We let A = {0} and R = { (0,0) }. The relation R is an equivalence relation because: R is reflexive: for a ϵ A, (a, a) ϵ R, R is symmetric: for a, b ϵ A, if (a, b) ϵ R then (b, a) ϵ R, and R is transitive: for a, b, c ϵ A, if (a, b), (b, c) ϵ R then (a, c) ϵ R.
It isn't equivalent set ig Cuz see It ain't a transitive set, as it doesn't even have a,b,c to begin with So with that logic it can't be transitive, nay???
Thanks Sean! btw I think there is a equivalence relation because it satisfies all three properties. for all x in A (x,x) is in the relation, Since we only have one element in the set, which is just a pair of zero's then we will have symmetry since both the first and last entry of the pair are the same, We fufill the transitive property automatically since there is only one element in the relation.
maybe you could talk about partial order and total order sets ? It's in the same theme ( and to be honest, I didn't fully understand it and you're the best maths teacher on the net, so... pls ? :) )
This is an equivalence relation.for intuition imagine two ellipses(which you will see in every explanation of relation as a mapping pictorial representation) each containing 0 as a member.Since the relation is defined "in" the set {0} which means that the relation is made between the members of same set,the two sets whose members which we are going to relate are equivalent.But for convinience lets name the 1st ellipse as X and the second ellipse as Y with a known factX =Y={0}.Now, in this case 0 in X is related to 0 in Y (so all members of setA is related to itself),so it is reflexive. Since 0 in X is related to 0 in Y implies 0 in X is related to 0 in Y,it is symmetric.Since 0 in X is related to 0 in Y and 0 in X is related to 0 in Y implies 0 in X is related to 0 in Y, it is transitive.Therefore it is an equivalence relation🎉
Mr. Shawn, please make a video on how to calculate all possible relations of a given non-empty set; additionally, how to calculate all possible, minimum and maximum reflexive, symmetric, transitive, identity relations.
This definition of relation is often given, but has drawbacks. Consider the pair-set R={(a,a)}. We can work out if it's transitive, symmetric, or irreflexive just by looking at it, so those are genuine properties of a relation defined that way. But we cannot know if it's reflexive or surjective without specifying a context, because {(a,a)} is a subset of infinitely many Cartesian products. So reflexivity and surjectivity are not properties of R. For example, R is reflexive wrt {a}, but not wrt {a,b}. A better definition of relation is as a triple (X,Y,P), where the pair-set P is a subset of XxY. Then reflexivity and surjectivity can be specified as properties of the relation, since the "context" Cartesian product is part of the object used to represent the relation.
Absolute stunner of a video 🙏🏻 so for this new question I have on this new video (I also asked two on the equivalence relations video), what do you mean by vacuously true transitively? What would be a reflexive that’s vacuously true or a symmetric that’s vacumously true? Thanks kind god!
Hey lovely video and a second question: if we let A = {} do we then say that bill set is an equivalence relation because all three properties are vacuously true? Or is it a non starter since we can’t create an actual relation so no relation exists ? Or can the null set be a subset of null set X null set? Cuz then we can say R = {} also! Right?
I understood everything up until the transitive part in (0,0). I do not know where this comment section keeps getting the non-existent extra (0,0) from
I think the reason you're getting confused is becasue you are looking for two elements in the set {(0,0)}. But if you remember, when we write down sets, we don't repeat the ordered pairs. So in this case, x, y, and z are all 0's. So yes, you could write { (0,0), (0,0)} but that is. the same as {(0,0)} we just don't write it twice like we also don't write down ordered pairs twice in functions, (because it leads to the same point). We could have all the letters of the alphabet in a set, if they are all the same number, then we just write it once.
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my best math teacher ever, i watch every videos and i understand them all. Deadass there should be more recognition for him.
Thanks a lot!
We let A = {0} and R = { (0,0) }. The relation R is an equivalence relation because:
R is reflexive: for a ϵ A, (a, a) ϵ R,
R is symmetric: for a, b ϵ A, if (a, b) ϵ R then (b, a) ϵ R, and
R is transitive: for a, b, c ϵ A, if (a, b), (b, c) ϵ R then (a, c) ϵ R.
It isn't equivalent set ig
Cuz see
It ain't a transitive set, as it doesn't even have a,b,c to begin with
So with that logic it can't be transitive, nay???
THIS WAS SO EASILY EXPLAINED! THANK YOU!
Glad to help! Thanks for watching!
Coming from my official Uni Script: So much this!!! I thought im just to stupid, turns out it was just not really explained there at all.
How did you say cream shaft with a straight face bahahah 🙌
"Let's say Alice is a weirdo and spends time shaking her own hand" 😂 Brilliant!
Thanks Sean!
btw I think there is a equivalence relation because it satisfies all three properties.
for all x in A (x,x) is in the relation,
Since we only have one element in the set, which is just a pair of zero's then we will have symmetry since both the first and last entry of the pair are the same,
We fufill the transitive property automatically since there is only one element in the relation.
maybe you could talk about partial order and total order sets ? It's in the same theme ( and to be honest, I didn't fully understand it and you're the best maths teacher on the net, so... pls ? :) )
This is an equivalence relation.for intuition imagine two ellipses(which you will see in every explanation of relation as a mapping pictorial representation) each containing 0 as a member.Since the relation is defined "in" the set {0} which means that the relation is made between the members of same set,the two sets whose members which we are going to relate are equivalent.But for convinience lets name the 1st ellipse as X and the second ellipse as Y with a known factX =Y={0}.Now, in this case 0 in X is related to 0 in Y (so all members of setA is related to itself),so it is reflexive. Since 0 in X is related to 0 in Y implies 0 in X is related to 0 in Y,it is symmetric.Since 0 in X is related to 0 in Y and 0 in X is related to 0 in Y implies 0 in X is related to 0 in Y, it is transitive.Therefore it is an equivalence relation🎉
Thank you so much for this detailed explanation! This is a lot better than what my professor explains in class. Thanks!
Glad to help - thanks for watching!
Thx for this helpful video. I have a test on this today and I was baffled trying to read the book.😁
You're very welcome, so glad it helped and I hope your test went well!
I think the relation on the set A ={0} does satisfy the equivalence class because if you take the (
You're correct, right on! Thanks for watching!
Hi! could you expand on the (
Mr. Shawn, please make a video on how to calculate all possible relations of a given non-empty set; additionally, how to calculate all possible, minimum and maximum reflexive, symmetric, transitive, identity relations.
This is explained well. It is an important topic which leads to deeper mathematics topics.
Thank you! Indeed it is, and there is definitely a lot more to say on the topic!
This definition of relation is often given, but has drawbacks. Consider the pair-set R={(a,a)}. We can work out if it's transitive, symmetric, or irreflexive just by looking at it, so those are genuine properties of a relation defined that way. But we cannot know if it's reflexive or surjective without specifying a context, because {(a,a)} is a subset of infinitely many Cartesian products. So reflexivity and surjectivity are not properties of R. For example, R is reflexive wrt {a}, but not wrt {a,b}.
A better definition of relation is as a triple (X,Y,P), where the pair-set P is a subset of XxY. Then reflexivity and surjectivity can be specified as properties of the relation, since the "context" Cartesian product is part of the object used to represent the relation.
Absolute stunner of a video 🙏🏻 so for this new question I have on this new video (I also asked two on the equivalence relations video), what do you mean by vacuously true transitively? What would be a reflexive that’s vacuously true or a symmetric that’s vacumously true? Thanks kind god!
Hey lovely video and a second question: if we let A = {} do we then say that bill set is an equivalence relation because all three properties are vacuously true? Or is it a non starter since we can’t create an actual relation so no relation exists ? Or can the null set be a subset of null set X null set? Cuz then we can say R = {} also! Right?
AMAZING!!!
Thanks Kevin!
I love you man
love you too
it looks reflexve
I understood everything up until the transitive part in (0,0). I do not know where this comment section keeps getting the non-existent extra (0,0) from
I think the reason you're getting confused is becasue you are looking for two elements in the set {(0,0)}. But if you remember, when we write down sets, we don't repeat the ordered pairs. So in this case, x, y, and z are all 0's. So yes, you could write { (0,0), (0,0)} but that is. the same as {(0,0)} we just don't write it twice like we also don't write down ordered pairs twice in functions, (because it leads to the same point). We could have all the letters of the alphabet in a set, if they are all the same number, then we just write it once.
Sorry if my explanation is super wordy.
@@chiviza thanks
@@chiviza i was also confused by the same thing, but your explanation makes sense! Appreciate it :D
Cream Shaft
A good man, that cream shaft!