbin. Thanks for watching!

[@littlemiss9706]

@@WrathofMath okkkkaaaay now I get it :0 so the 0 with a line through is a set by itself and { } is a set by itself. so { } is not an empty set when we put a 0 with a line through, and a { { } } is not an empty set. It's the set containing the empty set. (sorry for my bad explanation) That's how I under stood it. and also please ignore the suggestion i gave about having different methods😂 now that I think of it I want the easiest and fastest way to solve questions :D so pls ignore that😅😆 Hmmm I never knew how many graph lessons there are until you asked which one exactly lol😂 OK so there is a lesson we'll have really soon about "Relations and Functions" it's the lesson that includes stuff like slopes, domain, relation, range etc. BUT this includes things like R = {(x , y): y=|x|} it includes other lessons like: A) Sum of Functions B) Difference of Functions C) Product of Functions , etc... a video will really help me and other students ;)😛 YAY! you should actually make physics video but maybe make a whole channel about it cuz your KZbin channel name is "Wrath of Math" ✌ videos like: 1) The first condition of equilibrium 2) Average Velocity and Instantaneous Velocity 3) Graphical Study of Motion 4) Graphical Study of uniform motion 5) The effect of Force related to shape on a body 6) Effects of Force Related to the Change in motion state of a body 7) Hooke's Law of Elasticity but there are sooooo many calculations in these soooo much😩 (these are too many requests but there are not many helpful physics videos here 🙀) Thank you a lot! I'm definitely subscribing and turning the post notification on! you're really nice to spend time and actually reply to your comments❤

[@WrathofMath]

Exactly! The 0 with a line through it is a set, and it is the same as { }, they’re both the empty set. As long as I am understanding you correctly, it sounds like you have got it down! I always try to provide the best, or most illuminating way to solve a problem in the context of the current lesson. Sometimes in a lesson I will go through a problem in a slow way that I normally wouldn’t on my own, but once you do similar problems enough, you can really speed up your own process. That is some great material on functions! I already have a lesson on relations and one on functions here on the channel that you might find helpful. But certainly I can address some of those other topics in their own videos as well. I will probably try to limit myself only to physics topics that are heavily mathematical, so that it is in keeping with the channel brand, and like you say, many physics topics are very mathematical and have many computations in them, so there is a lot of material that could be covered. Thanks so much for subscribing and for your comments! I appreciate all the requests; I am always asking for more requests! I will get working on some of these lessons once I return home from Baltimore, which will be next week. Thanks for watching!

[@LigayaNazareno]

So power set is the set of all sets???

[@katsojohnobotsang2484]

this really helped me a lot bruh.... thumbs up!

[@WrathofMath]

Glad to hear it, thanks for watching! Let me know if there are any other lessons you would like to see on the channel.

[@jahidulhaque1601]

Thank you so much ❤️ from Bangladesh 🇧🇩🇧🇩

[@WrathofMath]

My pleasure! Thanks so much for watching!

[@camille7044]

Great video,thanks for the clear explanation

[@WrathofMath]

Glad to help, thanks for watching!

[@Riya.79]

thanks for amazing concept clearance💗❤️

[@WrathofMath]

My pleasure! Thanks a lot for watching!

[@Hamza-Shreef]

Man! you 're awesome. the best explanation for this point...👍❤

[@WrathofMath]

Thanks a lot! Glad it helped!

[@meghanamagei4016]

Ur explanation is too nice

[@WrathofMath]

Glad it was clear, thanks for wacthing!

[@eetkaur2023]

Thank you so much sir.You explained it really amazing.😊

[@WrathofMath]

Glad it was clear, thank you for watching!

[@sunkarakomali1687]

Wow 🤩🤩very nice😊... Thank you❤ soooo much sir

[@WrathofMath]

Thanks a lot for watching! :)

[@sunkarakomali1687]

@@WrathofMath thank ❤you soooo much.... U, r hepled in my how work sir 🙂🙂🙂🥰🥰

[@bamelillian4920]

Thanks able to understand better than when I read it from a textbook

[@WrathofMath]

Thanks for watching, I am glad it helped! Let me know if you have any video requests!

[@marcianangeloavila5783]

Nice explanation you really helped me for my examination

[@WrathofMath]

Thank you! I am glad it helped!

[@Bhaiam233]

Awesome sir. Your explanation is very effective

[@WrathofMath]

Glad it helped! Thanks for watching!

[@lordfnord5768]

In the world where competent people live, however, power sets usually come with matching and rationally placed sets of brackets.

[@tharinmahale9878]

Much better than my uni lecture : )

[@WrathofMath]

Thank you, glad it was clear!

[@nilasteaching6102]

Thank u for this video sir😊

[@WrathofMath]

You're very welcome! Let me know if you have any video requests! :)

[@nilasteaching6102]

Glad that u replied sir....It'll be great if we get some videos related to physics calculations . Just a request sir . 😊

[@Aditya-cw1qf]

Thanks a lot..... Understood everything.... Thanks a lot👍

[@WrathofMath]

Glad to hear it! Thanks for watching!

[@VisaliniKumaraswamy]

Nice explanation... Your channel should have got more subscribers.. And it has got a very nice name... Wrath of Math...

[@WrathofMath]

Thank you very much! Wrath of Math is growing every day, I’m excited to keep growing the channel and reaching more people, and new lessons are coming very soon. If there are any lessons you’d like to see, let me know!

[@VisaliniKumaraswamy]

Could you post more on Fuzzy sets and operations on it especially inference in fuzzy sets...

[@VisaliniKumaraswamy]

Also, a small suggestion, kindly increase the speed of your explanation, I understand that you are making videos for every kind of learner, yet it is what I felt.. Just explain the brewed content in the first 1 min and then explain briefly... It would suit people who are skimming for the answers... Also add a nice thumbnail to the videos...

[@WrathofMath]

I have not actually heard of fuzzy sets before, I will learn more about them at a later date and do a lesson on them when I feel I can teach it effectively. This will probably not be able to benefit you, but hopefully it will benefit others in the future. Thanks for the recommendation! I appreciate that you found the explanation a little slow, I have actually not got that feedback before that I can recall. I do try to make my lessons easy for all to understand, but at the same time, I know some people will need more guidance than others if they are less comfortable or familiar with a topic. For this reason, I have done things like split up videos on similar topics (for example, set intersection and union), but have also recorded a separate lesson that goes over both of them in the same lesson a little faster. Doing something like that obviously takes more time, however, and has the downside of covering the same topic(s) twice instead of adding new topics to the channel. Additionally I think it best, when recording a lesson, to lean towards explaining too much than to risk explaining too little. The reason being that someone who doesn't need that much explanation on a topic can skip ahead and fast forward through explanations and examples they do not need, and still learn from the video, that is, they can take the "excess" explanation out. But if my explanation is not clear enough for someone, they cannot add more explanations and examples into the video in the same way that the other group can take them out. If you find my explanations a bit too slow, and for anyone else who does, I would say try any combination of the following things. 1) Skip through explanations and examples you do not need. If you are on a computer, the "L" key will fast forward 10 seconds, "K" will pause, and "J" will rewind 10 seconds. To make sure that works correctly, you just have to make sure your browser is "focused" on the page playing the video (this is for PC users, but I am not sure about Mac). To do this, simply click the white space to the left of the video. If you are on mobile, double tapping the left side of the video will rewind 10 seconds, double tapping the right side will fast forward ten seconds. Try using those shortcuts to more easily skip parts of lessons you do not need/want! 2) In all of my lesson descriptions, I try to type out an explanation of the content covered in the video. This can be a bit hard sometimes as math notation cannot always be clearly written in a KZbin description, but for some lessons you might find simply reading the description to be enough to understand the material. This will almost always be quicker than watching the video. It is there to supplement the video, or replace it, as needed by the viewer. 3) In my experience the quickest way to learn a math concept is to read it. A definition will usually do if it is a field I am familiar enough with. If you are finding video lessons to be more in depth than you need, or to go slower than you would like, maybe you'd be fine just reading the definition of something rather than listening and watching an in depth explanation with examples. For example (there could be some irony here), if you understand the basics of set theory well enough but do not know any set operations, the written definition of union is probably more than enough for you to understand what the union of two sets is. Thus, reading the definition would be a more efficient and preferable method of learning than to watch a video lesson on it. My point being, sometimes just Googling what you want to learn and clicking on one of the first text-based results will be the quickest way to learn something. Especially if it is something you once knew but you need a quick refresher. I realize this response may be more comprehensive than you expected (again I sense some irony), but I write my comment replies with the expectation that more than just the OP will read them, so should anyone else also find my lessons too slow, I hope these suggestions will either help make my lessons work for them, or help them find a different solution to learning mathematics on their terms. I also want to mention that I don't try to make my lessons slow, per se, I just try to make sure I am in depth, comprehensive, and deliberate with all that I say about the topic at hand. I appreciate the feedback on the thumbnails. I actually used to use more stylized custom-made thumbnails if you look at my older lessons. The reason I stopped is that it takes a lot of extra time to make those thumbnails, and the end product, while it looks nice, has the weakness of not communicating to the prospective viewer what style of video it is. By that, I mean if you look at the old thumbnails, you would not know that the video is an overhead shot of a hand working on paper on a table. Some people might prefer such style of lessons, while others may not, so I wanted to let the viewer know upfront what type of videos the lessons are. That way, they will have a better idea of what they are getting before they click. I do like the look of the old thumbnails, however. And I am happy to say that I am going back to a more stylized thumbnail soon that has the lesson title on it and all that, but will also accurately portray the style of the video. So stay tuned for that! Sorry for the novel, I can really ramble on in these comment sections. Thanks for the feedback!

[@TB12Pats]

Thanks. I have to write a program to find the powerset and I didn't even know what a power set was.

[@mathspointforahsecstudents2431]

beautiful explanation by experienced teacher

[@WrathofMath]

Thanks a lot for watchiing!

[@hyysonin]

Gotta watch this to advance my studies in Grade 7! Hope this works :)

[@WrathofMath]

I hope it helps, thanks for checking out the channel! Let me know if you have any questions and I can try to help clear them up here in the comments or do a video lesson on it! I also just started a live show on the channel, the next episode is this Thursday at 7pm EST, and you can drop by and ask math questions and get them answered live if you're interested! :)

[@hyysonin]

@@WrathofMath Okay! :)

[@intheinterestofafricaokwuw5328]

Thanks for lessons, I will be needing help from your platform in understanding the mathematical economics for the program I am my MSc in financial economics .

[@joel7034]

This class was superb ❤💫

[@WrathofMath]

Thank you!

[@joel7034]

@@WrathofMath ❤💫

[@simphiwedlamini.]

what is the cardinality stuff?

[@WrathofMath]

Thanks for watching! You mean what is cardinality? I have a lesson on it, but the cardinality of a set is just the number of elements in a set, which can be a little tricky to see clearly in power sets. Does that answer your question?

[@simphiwedlamini.]

Wrath of Math thanks for replying but I mean like I didn't understand how you calculated for n....it's always 2^n meaning all the sets will always be of base 2....oh ok i think I just understood while typing it I'm making it difficult on myself....thank you

[@WrathofMath]

Oh yes, just to be sure I will explain it further here. Suppose the cardinality of the set A is n. Then the cardinality of the power set of A is 2^n. Why is this true? Well, we have to think about this question: "How many subsets of A can we create?". When creating a subset of A, we have two choices for each element: include it, or don't include it. Thus, there are 2*2*2*...(n times) = 2^n different subsets of A. Therefore, by definition of power set, the power set of A has cardinality 2^n. Does that make sense? Let me know if you ever have any lesson requests!

[@simphiwedlamini.]

Wrath of Math yes thank you that was exactly it thanks for that +1 subscriber

[@WrathofMath]

That's 1500! Thanks a lot, appreciate the support!

[@usuck2073]

is the power set the family of all sets ? thank you so much !!

[@MikeRosoftJH]

Given set X, P(X), or powerset of set X, is the set of all subsets of X. For example, if N is the set of all natural numbers, then P(N) is the set of all sets of natural numbers; some sets that P(N) contains are the set {1,2,3}, or the set of all odd numbers, or the set of all prime numbers, or the empty set, or the set of all natural numbers itself, and so on. (The theorem is: no set can be mapped one-to-one with the set of all its subsets.) The set of all sets does not exist (the class of all sets is not a set, it's a proper class).

[@_szevn]

I opened a new tab for like 10 seconds and came back to google meet i didnt know what the hell my teacher is talking about, This vid helped me alot at my exams

[@WrathofMath]

So glad it helped, thanks for watching!

[@Annihilater98]

Thanks for solving my problem ❤️

[@WrathofMath]

My pleasure, thanks for watching!

[@Annihilater98]

@@WrathofMath most welcome

[@naif9464]

Thank you very much! Extremely appreciated.

[@WrathofMath]

No problem, thanks for watching! Let me know if you ever have any video requests!

[@PMRESCHRISTOPHERKEENEBALGENIO]

is the {{ } part of the power set counting? Because our math teacher given us a question and he said that it need to be 32 power sets and i gave all the answer and there is still 4 missing to complete 32 power sets... do i need to put in the {{ }so it counts as 1 power set?

[@WrathofMath]

I am not sure what you mean by “the {{}”. Two subsets people often miss when constructing the power set of A are the empty set: { }, and the set A itself. If your power set is missing 4 elements (meaning you have missed 4 subsets of the set being considered), then 2 of the elements you are missing could be { } and the set itself, but I could not give you any idea what the other 2 may be. Have I misinterpreted your question? If you have a more general question about subsets/power sets, I can try to answer that, but if you simply are missing two elements in your power set, you will simply have to look closely and track them down. I will say, however, to have you write out, by hand, the power set of a set with cardinality 5, is a massive waste of time. Reading your question again, I see you said 32 “power sets”, not 32 subsets, so I might have totally misinterpreted your question.

[@jasnoorsingh1570]

I used to study from indian utube class 11 tutors. I found u easier than them

[@WrathofMath]

I'm glad you find my lessons helpful! Thanks so much for watching :)

[@12.aakashmahajan7]

Thanks for making it easy to understand 🙂

[@WrathofMath]

My pleasure - I do my best! Thanks for watching and let me know if you ever have any questions!

[@Mmmmm-vp4dc]

@@WrathofMath um.. hello?! i have homework, and it says, how many elements are there in power set if; ___ does that mean i count all the elements of all the subsets of the original set?

[@Liz-fn2dj]

thank you for this! this is very helpful

[@WrathofMath]

Glad it helped, thanks for watching!

[@pakistaninstituteofmedical7185]

number of elements in power set of {3,4,5,6} will be what

[@WrathofMath]

Thanks for watching and for the question! Check out this lesson and let me know if it helps: kzbin.info/www/bejne/bXSaemuJiNiLl6c

[@pakistaninstituteofmedical7185]

I need more help please my papers are one 15 July 2020 I will be very thankful

[@djefardeur7958]

allright...ready for my test...haha

[@WrathofMath]

Glad to hear it! Hope you did well.

[@djefardeur7958]

yep

[@sehammohmd4727]

You helped so much thank uu♥️♥️🤩

[@WrathofMath]

I'm glad to hear that, thanks a lot for watching!

[@ridafatima8475]

Thanks sir ,👌👍✌️👌 👍

[@WrathofMath]

You're welcome, thanks for watching!

[@siddharthatiwari0001]

Very nice explanation sir .

[@WrathofMath]

Thank you! Glad it was clear!

[@gautamarora6516]

Thank you! That helped me a lot while solving some coding problems :)

[@WrathofMath]

Glad to hear it, thanks for watching!

[@VishnuSingh-dx4jx]

Thank you You are great sir

[@WrathofMath]

Thank you! I am glad it helped.

[@mkgaming0.089]

Can you tell me if set A consists of 4 element, then how many element areinP(A)

[@nivethatommu5741]

2^4=16

[@varunshukla7872]

Nyc and simple explanation... Totally love it

[@WrathofMath]

Thank you! Let me know if you have any lesson requests and thanks for watching! :)

[@varunshukla7872]

Can u make a video on calculus, as a series. That will I really appreciate. Thank you 😊😊

[@WrathofMath]

You mean a whole series on Calculus? It is definitely coming! Sorry I didn't see this comment earlier, not sure how I missed it. Thanks for your support and one of my goals is to have full courses on subjects as opposed to just various lessons, so it will come!

[@varunshukla7872]

Yeah.. It will definitely come in handy.. :) Thanks

[@recklesspotato4816]

What if there's a lot of elements in the subset is there a way to shortcut the power set

[@WrathofMath]

Do you mean if there are a lot of elements in the original set? I'm not sure what you mean by "shortcut the power set". A couple things to know are that the power set of A will have 2^n elements if A has n elements. So if n is big, and we want to write out the power set, we would have to write out all 2^n elements in it. This, of course, is impractical so we use the notation P(A) to denote the power set of A quickly. Hope that helps!

[@mahboobali5210]

what would the answer of P(A)U A be?

[@WrathofMath]

Thanks for watching and I am not sure what you mean. You're asking for the answer, but what is the question? As for the set you named, P(A) U A is, by definition, the set of all elements that are in P(A) or A. In other words, P(A) U A is the set of all elements that are in A or are subsets of A.

[@mahboobali5210]

@@WrathofMath Let's say we use your example A={1,2,3}, would the answer of question P(A)U A just be =P(A)?

[@WrathofMath]

Not quite, because for example, A contains 1, whereas 1 is not an element of P(A) because 1 is not a subset of A. So P(A) U A, which also contains 1, will not equal P(A). Does that make sense?

[@mahboobali5210]

@@WrathofMath so the elements In the power set of P(A) are subsets and in A they are just elements?

[@WrathofMath]

That's correct in this example, but in general there is nothing stopping any set from containing sets or subsets. By definition, every element of P(A) has to be a subset of A. In our case, A = { 1, 2, 3 }, and so A contains numbers, not sets (if you dig all the way down to the foundations of mathematics, you could argue numbers are defined as sets, but let's not go there for now). However we could just as easily consider a set like A = { 1, {1}, { }, {1, 2} }. Here, A contains 4 elements. Three of its elements are sets, including {1} and { } which also happen to be subsets of A. Then, P(A) contains all subsets of A. Point being, the power set isn't special for containing subsets, any set can contain basically anything. Does that help?

[@djprodluigi]

but also some books put 0 are also being one of the elements

[@faheemnazir9502]

Thanks a lot sir!

[@WrathofMath]

You're very welcome!

[@davidriman3732]

why is a null set part of the subset

[@c.danielpremkumar8495]

In all these examples, why is the base 2 used ? (As in 2^n)

[@WrathofMath]

Because there are 2 choices for each element. To count the subsets, we count how many ways we could construct a subset. And in constructing a subset, for each element we have 2 choices - include it or do not include it. Does that help?

[@c.d.premkumar6867]

Thanks very much. I appreciate your explanation.

[@teenworld6130]

buddy what to do if we are asked to find the power of set A (0,0)

[@asadahmadrcs]

Thank you Sir 🇮🇳

[@WrathofMath]

My pleasure, thanks for watching!

[@harleneoyzon2013]

then how to list subsets if the given question were words?

[@WrathofMath]

Could you give me an example of what you mean? I am not sure what you mean.

[@baohsu6695]

I need help! How to find the power set of these? {c,a,{a,c},{{a,c}}}

[@WrathofMath]

We will let the set you described be A. So A = { c, a, {a, c }, { {a, c } } }. Remember that the power set of A, P(A), is the set containing all subsets of A. To start identifying the subsets, you need to make sure you know what the elements of A are, which is usually the trickiest part when we first start dealing with power sets, because it is not always clear. Remember that anything can be an element of a set. The elements can be numbers, or sets, or functions, or anything else. One strategy I found useful was color coding my commas. If a comma separates elements of A, make it one color, any other commas should be a different color. This makes it easy to figure out what exactly the elements of A are. So if you open up the set A, with an open bracket ' { ', you are using the color green (as an example) for your commas. So you write the elements c and a, giving us '{ c, a, ' and those two commas are green. Then, you begin to write the next element, which is itself a set. As soon as you open up a different set, you start to use a different color for your commas until you close that set. So you write '{ c, a, {a, c' and that third comma is red, for example, because it is not separating elements of the set A. Then we close that inner set, so we can go back to using green commas. So we have { c, a, { a, c }, where now the first, second, and fourth commas are all green. Once you have written out a set in this way, the number of elements it has is one more than the total number of green commas (because every element of A has a green comma after it except the last element). Now, let's say you have n elements in A. Then we know the power set of A has to have 2^n elements in it (if you're not familiar with that formula, I just uploaded a lesson on it yesterday explaining what it is and why it works, so you might be interested in that). Now, let's identify the elements of A and see just how many elements are in it. The elements of A are c a { a, c } and { { a, c} }. So A has 4 elements. Thus, the cardinality of the power set of A is 2^4 = 2*2*2*2 = 16. So if you don't have 16 elements when you write out the power set, you know you are missing some. I will start you off by writing all two-element subsets of A. The two-element subsets of A are { c, a } (notice how this is both a subset and an element of A, it's tricky) { c, { a, c } } { c, { { a, c } } } { a, { a, c } } { a, { { a, c } } } and { { a, c }, { { a, c } } }. Those are all of the two-element subsets of A. The power set contains all of those subsets, as well as every other subset of A. I know that the bit about the commas is tough too follow over plaintext, but hopefully this helped. So all you have to do is find the rest of the subsets of A and then put all of the subsets into one set, and that is the power set. Thanks for watching, and please do let me know if you have any lesson requests for the channel!

[@123fyn]

I have one question why we study set ? What are implications of it ?

[@WrathofMath]

Thanks for watching and there are lots of reasons to study sets! In most formulations, set theory is the foundation of mathematics, the barest of starting points with some axioms. That is on its own philosophically interesting; sets are used very often to help describe a result in other areas of mathematics. They will be very important if you study real analysis, for example, where you'd prove calculus. They also are a great place to start trying your hand at real proofs, which make math what it is by my estimation!