PARTIAL ORDERS - DISCRETE MATHEMATICS

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In this video we discuss partial orders and Hasse Diagrams.
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We introduce the concept of asymmetry and partial orders.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

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22 май 2015

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Комментарии : 206

@khaledb8618 4 года назад

It's 4 am rn, and I have an exam at 10, wish me luck

@Jessedegans 4 года назад

How did it go?

@navjotsingh2251 4 года назад

Khaled B first of all, that type of sleeping pattern is damaging to you in the long run please fix this. Second of all, how did you do in the exam?

@rainbow6siege345 4 года назад

@@navjotsingh2251 He's dead

@gmenos6252 4 года назад

Hope your exams went ok

@blizzaroxxx 3 года назад

@Xiorth_YT 8 лет назад

Have my discrete math exam tomorrow morning. Just wanted to say thanks for the videos, they've been great!!

@atidyshirt 3 года назад

Have mine this afternoon, this just saved my ass for antisymmetric relations

@bestyoueverhad.2408 2 года назад

@@atidyshirt have mine this friday

@atidyshirt 2 года назад

@@bestyoueverhad.2408 gl

@goncalomatias3637 2 года назад

Have mine tomorrow ahaha

@bassitirfan7446 Год назад

so howd u guys do?

@grigoryshepelev8149 6 лет назад

I've found this video after I had some struggle with understanding "How to prove it" book, which opened a world of beautifull set theory for me. Thank you for those.

@ShanaAngliang 3 года назад

I like how you mentioned that Hasse Diagrams are used to make relation diagrams clearer, this video has cleared some of my doubts about PO, thank you so much!

@rudyeilabouni 7 лет назад

You have such a great channel man! I'm studying computer Science and our math prof. does nothing except read out definitions and write them on the board all lecture long... You're really helping me understand what we're actually learning! Cheers man!

@eduardorivera508 6 лет назад

Thanks for this. Definitely will start binging on these lectures from now on! I love that you explain what each concept means as you introduce them. My professor just mentions them and sort of expects us to know what it means. If it wasn't for this video, I wouldn't have known to have NOT thought of antisymmetry as "not symmetric". No wonder I was confused the entire lecture. Granted, I could have asked out loud, but our class is very quiet. It seems this course is particularly a very intimidating one.

@MrGreyScreen 9 лет назад

You're a better teacher than my lecturer.

@DanielDupriest Год назад

This is one topic I think I never really figured out from my CS classes. Thank you for the clear and concise explanation!

@MohammedAlAli 7 лет назад

Thanks Trevor. This is helpful for my Advanced Graph Theory class. We are talking about Comparability Graphs as well as partial order and transitive orientation.

@user-sf5bt8eb4y 5 лет назад

hey @TheTrevTutor , you are a god send for your discrete math lessons! you are really doing a good thing here, really helpful for students with crappy lecturers

@D.2023 6 лет назад

Clean, perfect explantation. You helped a lot! Thanks!

@adrianalexisoscar1369 6 лет назад

it's easier if you explain transitive inequalities this way 2

@LuaneCarolineAquinoCavalcanti 8 лет назад

best tutorial about hasse diagrams, thanks !

@miamiboi92 4 года назад

my dawg Trev killin it on the teaching game, thx bruh

@tallalomar3531 5 лет назад

dude you are the best I have seen so far keep up the good work..

@ahmedhussein660 4 года назад

Very clearly explained! Thanks a lot.

@Kri38 8 лет назад

thanks for the video man, really appreciate it!

@andywei8963 5 лет назад

perfect explanations, thanks

@hell4eg 8 лет назад

Thank you for this lessons!

@JamesBrodski 2 года назад

Amazing video. Thank you so much. I will pass my exam because of you.

@AnjaliChadha 8 лет назад

Lucid explanation. Thanks!

@orionwolf-hubbard6895 6 лет назад

Thank you! This was very helpful.

@stelpveri4679 6 лет назад

Thanks for explaining why the diagram looks the way it does

@MRKS8 4 года назад

thumbs up. Clear and concise.

@irmachan1 8 лет назад

Thank you so much, it really did help.

@Omer-es7wo 5 лет назад

thank you soo much, all the best for future videos!!!

@theone0201 7 лет назад

Thanks mate, you've helped alot :)

@pizzapunt7763 Год назад

Very helpful, thanks

@tadiwanashemadongorere2374 Год назад

Amazing work!!!

@baovoquoc6358 8 лет назад

Thanks, sir.

@bkevinF 8 лет назад

Hi @TheTrevTutor, thank you for this one. It makes more sense to answer my modules. And also, do you have something that discuss Operations on Relations? Like Complement of a relations, inverse of a relation, composite product, R restricted to X and Image of x under R.

@saladprayer8239 8 лет назад

Thank you so much, man.

@gazamisehawoh 3 года назад

thank you this really helped me

@novanskaagintaganesha4376 7 лет назад

its very helpful ! thanks sir

@davidjohnson-my6sr 7 лет назад

3:31: the equivalence class of a is {a,b} by reflexivity.

@purnimasaikia7776 7 лет назад

Thank u so much , really very helpful !

@jemand1685 2 года назад

Thanks for the video

@adarsh350 4 года назад

perfect explanation

@Manikandan-nn2bw 2 года назад

Perfecto... And thanks for book suggestion.

@brianc5617 Год назад

Love the videos, thanks for doing them! Minor correction: Hasse diagram's are named after Helmut Hasse with Hasse pronounced as hAss-uh

@jayantabiswas5689 8 лет назад

sir, if u give more video with example of how to find maximal and minimal number n also for greatest nd least elements ,it will b helpful thax for giving this video

@TheYagga 7 лет назад

yes please.. great video

@Aaztha 7 лет назад

Thank You so much!

@GoodBalak 8 лет назад

Great Vid! Cheers!

@marioksoresalhillick299 3 года назад

2:15, that looks absolutely beautiful!

@leocomerford 5 лет назад

0:31 For symmetry, if A has a *particular* relation to B, then we expect B to have *that same* relation to A. If A is related to B then B is *always* related to A in *some* way. If A is the father of B, a very non-symmetric relation, then B is the son of A.

@tinysosig 4 года назад

12:46 Trevor you said "We know in a partial order, everything is going to be symmetric", but I think you meant antisymmetric? Correct me if I'm wrong, wanna make sure I'm understanding this correctly.

@tet5951 2 года назад

same

@purpose_is_empty 2 года назад

He probably actually meant reflexive, because the next step was removing the reflexive arrows.

@mimslilas15 8 лет назад

Thank you for your videos! it makes everything look simple :)

@Trevtutor 8 лет назад

+Marielle Huot Glad I can help :)

@ahmedal-tayy7332 3 года назад

Online Uni is a scam. Im paying 9k this year and all i get is mumbling and a squeaky chair in the recorded lectures. You my man have saved me from failing the maths module in my computer science course.

@pushkar9021 7 лет назад

thank you so much .grt work

@quocbaoha8373 2 года назад

thank you Sir, as Vajazle had said, they had been great

@smoothbrain 2 года назад

Great vid my guy

@nangalucia7lucia667 3 года назад

Thank u Sir. Ur video is helpful. Pls make me understand the difference between equivalence class and equivalence relation and also proofs

@ngelemar 4 года назад

Life saver💯

@-a5624 5 лет назад

my prof has a link to your channel posted on the online website lol. Your channel is definitely more helpful than his lectures...so thank you :)

@utkarshjauhari1443 2 года назад

Useful topics....

@ProphetPakoKadosh 7 лет назад

thanks guys.

@adiletdaniyarov5737 5 лет назад

THe only good discrete math teacher for the whole of the planet

@alialaa8824 7 лет назад

Thank you so much these wonderful videos! I'm having a trouble with reading mathematics notations related to set theory. How can I improve my awareness of reading these notations? I have a course in college that deals with theories of sets and graphs, and I can't understand all the notations especially when it comes to functions and relations that are a bit complex. What do you recommend?

@dellokrd9916 2 года назад

Great Vid

@jandomingo7162 7 лет назад

I couldn't find Partial Orders in the Book of Proof. Does anyone know if it is actually covered in the book?

@neuralworknet 6 месяцев назад

Omg so helpful!

@georghieronymus9935 6 лет назад

Thank you for the informative video. Any prospects for making a video on equivlance classes and partitions?

@IndigoStat 5 лет назад

I owe you my life.

@shivarammuthukumaraswamy7164 4 года назад

Thank you

@surajmu4169 8 лет назад

You have a video on extremal elements in a poset?? This video was good!

@BusaBarnabas 8 лет назад

At 12:48 you mentioned that, "we know that in a partial order, everything is going to be symmetric..." I am quite sure you meant to say, everything is going to be reflexive.

@AirTimeEh 7 лет назад

ya i thought a partial order was if R is reflexive, antisymmetric and transitive. staff.scem.uws.edu.au/cgi-bin/cgiwrap/zhuhan/dmath/dm_readall.cgi?page=20

@evancornish656 6 лет назад

you're right, he made a lot of mistakes in this video.

@xiaoyulyu 3 года назад

I was confused at this part, thx

@tiku.1414 6 лет назад

+TheTrevTutor So is the "=" relation,an antisymmetric relation,because a=b and b = a implies that a = b.

@purpledorii 3 месяца назад

Thank u 🙏

@george4746 3 года назад

Thanks

@lifehts74 5 лет назад

Awesome 😍😍😍😍

@ham8818 2 года назад

Amazing

@sperera5916 7 лет назад

12:41 Hasse Diagram, you said it is Symmetric, please explain how. Thanks

@hlo0o0o0le 3 года назад

thanks

@nadeemjq 5 лет назад

Was the conclusion from 11:10 that the set is antisymmetric or not? Not sure what to make of "Yeah, we're looking good here."

@satyamsinghs786 6 лет назад

I want to know that we delete reflexcivity and transitivity in hasse diagram to make it more clear can i say that 3R1 and 1R2 -->3R2 from hasse diagram since we remove transitivity so i have that doubt plz clear it as soon as possible your lecture are really nice it helped me alot in learning dicrete mathematics thanks for helping us. regards satyam singh IIT BHUBANESWAR INDIA

@nadeemjq 5 лет назад

This video was exceptionally difficult to follow... Several places it's difficult to see how you're thinking. For example, from 10:40, it's not clear how you are checking for reflexivity. You are merely pointing out the pairs, and not making it clear how that is a check for reflexivity. Anyways, been watching your videos from scratch, and they are lifesavers! :)

@njabulomahlalela2912 6 лет назад

You're good bra!

@arkadiuszzdanowski3843 7 лет назад

you're confusing equivalence class and equivalence relation

@JasonJason210 5 лет назад

Thanks. I find 2:45 onwards confusing. Which is set Y?

@NoraAlfraidi 4 года назад

When we draw hoss diagram we have to Remove a reflexive sign?

@SanJeev-md2zl 6 лет назад

Nice lesson topic 👌 OK 👌 👌 👌

@jawdatkour536 6 лет назад

Liked you ....thanks

@deathstalkr_ 6 лет назад

For a given poset can we have more than one Hasse diagram?

@kempisabel9945 5 лет назад

you have saved my exam! TT

@SuegroLM 2 года назад

I was following up quite well until reached around 11:09 where you explained antisymmetry so vaguely in comparison with the previously explained Reflective and Transitive conditions, from my point of view, I would have liked a better elaboration there, to be honest, 😂 was trying to figure out what was all this about but anyway... before that, I may say it had been a great video.

@escape2064 4 года назад

You keep saying "we know partial orders are symmetric" but before that you said they are antisymmetric ..... soo which is it?

@mcsgone4683 4 года назад

Partial orders are antisymmetric (example: if a

@snickerdoodle538 4 года назад

He meant to say reflexive, as he is talking about removing the reflexive edges in the transfer from a graph representation to a Hasse diagram

@MK-mp3cj 6 лет назад

Great

@lobnaabdelhamed1234 7 лет назад

is there any video for closure of relations ?

@Engineer_With_A_Life 8 лет назад

ossum video, now i am cleared with poset but still i confused in symmetric and antisymetric relation both look same :(

@oumaimaalazhari8704 3 года назад

Please where can I find the 3rd part of relations, I really need it

@silentrobi2905 7 лет назад

i think it would be like what I see from the book is: [x] ^ [y] != {} cz their are reflexive elements in those set. isn't it, if I am not wrong sir?

@thunderbeast9831 3 года назад

I have a question, should we not write "x divides y" as y/x ?

@edgardobaldovinojr.3565 8 лет назад

Hi need some help here, 'cuz im really confused about the antisymmetric property, why is that the relation "greater than" considered as antisymmetric and for this T = {(a,c),(b,d),(d,c)} in relation to X ={a,b,c,d} is considered also antisymmetric . :( please i'm so confused

@nethajis1384 8 месяцев назад

How many partial order relations are possible on set of n elements?

@majidalismaili575 3 года назад

Which text book are you using?

@deannac.7199 8 лет назад

I'm a bit confused because my professor introduces antisymmetry as aRb bRa when a does not equal b. So i dont quite u derstand why you say aRb bRa when a=b when that is the definition of symmetry

@Trevtutor 8 лет назад

+Deanna Camacho What we're saying is that if aRb and bRa, then a=b. The definition of symmetry states that if aRb then bRa, so we don't always have that a=b.

@hovhadovah 7 лет назад

Note: symmetry does not mean aRb implies bRa, but rather aRb iff bRa

@Trevtutor 7 лет назад

aRb -> bRa comes out to be that aRb iff bRa. Since 3R2 implies that 2R3 is in the set. But 2R3 in the set implies 3R2 in the set. The simple definition of symmetry is for all a,b, aRb -> bRa.

@amarindersingh8678 7 лет назад

Hey man i have a question. If partial order and total order both are asymmetric, reflexive and transitive then what is the difference between them?

@manuhortet 7 лет назад

A binary relation is a partial order if it is reflexive, antisymmetric and transitive. But inside partial relations, there are other two types of relations: total order and well-order. What I am saying is that every total ordered set is partially ordered too. The conditions for a partial ordered set to be a totally ordered is that every pair is comparable (xRy is always true)

@sperera5916 7 лет назад

I have 2 questions. time line 8:29 1. if 2=2 is reflexive, then why x