Start Learning Sets 2 | Predicates, Equality and Subsets

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  • Опубліковано 1 січ 2025

КОМЕНТАРІ • 40

  • @sebastiandierks7919
    @sebastiandierks7919 4 роки тому +15

    Can't stop hearing "pretty cat"😁

  • @zealous919
    @zealous919 2 роки тому +4

    I really enjoy the way you’ve presented set theory using logic. Have not seen it done this way before! Thank you

  • @theoendre6484
    @theoendre6484 4 роки тому +3

    Great lecture, as always.

  • @evionlast
    @evionlast 4 роки тому +1

    Very good introduction to sets

  • @celkat
    @celkat 4 роки тому +2

    Thank you for your excellent content. Question re determining set equality (around 8:44): how do we, in practice, *check all possible x* with the biconditional? Surely there are too many x for an exhaustive check.

    • @brightsideofmaths
      @brightsideofmaths  4 роки тому +1

      Thanks a lot! In practice, we might have more knowledge about the sets we consider and that is what we surely would use then. Of course, I will deal with practical examples later :)

  • @hftconsultancy
    @hftconsultancy 3 роки тому +4

    For All x in set A (we can see the set above) are planets, Why is it False should it be True? 6:18

    • @angelmendez-rivera351
      @angelmendez-rivera351 3 роки тому +3

      It did not say "for all x in set A," it merely said "for all x."

    • @MrOvipare
      @MrOvipare 3 роки тому

      @@angelmendez-rivera351 I had the same question. Shouldn't we always define the set in which x exists before trying to answer a predicate about it? Otherwise, it seems to me that every predicate using "for all" would carry no information.

    • @angelmendez-rivera351
      @angelmendez-rivera351 3 роки тому +3

      @@MrOvipare That is a very good question. This gets into some technical and difficult details about quantifiers and domain of discourse. For example, there is no such a thing as a set of all sets. There is a class of all sets, but there is no class of all classes. Quantifying over every mathematical object seems impossible without a well-defined notion of "universe" that can avoid the quantification problem altogether. But you are right: in most contexts, where the domain of discourse is restricted, you can talk about universal quantification by specifying sets, and doing otherwise is completely meaningless.

    • @MrOvipare
      @MrOvipare 3 роки тому

      @@angelmendez-rivera351 interesting, thanks for your input! I’m glad to be visit these topics that were not really covered in my engineering physics program. I’m not entirely sure of what a class is, formally, but that will come soon I suppose!

    • @rsmotta
      @rsmotta 2 роки тому

      for me: x = {2, 4, 6, 8,..} so both are false

  • @jungakira
    @jungakira 4 місяці тому

    amazing. Gracias

  • @enasgeravi4372
    @enasgeravi4372 2 роки тому +1

    شكرا و جزاك الله خيرا

  • @AnythingGoesCodes
    @AnythingGoesCodes Рік тому +3

    RIP Pluto

  • @enasgeravi4372
    @enasgeravi4372 2 роки тому

    Thanks

  • @harrisonmacdonald95
    @harrisonmacdonald95 Рік тому +1

    Could you possible update the quizzes on your Steady to be longer and contain more complex/challenging questions? I am happy to support your channel; however, I find that I learn better when quiz questions require me to take the concepts I've learned and apply them in a new way in order to arrive at the correct answer. Thanks for the any consideration!

    • @brightsideofmaths
      @brightsideofmaths  Рік тому +1

      Thank you very much! I am working on more exercises regarding the videos :)

  • @Penrose707
    @Penrose707 2 роки тому

    Danke schön

  • @oldsachem
    @oldsachem 17 днів тому

    Is the null set a subset of every set? Why?

  • @ProFatXuanAll
    @ProFatXuanAll 2 роки тому

    Is it safe to say the statement "all objects"?
    Is the statement assert that there is a set consist of all objects?

    • @brightsideofmaths
      @brightsideofmaths  2 роки тому +1

      It is always good to think in sets. However, for understanding quantifiers, you can just start think of x being anything.

  • @oldsachem
    @oldsachem 17 днів тому

    Isn't it impossible for a set to include infinity as an element?

  • @myexflower
    @myexflower 2 роки тому

    Hello. I have never seen such a set: {2, 2, 2, 3, 3, 5}. What did you mean here?

  • @mohanish007
    @mohanish007 Рік тому

    Do values in quantifiers have domain ?
    like ∀x : x - 1 < x, can x here be anything or can we specify to it to some domain

    • @brightsideofmaths
      @brightsideofmaths  Рік тому

      In this writing x can be anything. However, usually later it always comes from a set.

  • @celestialowl8865
    @celestialowl8865 Рік тому

    If the definition of a subset is only that all values of set A are in set B, cant set B be a subset of itself? Or are subsets not meant to be smaller than the parent set and this is completely valid. I expexted a subset to also be defined as a set which doesnt contain all elements of the parent set.

    • @brightsideofmaths
      @brightsideofmaths  Рік тому

      Yes, equality is definitely possible. It like the less or equal sign ≤

    • @celestialowl8865
      @celestialowl8865 Рік тому

      @@brightsideofmaths Thank you for the fast response, you explained it in the next video immediately haha.

  • @amitsett8117
    @amitsett8117 3 роки тому

    Great content. Do you have a patreon account that people can support you on?

    • @brightsideofmaths
      @brightsideofmaths  3 роки тому

      Thank you very much. I didn't want to confuse people, so I only have Steady (which works exactly like Patreon). For all other people, I just have Paypal: www.paypal.com/paypalme/brightmaths
      Thanks for asking and please enjoy the videos :)

  • @oldsachem
    @oldsachem 17 днів тому

    Isn't the notion of "infinity" logically a predicate with no definite meaning?

  • @emeliakathy3411
    @emeliakathy3411 4 роки тому

    2:32 I like that😍💋 💝💖❤️