Intro to Relations | Discrete Math

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  • เผยแพร่เมื่อ 22 ธ.ค. 2024

ความคิดเห็น • 46

  • @skywalkerluke694
    @skywalkerluke694 ปีที่แล้ว +10

    my best math teacher ever, i watch every videos and i understand them all. Deadass there should be more recognition for him.

  • @GarethThompson-pr3vn
    @GarethThompson-pr3vn 4 หลายเดือนก่อน +5

    "Let's say Alice is a weirdo and spends time shaking her own hand" 😂 Brilliant!

  • @MathCuriousity
    @MathCuriousity ปีที่แล้ว +10

    How did you say cream shaft with a straight face bahahah 🙌

  • @azizhani33
    @azizhani33 3 ปีที่แล้ว +11

    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.

    • @fahadf_patel
      @fahadf_patel 9 หลายเดือนก่อน +3

      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???

    • @nura8578
      @nura8578 หลายเดือนก่อน

      @@fahadf_patel It's vacuously true because there's no counterexamples

  • @TusharDeb
    @TusharDeb 2 ปีที่แล้ว +12

    THIS WAS SO EASILY EXPLAINED! THANK YOU!

    • @WrathofMath
      @WrathofMath  2 ปีที่แล้ว +2

      Glad to help! Thanks for watching!

    • @Chetulertusurunu
      @Chetulertusurunu ปีที่แล้ว

      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.

  • @thijsg717
    @thijsg717 2 หลายเดือนก่อน +1

    This man is the goat.

  • @charlesmaurice1047
    @charlesmaurice1047 4 ปีที่แล้ว +3

    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 ? :) )

  • @jingyiwang5113
    @jingyiwang5113 ปีที่แล้ว

    Thank you so much for this detailed explanation! This is a lot better than what my professor explains in class. Thanks!

    • @WrathofMath
      @WrathofMath  ปีที่แล้ว

      Glad to help - thanks for watching!

  • @Victual88
    @Victual88 5 หลายเดือนก่อน

    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.

  • @AnoyingGamersNL
    @AnoyingGamersNL 4 ปีที่แล้ว +3

    I think the relation on the set A ={0} does satisfy the equivalence class because if you take the (

    • @WrathofMath
      @WrathofMath  4 ปีที่แล้ว +5

      You're correct, right on! Thanks for watching!

    • @safa-uc1mk
      @safa-uc1mk ปีที่แล้ว +1

      Hi! could you expand on the (

  • @lolbro2697
    @lolbro2697 หลายเดือนก่อน

    Unbelievable clarity, thank you so much

    • @WrathofMath
      @WrathofMath  หลายเดือนก่อน

      Thanks for watching!

  • @emmanuelceliz7819
    @emmanuelceliz7819 2 หลายเดือนก่อน +3

    Textbooks are increasingly becoming less important with math teachers like this TH-cam channel.

  • @andrewjustin256
    @andrewjustin256 ปีที่แล้ว

    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.

  • @MathCuriousity
    @MathCuriousity ปีที่แล้ว +1

    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!

  • @Suraj-xz8gi
    @Suraj-xz8gi 5 หลายเดือนก่อน

    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🎉

  • @Gernexty
    @Gernexty 3 ปีที่แล้ว +2

    Thx for this helpful video. I have a test on this today and I was baffled trying to read the book.😁

    • @WrathofMath
      @WrathofMath  3 ปีที่แล้ว

      You're very welcome, so glad it helped and I hope your test went well!

  • @md_pedia1
    @md_pedia1 2 หลายเดือนก่อน +1

    Tnx a ton man ❤❤ u r a lifesaver

    • @WrathofMath
      @WrathofMath  2 หลายเดือนก่อน +1

      Thanks for watching!

  • @IbraheemAdebodunFasure
    @IbraheemAdebodunFasure หลายเดือนก่อน

    Thanks for your tutorial it helped alot

  • @christaylor6499
    @christaylor6499 ปีที่แล้ว

    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.

  • @TranquilSeaOfMath
    @TranquilSeaOfMath 3 ปีที่แล้ว

    This is explained well. It is an important topic which leads to deeper mathematics topics.

    • @WrathofMath
      @WrathofMath  3 ปีที่แล้ว

      Thank you! Indeed it is, and there is definitely a lot more to say on the topic!

  • @MathCuriousity
    @MathCuriousity ปีที่แล้ว

    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?

  • @_kevin_wong_
    @_kevin_wong_ 3 ปีที่แล้ว +3

    AMAZING!!!

  • @AshleeKusiima
    @AshleeKusiima 2 หลายเดือนก่อน

    It’s reflexive

  • @amydash796
    @amydash796 ปีที่แล้ว

    I love you man

  • @natsibm2488
    @natsibm2488 3 ปีที่แล้ว +1

    it looks reflexve

  • @labiribiri1901
    @labiribiri1901 ปีที่แล้ว +2

    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

    • @chiviza
      @chiviza ปีที่แล้ว +6

      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.

    • @chiviza
      @chiviza ปีที่แล้ว +1

      Sorry if my explanation is super wordy.

    • @labiribiri1901
      @labiribiri1901 ปีที่แล้ว

      @@chiviza thanks

    • @safa-uc1mk
      @safa-uc1mk ปีที่แล้ว +2

      @@chiviza i was also confused by the same thing, but your explanation makes sense! Appreciate it :D

  • @TheBlimpFruit
    @TheBlimpFruit 4 ปีที่แล้ว +2

    Cream Shaft

    • @WrathofMath
      @WrathofMath  4 ปีที่แล้ว +1

      A good man, that cream shaft!