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...
Discrete Math playlist: • Discrete Math
Discrete Math exercises: • Discrete Math Exercises
◉Textbooks I Like◉
Graph Theory: amzn.to/3JHQtZj
Real Analysis: amzn.to/3CMdgjI
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
Statistics: amzn.to/3tsaEER
Abstract Algebra: amzn.to/3IjoZaO
Discrete Math: amzn.to/3qfhoUn
Number Theory: amzn.to/3JqpOQd
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons
◆ Donate on PayPal: www.paypal.me/wrathofmath
Thanks to Petar, dric, Rolf Waefler, Robert Rennie, Barbara Sharrock, Joshua Gray, Karl Kristiansen, Katy, Mohamad Nossier, and Shadow Master for their generous support on Patreon!
Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: crayonangel.bandcamp.com/
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● Facebook: / wrathofmath
● Twitter: / wrathofmathedu
My Math Rap channel: / @mathbars2020

Пікірлер: 37

  • @shayanzaidi2836
    @shayanzaidi28364 ай бұрын

    Getting through discrete maths without a teacher is an absolute nightmare. I'm so glad I found your channel!!

  • @Xorked
    @Xorked Жыл бұрын

    Honestly the best math channel I've seen for Discrete Mathematics, great work

  • @WrathofMath

    @WrathofMath

    Жыл бұрын

    Thank you! Let me know if you have any requests!

  • @jingyiwang5113
    @jingyiwang511311 ай бұрын

    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!

  • @AManWithaZ
    @AManWithaZ Жыл бұрын

    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.

  • @Eggtamaa
    @Eggtamaa8 ай бұрын

    man this 16 minute video covered so much. thank you and please continue making videos!

  • @WrathofMath

    @WrathofMath

    8 ай бұрын

    Thank you - will do!

  • @punditgi
    @punditgi Жыл бұрын

    Nothing partial about the quality of this lesson!

  • @djdanzo206

    @djdanzo206

    Ай бұрын

    😆

  • @ea1766
    @ea1766 Жыл бұрын

    This is my go to guy for discrete maths.

  • @Leo-ng7lq
    @Leo-ng7lq18 күн бұрын

    I dont even speak english that well, and yet i could understand every single thing. Thanks!!

  • @WrathofMath

    @WrathofMath

    17 күн бұрын

    Awesome, thanks for watching!

  • @DrunkenJanitor
    @DrunkenJanitorАй бұрын

    Great Video Helped out a lot, Thankyou!

  • @joanofarc108
    @joanofarc108 Жыл бұрын

    Thank you so much! Clear and informative!

  • @WrathofMath

    @WrathofMath

    Жыл бұрын

    Glad to hear it, thank you for watching!

  • @priya-fz5pj
    @priya-fz5pj8 ай бұрын

    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

    @WrathofMath

    8 ай бұрын

    Thank you so much 😀

  • @AC-vp8fb
    @AC-vp8fb3 күн бұрын

    Very helpful thank you good sir

  • @ruixiaozheng
    @ruixiaozheng6 ай бұрын

    amazing video!!!!!!!!

  • @musicheals2263
    @musicheals22632 ай бұрын

    Thank you so much sir I was preparing for my entrance exam, and I got your video which was very easy to understand

  • @WrathofMath

    @WrathofMath

    2 ай бұрын

    Glad it helped, good luck!

  • @hiklnh
    @hiklnh3 ай бұрын

    thanks so much exam is some min away thanks

  • @roblox21242
    @roblox212429 ай бұрын

    Do you have a course playlist for Discrete Math?

  • @nadred5396
    @nadred53968 ай бұрын

    this guy is literally jesus himself re-incarnated as the math god , all hail Shawn

  • @myronparaskevopoulos2341
    @myronparaskevopoulos23418 ай бұрын

    🎯 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

  • @alexandrosvardakostas6270
    @alexandrosvardakostas6270Ай бұрын

    Thanks!

  • @WrathofMath

    @WrathofMath

    Ай бұрын

    Glad to help, thanks so much!

  • @promisingnotes8597
    @promisingnotes85975 ай бұрын

    Is the "maximun" and "minimum" the same as "upper bound" and "lower bound" respectively?

  • @the.graduate
    @the.graduate20 күн бұрын

    You earned one more suscription by this vid!❤ love you to deaaaaaaath

  • @WrathofMath

    @WrathofMath

    20 күн бұрын

    Thank you! ❤

  • @the.graduate

    @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

    @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

    @the.graduate

    20 күн бұрын

    @@WrathofMath THANK YOU SOOOOO MUCHHHHH😭😭😭😭😭😭💓💓

  • @rtxa
    @rtxa4 ай бұрын

    Very nice video but I miss that you didn't talk about upper and lower bound :(

  • @WrathofMath

    @WrathofMath

    4 ай бұрын

    Thank you - I definitely still have lots more videos to make about Hasse Diagrams and other discrete math stuff!

  • @mrboyban
    @mrboyban Жыл бұрын

    bang bang on on

  • @wednesdayaddams718
    @wednesdayaddams7188 ай бұрын

    😴Slept literally after knowing this