Proper Subsets vs Improper Subsets | Set Theory

[@WrathofMath]

Here's a question: how should we name sets? I cover this topic in rap form on my new math rap channel! kzbin.info/www/bejne/gmebp5KNaZWGj9E

[@MathCuriousity]

Love your presentations and may I ask a couple humble questions friend: 1) Can I say a “subset relation” is an equivalence relation since a set is its own subset so it satisfies the reflexive property. But what about the symmetric ? Can I say aRa and trivially aRa so it’s symmetric too? As for transitive this is where I am confusion: if we have a b and c, can the a b and c all be the same object? Like they all are the object “a” so then a is a subset of a and a is a subset of a then a is a subset of a therefor transitive? But if it’s not all “a’s” then we cannot say for sure it’s gonna be transitive right?! 2) I been perusing differing KZbin videos and it seems there are two completely different equivalence relation definitions. Is this because one has to do with set theory and one has to just do with something more basic? Or maybe I’m confused and there is only one definition but it’s explained differently ?

[@sayanmitra9934]

you made me understand so easily thank you! sir. Hope this channel gets popular soon

[@WrathofMath]

So glad it helped, thanks for watching! It is not my words, but your mind and thinking that made you understand! The lessons just help you connect the dots yourself :)

[@SachinKumar-oq7re]

I was confused between subsets and improper subsets as both have same signs to denote and also the answers in Google was not satisfactory but you made clear everything......Thank you so much❤❤❤

[@WrathofMath]

You’re very welcome, so glad it helped! Thanks for watching and let me know if you ever have any lesson requests!

[@gregadams7293]

@2:00--Minor point, but...I learned to write the subset sign as a capital U laying on its side, rather than a C, and all the math fonts I've ever seen look more like a U than a C. FWIW.

[@WrathofMath]

Thank you, that is a more accurate way to describe it indeed! I will keep that advice in tow for describing the symbol to people in the future. I will also add that to the description, thanks again!

[@GLAZE_CLOUD]

I'm in class 6th and your video help me thank you very much 💐 I always watch ur video if I've problems THANKS ☺️☺️☺️❤️"YOU ARE THE BEST"

[@WrathofMath]

So glad the lessons are helpful, thanks a lot for watching! Let me know if you ever have any video requests!

[@anmol3]

thanks. cleared my concepts.

[@WrathofMath]

Glad it helped! Thanks for watching!

[@dr.athilakshmiram5474]

It helped me for Online class. Thank u sir

[@WrathofMath]

You're very welcome, I am glad it helped! Thanks for watching!

[@prathamkune]

Thanks sir your vedio helped me a lot❤❤❤❤❤❤❤

[@NoTimeWaste1]

Thank you so much!! Your explanation was awesome.

[@jyoshnapanigrahi7680]

One of the best maths channels!!!!!!

[@WrathofMath]

Thanks, Jyoshna! I appreciate that, I do my best!

[@prathamkune]

Is a null set a improper set of any set

[@harrisonjervis5819]

Thank you sir for this thorough explanation in minutes.

[@WrathofMath]

Glad to help, thanks for watching!

[@johnaleckpascua5724]

Thank you Sir.Sean it helped me finish my module in minutes tysm

[@WrathofMath]

So glad it helped! Thanks for watching!

[@Vivek_m2104]

Thanks a lot for clearing my doubt sir

[@WrathofMath]

My pleasure, thanks for watching!

[@amanpal6280]

It's worth watching sir 😊😊 Thanks a lot

[@WrathofMath]

Glad to help, thanks for watching!

[@じゃみっと]

Thanks so much!! Very helpful

[@WrathofMath]

Glad to hear it! Thanks for watching!

[@codeTuber033]

Thanks a lot ....my teacher couldn't explain me that but you did sir 😊😊

[@WrathofMath]

So glad it helped! You're welcome and thanks for watching!

[@shinchikudung1125]

After watched many other videos, this is the first video that makes me understand. Thank you sir, you deserved my subscribe

[@WrathofMath]

So glad it helped! Thanks for watching and subscribing!

[@nivearose5694]

thank you, YESSSS this helps!

[@WrathofMath]

Thanks for watching and I am so glad it helped!

[@charliw6075]

absolute lifesaver thank you so much bro you are so clear and concise and teach everything and only what i was looking for !!!!!!

[@WrathofMath]

Glad to help, thanks for watching!

[@MusicToMyEars486]

Ty so much your literally a life saver may god be with u

[@WrathofMath]

Thank you!

[@michaelritzestillore5861]

I watched this video twice and really help me with my homework. Thank you so much this video helped me. God bless you.

[@WrathofMath]

So glad it helped! Thank you very much for watching!

[@yashnegi8021]

Hey! What a great video! Could you please tell how do we represent phi (null set) is a subset of a superset?

[@mesumabbas9481]

You just made your question tricky. A superset is a parent set so you can easily write that { } is *subset* of super set ( or parent set)

[@じゃみっと]

Are φ and ø really the same?

[@kshitijtiwari817]

Thank you sir it helped me a lot 🙌🙌🙌 thanks from INDIA

[@WrathofMath]

Glad to hear it, thanks for watching!

[@ShikhartakGk]

Thanks sir for this video

[@WrathofMath]

My pleasure, thanks for watching!

[@adamabdoni4119]

this really helped, tysm!

[@sergiorobel8884]

Full of respect from Philipines

[@geeth17]

thanks man .....video was awesome.....you cleared my doubt ....may your channel grow

[@WrathofMath]

I'm glad it helped, thanks for watching!

[@geeth17]

@@WrathofMath no problem ...keep the good work

[@ShagunVerma-ou4ry]

Thank you so much. I'm finally clear on the difference between subsets, proper subets and improper subsets. I had been struggling since two weeks for the concept clarification but didn't get a proper answer. But that's no more the case.🙂

[@carenthusiast4666]

Yes it helped. Thank you very much for the explanation. You are a great teacher.

[@WrathofMath]

+Car Enthusiast You are very welcome, I am glad it helped! And thanks a lot! :)

[@markovujanic]

wow my man, I got it. Thanks. Analogy with 3 and numbers where spot on.

[@aswathyypramod]

Omg! Thank you soooo muchhh! I watched a lot of videos &now only I got the concept of improper subset!

[@WrathofMath]

So glad it helped, you're welcome and thanks for watching!

[@Alma60251]

Thanks again, it helped a lot. Your supporter here

[@WrathofMath]

You're very welcome, I'm glad it helped and thanks for your support! Let me know if you ever have any lesson requests!

[@siddhavinayakacharya5409]

sir whether the arrangement of number inside the set should be same in order to become A=B or 2 sets equal

[@WrathofMath]

Are you asking if the order of the numbers in the sets is important? The order is not important! Sets are unordered. So for example, { 0, 1, 2 } = { 1, 2, 0 }. Does that help? Sets are defined entirely by the elements they contain.

[@siddhavinayakacharya5409]

@@WrathofMath sir thank u this is the question i want help from you thank u so much when will you do a live session on youtube

[@WrathofMath]

You're very welcome! I'm not sure. For the three live shows I did, there was not enough of an audience to justify all the time and energy put into it. So in that regard, I will do another show when I have a larger audience, maybe 3,000 subscribers would make for a more active live show. But it is also very hard to answer math questions effectively live, when you don't know what questions will be asked, because it is such a huge subject. There are so many things I once knew how to do that I no longer remember, so I am thinking also of how I can be a more effective live instructor for next time. Thanks for asking though, I know some people are looking forward to the next show, and it will happen!

[@marjoriebautista7690]

GREAT video!

[@WrathofMath]

Thank you!

[@wajidbirhmani1941]

Sir it's good very nice make these types of videos regarding math

[@WrathofMath]

Thanks for watching and it's my pleasure to make them! Let me know if you ever have any video requests!

[@wajidbirhmani1941]

Yes dear sir I study in class 8 in Pakistan I need your help Please send me your WhatsApp number Please

[@techwhizX]

I finally understood 🥳🥳

[@WrathofMath]

Glad to hear it, thanks for watching!

[@reparo423]

Thanks from India 🤗🙏

[@WrathofMath]

You're very welcome, thank you for watching!

[@gokulkrish9166]

whats the difference between super set and proper subset

[@athisii_ekhe6167]

Cleared out my doubt. Thanks.

[@WrathofMath]

You're welcome, I am glad it helped! Let me know if you ever have any video requests!

[@whitesky8013]

Ive been searching this for like a half a day and been watching vids but their point is pointless from what i am looking and from your video 2:02 I already get it so thank you godbless u i wish you blessing and hope that you do more tutorial i iwsh you were my teacher

[@shalamkhan4301]

Nice explanation

[@WrathofMath]

Thanks!

[@orangeinfotainment620]

thank you so much

[@WrathofMath]

Welcome 😊

[@kevinscott8654]

Helpful! thank you.

[@WrathofMath]

+Kevin Scott No problem, glad it helped!

[@yashwiniseth]

What is the difference between an equal set and an improper subset? Please explain it with an example for a set A={1,2,3,4}

[@progaminginternational6799]

They are similar

[@mdshadman9631]

Please explain modulus

[@riddhimasingh2405]

Thank you so much !

[@WrathofMath]

You're welcome!

[@siddhavinayakacharya5409]

sir {0,1}=A and B={0,1,2} here why u are saying that A is subset of B and also A is equal to B at 1:37 and 1:41 help me sir

[@WrathofMath]

I think I understand your question, and it's a good one. It's me being sloppy with my notation that is causing that confusion, I apologize for that. The set A = { 0, 1 } is a subset of B = { 0, 1, 2 } by definition of subset. When I wrote A = B I was just describing the notation. In other words, they're not the same As and Bs, and I could see that being really confusing so I am sorry about that! Does that clear it up?

[@siddhavinayakacharya5409]

@@WrathofMath yes sir

[@aks_2401]

thnx!helped alot

[@WrathofMath]

+Akshat Saini No problem, glad it helped!

[@briannahoff8589]

Cleared up in one minute what I could not understand from the text in one hour. Thanks!

[@khanAbdullah]

Is empty set a proper set or improper set ? And why empty set is a set ?

[@koteswararaovasadi252]

Sir how to find Improper subset formula

[@WrathofMath]

do you mean to find how many improper subsets a set has?

[@anoopfrancismassey3512]

How many proper subsets does the factors of factorial 12 have

[@maryeemrasool2075]

really helpful

[@WrathofMath]

Glad to hear it, thanks for watching!

[@maths.musicofreason7776]

Excellent👍👍👍

[@AtulSingh-hm6gn]

Bro what is a null set is it proper or improper

[@WrathofMath]

The null set (or empty set) is always a proper subset of every set except itself because: a proper subset of A is a set B such that every element in B is in A, but not every element in A is in B.

[@sperera5916]

Thanks alot!

[@WrathofMath]

+S Perera No problem, glad you found it helpful!

[@MAKOS-ky5my]

Throw some game references and you're the next game theory

[@WrathofMath]

Good news kzbin.info/www/bejne/f33dY5KEiM2NnKM

[@MAKOS-ky5my]

YESSSSSSSSSSSS

[@MAKOS-ky5my]

Man thanks you save me arse today I had a test and if it wasn't because of you I. Would have failed

[@WrathofMath]

Glad to be able to help! But you take credit, you did the work to learn the material!

[@isabellabarbour460]

Thank you I can grasp this.

[@WrathofMath]

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

[@PathFindersAcademy]

Phi empty set is improper set but Phi is not equal to A how u say that the set which is

[@WrathofMath]

Thanks for watching and good question! Some definitions of "improper subset" consider the empty set to be an improper subset as well, but most I have seen do not. So just be aware what definition is being used if it is important! In my experience, "proper subset" is usually used to describe a subset of A not equal to A, and if we want it to be nonempty as well we say "proper nonempty subset". Hope that helps!

[@PathFindersAcademy]

@@WrathofMath means that empty is proper set

[@lalalostyou6858]

Thank you so much, God bless you!

[@WrathofMath]

My pleasure, thanks for watching!

[@majidshah2945]

Please answer.... Phi is improper set Or not

[@vorseil3230]

thanks soooo much.. i aced the quiz

[@WrathofMath]

Good work, I'm glad to hear that! You're very welcome and thanks for watching! Let me know if you ever have any video requests!

[@ahmedomed49]

thanks and keep going

[@RajendraSingh-s9p]

Your video helps me a lot. This is a small doubt which can create huge problem in understanding set. Thanks from india

[@altheapalis]

Thank you! 🙂

[@WrathofMath]

My pleasure, thanks for watching and let me know if you ever have any lesson requests!

[@b_evergreen]

Thank you

[@shabhuiyan5122]

Can we say that all proper subsets are improper also?Please reply.I am in confusion

[@WrathofMath]

Thanks for watching and for the question! Proper and improper subsets are mutually exclusive, neither of them can be the other. A proper subset of S is a subset of S not equal to S. The only improper subset of S is S itself. Some definitions will say that "improper subsets" of S are S and the empty set, but even under this definition there is no overlap between proper and improper. This definition defines proper subsets to be nonempty subsets that are not equal to the set itself. I hope that helps!

[@shabhuiyan5122]

@@WrathofMath Thank you for your superb clarification. I didn’t see your reply previously .So, I am somewhat late to give you a big thanks

[@PrashantSingh-hb5ol]

Subset Symbol In set theory, a subset is denoted by the symbol ⊆ and read as 'is a subset of'. Using this symbol we can express subsets as follows: A ⊆ B; which means Set A is a subset of Set B. Note: A subset can be equal to the set. But this is appropriate definition According to it both symbol have same meaning

[@kyfiregaming244]

Thanks i now understand it

[@wowcraft3179]

This helped a lot ....tysm

[@WrathofMath]

I’m glad to hear it helped! You’re very welcome, thank you for watching!

[@nagm1745]

Thanks!

[@WrathofMath]

No problem, thank you for watching!

[@bhuvanbhaskardeo3537]

A very nice video

[@WrathofMath]

Thank you very much! Let me know if you ever have any video requests!

[@bhuvanbhaskardeo3537]

@@WrathofMath of course. Teachers like you make the students feel better and relax

[@ImranKhan-bn1wq]

Easily understood

[@WrathofMath]

Glad it was clear, thanks for watching and let me know if you have any questions!

[@ramansingh8095]

Question : Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ M.... True/false

[@MathCuriousity]

Love your presentations and may I ask a couple humble questions friend: 1) Can I say a “subset relation” is an equivalence relation since a set is its own subset so it satisfies the reflexive property. But what about the symmetric ? Can I say aRa and trivially aRa so it’s symmetric too? As for transitive this is where I am confusion: if we have a b and c, can the a b and c all be the same object? Like they all are the object “a” so then a is a subset of a and a is a subset of a then a is a subset of a therefor transitive? But if it’s not all “a’s” then we cannot say for sure it’s gonna be transitive right?! 2) I been perusing differing KZbin videos and it seems there are two completely different equivalence relation definitions. Is this because one has to do with set theory and one has to just do with something more basic? Or maybe I’m confused and there is only one definition but it’s explained differently ?

[@cyyluvjayy667]

I FINALLY FOUND IT

[@samar9542]

Hello.... Can you solve these questions please? 🥺🥺🥺🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻

[@manjuyadav2755]

How to know that in which question improper subset symbol also tells us a=b

[@WrathofMath]

Thanks for watching and remember that it doesn't tell us A=B, it tells us A=B OR A is a subset of B. That's probably what you meant, just want to be sure! As far as knowing what the symbol means in any given question, you just need to know what your textbook is using and what your teacher is using. Many textbooks have a notation glossary for handy reference. In my experience, using symbols to say A is a proper subset of B is uncommon. So generally if A is a subset of B, A may be a proper subset of B or it may equal B.

[@anjanikeshari6515]

Thank you sir

[@WrathofMath]

My pleasure! Thank you for your continued support!

[@sugandhgarg7226]

If A={1,2,3} then will {} a null set be a proper subset of A

[@WrathofMath]

By the definition in this video yes, and in my experience that is the most common definition. Some people will count empty sets as improper subsets, however. Most commonly in my experience the only "improper subset" is the set itself.

[@kyfiregaming244]

I mean now i understand it thanks

[@WrathofMath]

+Kyrone Miguel Ganongan You are welcome, I'm glad it helped!

[@shalamkhan4301]

Nice explanation

[@siddhavinayakacharya5409]

the video is awesome

[@WrathofMath]

Thank you, I'm glad it helped!

[@OsamaKhanzar]

If a number is not divisible by 3 how a we gonna do to get the correct answer

[@lifeofluxury6823]

good bro

[@komalmangi5210]

Then what is difference between improper and equal set??

[@navjotsayal]

But you must check glossary of symbols of the book u use

[@JehoshaphatAsher]

beautiful!!!

[@WrathofMath]

Thank you!

[@benjiemontas7492]

When youtube is better than school:

[@WrathofMath]

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

[@mgieeeydazai8524]

Thanks!UwU

[@WrathofMath]

You're very welcome! Thanks for watching and let me know if you have any questions!

[@samarjaved9648]

it's very interseting to practice

[@WrathofMath]

Thanks for watching!

[@AayushKumar-vp8ej]

Are ⊆ and ⊂ same? As some authors use both equally.

[@nyiaung8079]

I feel stupid. This is easy!

[@WrathofMath]

Thank you for watching - and since it's easy for you, you should feel smart! What is intelligence if not going from not understanding to understanding over and over again?

[@farrukhff6313]

I'm getting hang of this

[@WrathofMath]

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

[@farrukhff6313]

Thanks

[@edimalo7061]

I still don’t get it.

[@WrathofMath]

Do you have a question I can help clarify?

[@seemaabdool8611]

Oioi bacaca

[@Emmet_Moore]

Your channel name doesn't rhyme in Britain lol

[@WrathofMath]

Haha I know, another viewer told me that recently. Oh well, I still think it's a fine name! Thanks for watching! And stay tuned for my new Britain-based soup channel, Wrath of Broth!

[@ElnathanBehailu]

Thank you so much ☺

[@WrathofMath]

My pleasure, thanks for watching!

[@gokulkrish9166]

whats the difference between super set and proper subset

[@yashdodo]

Thank you sir .

[@WrathofMath]

No problem, thanks for watching!