Partially Ordered Sets and Hasse Diagrams | Discrete Math
We cover posets (partially ordered sets) and Hasse diagrams that represent them. We'll see examples of sets with partial orders on them, beginning with a power set and the subset relation. Partial orders are reflexive, transitive, and antisymmetric, which we discuss with examples. We also cover the construction of Hasse diagrams, as well as minimal, maximal, minimum, and maximum elements of a partially ordered set. #discretemathematics
Lesson on Hasse Diagrams: • Hasse Diagrams for Par...
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Пікірлер: 37
Getting through discrete maths without a teacher is an absolute nightmare. I'm so glad I found your channel!!
Honestly the best math channel I've seen for Discrete Mathematics, great work
@WrathofMath
Жыл бұрын
Thank you! Let me know if you have any requests!
I am really grateful for your patient and detailed explanation. This has helped me a lot as I am previewing for my discrete mathematics class for the coming fall semester. And I think that your videos are among the best discrete mathematics tutorial. I can watch your videos regularly as I proceed with my next semester as well. Thank you so much!
This video is a really great break-down on the fundamentals. PO sets and Hasse Diagrams have recently been on my mind because I've been trying to teach myself a subject involving filters and ultrafilters, and Hasse Diagrams are a great way to visualize them.
man this 16 minute video covered so much. thank you and please continue making videos!
@WrathofMath
8 ай бұрын
Thank you - will do!
Nothing partial about the quality of this lesson!
@djdanzo206
Ай бұрын
😆
This is my go to guy for discrete maths.
I dont even speak english that well, and yet i could understand every single thing. Thanks!!
@WrathofMath
17 күн бұрын
Awesome, thanks for watching!
Great Video Helped out a lot, Thankyou!
Thank you so much! Clear and informative!
@WrathofMath
Жыл бұрын
Glad to hear it, thank you for watching!
He is the best.. every time i have a doubt..there is never a chance it's not cleared by watching his videos..keep up the good work
@WrathofMath
8 ай бұрын
Thank you so much 😀
Very helpful thank you good sir
amazing video!!!!!!!!
Thank you so much sir I was preparing for my entrance exam, and I got your video which was very easy to understand
@WrathofMath
2 ай бұрын
Glad it helped, good luck!
thanks so much exam is some min away thanks
Do you have a course playlist for Discrete Math?
this guy is literally jesus himself re-incarnated as the math god , all hail Shawn
🎯 Key Takeaways for quick navigation: 00:27 📚 *A partially ordered set (poset) is defined by a relation that is reflexive, anti-symmetric, and transitive.* 02:48 🛠️ *The power set of a set, with the subset relation as the partial order, forms a poset.* 05:42 🔄 *Hasse diagrams visually represent posets without the need for arrows by ensuring a consistent direction of the relation.* 11:53 📈 *Maximal elements in a poset relate only to themselves and can be found at the tops of components in a Hasse diagram.* 13:24 📉 *Minimal elements in a poset relate only to themselves and can be found at the bottoms of components in a Hasse diagram.* Made with HARPA AI
Thanks!
@WrathofMath
Ай бұрын
Glad to help, thanks so much!
Is the "maximun" and "minimum" the same as "upper bound" and "lower bound" respectively?
You earned one more suscription by this vid!❤ love you to deaaaaaaath
@WrathofMath
20 күн бұрын
Thank you! ❤
@the.graduate
20 күн бұрын
@WrathofMath Hey, can I ask you a question?! When you say (A, R) is a POset, how do you read (A, R)? I mean, what these symbols ( , ) represent here? Does it mean that A has an R relation in its elements?
@WrathofMath
20 күн бұрын
That's correct, in general (A,R) is fairly ambiguous notation and can mean a lot of things, but in context we understand (A,R) is the set A with the partial order relation R on it.
@the.graduate
20 күн бұрын
@@WrathofMath THANK YOU SOOOOO MUCHHHHH😭😭😭😭😭😭💓💓
Very nice video but I miss that you didn't talk about upper and lower bound :(
@WrathofMath
4 ай бұрын
Thank you - I definitely still have lots more videos to make about Hasse Diagrams and other discrete math stuff!
bang bang on on
😴Slept literally after knowing this