Sorry i cant understand the part where a-b = 3k, where a-b is divisible by 3. May I know how did you get 3k? as I thought it will be k/3 instead. Sorry!
in case you didn't find out yet, that's a division with elements replaced. like if (15/k) = 3 -> 15 = 3k -> k = 5. so in this problem x - y = 3k, you can see as (x-y)/3 = k. if k is in Z, x-y is divisible by 3.
Hey may I ask a question: let’s say we have an equivalence relation aRb. Why can’t I represent this within set theory as set T comprising subset of Cartesian product of a and b, mapped to a set U which contains true or false? Thanks so much!!
@@HamblinMath hey friend! Sorry for not understanding but would you unpack your reply a bit? I don’t understand why people on Reddit told me relations like equivalence or just symmetrical or just reflexive are “meta” relations and can’t really be seen as relations between two sets and set theory doesn’t allow it.
@@HamblinMath to clarify my second reply to your reply: but I would very much like to know how we can do this with the truth/false as elements of the destination set!
@@MathCuriousity You *can* define a relation as a function from A x A to {True, False}, but I don't see any reason why you would, since the relation itself would be just the preimage of "True." The function doesn't gain you anything.
@@HamblinMath I don’t understand - the whole confusion I have is -if I have a reflexive relation for instance - it seems the ordered pair is of the elements a and b the relation acts on - but where is the “truth” stored ?
Finaly , what I expected...Very clear and to the point...Thank you!
wow thanks a lot, the best video that ive ever found about relations
In my opinion, if you are good at discrete math like this, you are a god damn genius
Best explanation I’ve come by ! Thank you !!!
Crystal clear 🎯
James you just helped me pass my midterm, thank you SO much for this explanation. It was not making sense in my head till now !!!!
Thank you very much.
This video truly deserves 72+1 likes and no dislike.
Excellent video James
Thank you James!
Thanks a lot
Thank you sir
Sorry i cant understand the part where a-b = 3k, where a-b is divisible by 3. May I know how did you get 3k? as I thought it will be k/3 instead. Sorry!
in case you didn't find out yet, that's a division with elements replaced. like if (15/k) = 3 -> 15 = 3k -> k = 5. so in this problem x - y = 3k, you can see as (x-y)/3 = k. if k is in Z, x-y is divisible by 3.
Gabriel thank you!!
Sir kia A intersection B equivalenc hy agar R or S equal houn
love you
Hey may I ask a question: let’s say we have an equivalence relation aRb. Why can’t I represent this within set theory as set T comprising subset of Cartesian product of a and b, mapped to a set U which contains true or false? Thanks so much!!
The mapping is unnecessary. Just make R be the set containing the ordered pairs you want.
@@HamblinMath hey friend! Sorry for not understanding but would you unpack your reply a bit? I don’t understand why people on Reddit told me relations like equivalence or just symmetrical or just reflexive are “meta” relations and can’t really be seen as relations between two sets and set theory doesn’t allow it.
@@HamblinMath to clarify my second reply to your reply: but I would very much like to know how we can do this with the truth/false as elements of the destination set!
@@MathCuriousity You *can* define a relation as a function from A x A to {True, False}, but I don't see any reason why you would, since the relation itself would be just the preimage of "True." The function doesn't gain you anything.
@@HamblinMath I don’t understand - the whole confusion I have is -if I have a reflexive relation for instance - it seems the ordered pair is of the elements a and b the relation acts on - but where is the “truth” stored ?
With examples that are even
could we have your social media to be in touch
thank you sir
thanks a lot sir