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

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[shayanzaidi]

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[Xorked]

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[anesp.a]

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[Eggtamaa]

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

[myronparaskevopoulos]

🎯 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.*

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[AManWithaZ]

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.

[jingyiwang]

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[DrunkenJanitor]

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[roblox]

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[seven-rz]

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

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[Liichess]

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[rtxa]

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