Antisymmetric Relations | Discrete Mathematics

[@WrathofMath]

Correction: At 1:30, the divides relation should have (2,6) in it.

[@swafly]

Oh man, I was having the hardest time understanding why some guy was saying that this relation is Antisymmetric. This cleared it up so much! Thank you

[@WrathofMath]

My pleasure, thanks for watching!

[@the.graduate]

Another masterpiece!❤ Thanks for answering my basic question, too! I'll be back for more!

[@WrathofMath]

Thanks so much! Let me know if you ever have any more questions!

[@Yahya-gb8zn]

I have been sitting here for an hour trying to understand this concept, and you just nailed it!

[@jingyiwang5113]

This is such an amazing video! I have been confused with this point for a really long time. I finally understand it. I am really grateful for your clear explanation!😀

[@WrathofMath]

So glad to help - thanks for watching!

[@changggul6663]

just found out that this video was posted 3 days ago, and I have exam about this 30 minutes laterr!! YOU HELPED ME A LOT! Thank you!

[@WrathofMath]

Thanks for watching, so glad I could help! Hope the exam went well!

[@changggul6663]

@@WrathofMath Just a quick update, I think I passed the exam LMAO just messed up the equivalence classes a little bit >.

[@slasankautube]

Perfect explanation in few second , i have solve all my problems from your single video , thanks lot bro

[@WrathofMath]

Glad to hear it - thanks for watching!

[@8ARSH8]

Greeting from Mauritius island...thanks so much for the video man, it really clear things for me😇

[@satabd]

Very clear, thank you, It helps my son to understand this subject

[@arimaulanaid]

Thank you for the explaination, now i get that not-symmetric and anti-symmetric is a different thing.

[@WrathofMath]

Glad to help!

[@tasnovashahrin5477]

Thank youuuu!!!!!!!

[@YuFow]

Fantastic, cleared all of my confusion within the first minute, thank you so much!

[@rickgrimes47]

Holy Maths! This channel is magnificent!

[@WrathofMath]

Thank you Pulkit! Let me know if you ever have any questions!

[@mj47_dreamer]

Very clear, thank you so much!!!!!

[@rahulshendre7089]

congrats for 100k subs man

[@WrathofMath]

Thank you!

[@EhsanulHaque-g8g]

you earn one more Subscriber Sir.

[@WrathofMath]

Thank you!

[@vivienshaanika]

well explained ..🙌🙌👏

[@WrathofMath]

Thank you 🙂

[@sourabshaik3741]

Finals Tomorrow! your channel is so helpful, thanks a ton!

[@WrathofMath]

Thanks so much, good luck and let me know if you ever have any questions!

[@maxwong3903]

Ty very much for the help! Really appreciate the work u put in!

[@WrathofMath]

My pleasure, thanks for watching and let me know if you have any requests!

[@ClamChowderSoup]

Thank god for this. I kept having trouble due to the x=y condition. I thought it was something necessary in order for things be antisymmetric. Turns out it’s just there for a disclaimer on reflexive pairs

[@WrathofMath]

I can totally see how that would be confusing. There are so many different ways a definition can be worded, and some ways are definitely clearer than others. I'm glad this could help!

[@nadred5396]

this guys a god

[@WrathofMath]

hurry up with my damn croissant

[@nadred5396]

@@WrathofMath sorry for the delay, got you the espresso too boss

[@dip-c5z]

But sir, in your first example given set A = {1,2,3,4,5,6}, how did (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) become antisymmetric?

[@8ARSH8]

antisymmetric definition: whenever we have (a,b) in set R , we will never have (b,a) in set R ,unless (a=b), so (1,1)(2,2)... can be present.😇

[@tosiah919]

At the 5:00 minute mark i dont understand how its antisymetric. Doesnt 1 relate to 1 in the (1,1) . Would it still be antisymetric if you added another (1,1) ( so now its two (1,1)'s ) the same way you added (4,2) to fight the (2,4)

[@tosiah919]

hmm nevermind i think i get it. In the next example at the 7:17 mark you say (a,a)(b,b) is antisymetric and you keep saying keyword: distinct so im guessing it must be two different numbers like how you said (a,b) (b,a) is not antisymetric which explains the (4,2) with (2,4) not being antisymetric . The (a,a) (b,b) explains why with (1,1) being exact same still antisymetirc because they are not distinct from each other

[@WrathofMath]

That's correct! For antisymmetry, when aRb and a is not equal to b, bRa must be false.

[@白小雪]

Why two distinct element is never related but still consider symmetry?

[@twolip2]

I've heard of another term 'asymmetric'. Whats the difference between antisymmetric and asymmetric? Also, thankyou so much for explanation🙌🙌

[@WrathofMath]

Asymmetric isn't really a common math term as far as I've seen, but it could be used to simply describe a relation which is not symmetric. Any relation with a pair (a,b) but not (b,a) would be an asymmetric relation. On the other hand, antisymmetry requires there is NO pair (a,b) where (b,a) is also in the relation. "Symmetric" requires all symmetries "Asymmetric" requires it not symmetric "Antisymmetric" requires all asymmetries, that is - if a relates to b then b does NOT relate to a.

[@twolip2]

@@WrathofMath got it, thankyou!

[@HarryInShape]

{(-2, 2), (-1, 1)} is it symmetric? is it antisymmetric?

[@adrianlowery4764]

Thank you thank you thank you!

[@WrathofMath]

So glad to help - thanks for watching!

[@sudjwgi1846]

legend👍

[@WrathofMath]

appreciate ya 👍

[@cyanoswag]

Thank you

[@CBanks-ql9xu]

Can you make a video on PMI?

[@WrathofMath]

Thanks for watching and the request! What about PMI do you want? I have plenty of proofs by induction, do you want a proof of the principle using the well-ordering principle? Or just an overview of the principle?

[@CBanks-ql9xu]

@@WrathofMath an overview of the principles please. Not so much a worked example but how to think through an induction problem. I find myself getting stuck half way through these types of problems

[@mahamadoudahani1095]

man you are good

[@WrathofMath]

Glad to help!

[@anriaskarovi935]

İ have a question why did you write (5,2) 5 not devides 2 nor 2 devides 5

[@anriaskarovi935]

4:13

[@yamatanoorochi3149]

thanks man

[@WrathofMath]

Happy to help!

[@georgelloyd2795]

you are still amazing

[@Jayygon-iv8wt]

why isn't (2,6) in the relation? am i missing something?

[@WrathofMath]

Nope, that's my bad! (2,6) should be in there

[@shahngofsyg7818]

Thanks

[@WrathofMath]

Glad to help!

[@jacobgurung6784]

Which note taking app is this?

[@WrathofMath]

Notability! It was really good, then they ruined the tool bar, now a lot of people (myself included) do not like it nearly as much.

[@aravindpradeep1265]

Super clear explanation Thank you sooo much! ❤️ You deserve way more subscribers.

[@WrathofMath]

Thank you! Glad to help!

[@ahmedsaid3434]

tHE GOAT

[@WrathofMath]

THANK YOU

[@elsenorperez3591]

fantistic

[@jihbdin1890]

Not clear

[@WrathofMath]

Sorry it didn't help, any questions I can help clear up?

[@georgelloyd2795]

you are still amazing

[@WrathofMath]

Thanks, George!