Relations and Functions: What is a Partial Order Relation? (POSET) Part 1

In this video, we define what it means for a relation to be a partial order (POSET). In particular, we define a partial order relation to be one that is reflexive, anti-symmetric, and transitive. We construct a partial ordering by considering a relation and closing it under the three requirements, hence ending with a partial order relation.

[@stephendavol5589]

Thanks for the great explanation!

[@admypz]

Hey this was a really good video. Also the accent is nice :D

[@stapleman007]

I'm pretty sure the only reason the Irish accent exists is to say "partial order". Everytime I hear it, it's like taking a sip of my beverage of choice!

[@yuehanxu5554]

Thank you for your video. That do help me a lot!

[@jeremiahhandcock1795]

very helpful, thank you!!

[@hujukai4815]

the Accent is really nIce

[@lucalaure547]

Hi, great video! quick question though, is the standard ordering of the naturals < a function?

[@MathsAndStats]

Hi Luca, First, a function requires that if a -> b (a mapped to b) and a -> c (a mapped to c) then b must = c. The ordering induced by < can be shown to violate that property. For example, (7, 9) holds and also (7, 10) but 9 != 10. We have two of the same domain value, mapped to different range values, actually; there are an infinite number of range values that allow you to violate the function definition. I hope that helps. Kindest regards. Jonathan

[@CommonMan77777]

Thank you!

[@nagavenkataprakash4837]

In btw y thare is no audio

[@MathsAndStats]

There is. Maybe the problem is with your provider? I've checked the audio and everything seems fine. Regards. Jonathan

[@nagavenkataprakash4837]

@@MathsAndStats Is it??

[@nagavenkataprakash4837]

@@MathsAndStats can u provide more vedios on discrete mathematics

[@MathsAndStats]

@@nagavenkataprakash4837 Here is a playlist covering Relations and Functions: kzbin.info/aero/PLJy0LHDLpgHGit0ZTuQPthM541cI7ZuAR

[@jadex9733]

Please could you make a video on this question: Prove that ⊆ is a partial order on the power set P(S) of a set S. I am incredibly confused by it thanks