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.
🎯 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
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!
@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?
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.
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
Thank you! Let me know if you have any requests!
Honestly You are a Lion in Discrete Mathematics... From Kerala,India .. Keep it up Sir
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.
🎯 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
man this 16 minute video covered so much. thank you and please continue making videos!
Thank you - will do!
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 is my go to guy for discrete maths.
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
Thank you so much 😀
Nothing partial about the quality of this lesson!
😆
Thanks!
Glad to help, thanks so much!
Thank you so much! Clear and informative!
Glad to hear it, thank you for watching!
I dont even speak english that well, and yet i could understand every single thing. Thanks!!
Awesome, thanks for watching!
Thank you so much sir
I was preparing for my entrance exam, and I got your video which was very easy to understand
Glad it helped, good luck!
8:00 literally saved me.
this guy is literally jesus himself re-incarnated as the math god , all hail Shawn
Great Video Helped out a lot, Thankyou!
Very helpful thank you good sir
Do you have a course playlist for Discrete Math?
thanks so much exam is some min away thanks
amazing video!!!!!!!!
Very nice video but I miss that you didn't talk about upper and lower bound :(
Thank you - I definitely still have lots more videos to make about Hasse Diagrams and other discrete math stuff!
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
Thank you! ❤
@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?
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.
@@WrathofMath THANK YOU SOOOOO MUCHHHHH😭😭😭😭😭😭💓💓
bang bang on on
😴Slept literally after knowing this