I think I asked a question about this in one of your other videos, and now I conveniently stumble upon this... Thanks a lot for the explanations! You're a life saver.
So glad it helped! Thanks for watching and it is my pleasure! Let me know if you have any questions, I try to respond to all the ones I can, but I do miss some!
This is a real beautiful math lesson, I cannot be grateful enough with you for delivering such a pleasure of topics. Yes I do know this is a topic displayed in any set theory book but what you can grasp just reading a book compared to the level of insight you get from this channel has a substantial significance. Thank you again so deeply.
Thanks a lot!!I am from India....Most cool thing about the video was the usage of different colours to write empty elements to get rid of the confusions.....Thanksssss
I am from India, I did not understand such questions of sets at all, thank you sir your way of explaining is very easy . I have shared your youtube channel with all my friends. Thankyou sir for your great explanation on this topic . Plz. Sir also make a video to solve physics, maths and chemistry in numerical in easy way
Cool thing I noticed was that the cardinalities of repeated powersets follow a sequence that is defined under tetration: ^n2(n is raised before the 2).
Technically (and logically), the correct conclusions to be drawn from the fact that a set is not a subset of A are 1) the proposition, "All the elements in the set are elements in A," is false, and 2) the set itself is not an element of A. So, since the empty set has no elements, then the proposition, "All the elements in the empty set are elements in A," is false. Therefore, if the empty set is not an element of A, then it's not a subset of A. I figure the real reason the empty set is always included in the power set is just because it's a convention, perhaps because it simplifies something somewhere. Though, I don't know what or where.
4:20 *_"The empty set isn't super weird. It's just a set that has no elements."_* ... So, you think that having a "set of no objects" isn't weird? Will I be able to impress the ladies with my beautiful "set of no Lamborghinis?"
@@WrathofMath All kidding aside, there is no such thing as an empty set (or "null set"), nor can a set be a _"collection of nothing."_ ... It's just one of those interesting things humanity comes up with to get around complex problems. Excellent video, by the way.
Thanks for watching and for the question! If you don’t have any typo in your question, then the answer is P(0) is not defined, and P({0}) = { {}, {0} }. {0} is just the set containing one element: 0, so we can take the power set of that easily. However, 0 is not a set, so we cannot take P(0). The power set function is only defined on sets. Does that help?
There would be no chaos like writing the power set of the power set of the power set of the power set of the power set of the empty set! I hope I never have to do it!
At least I gave a warning that there would be a lot of "set" haha! I shit myself when I did a take of this lesson, including the gigantic power set at the end, and realized there was a significant error earlier in the lesson, so had to do it all again!
@@WrathofMath NOOOOOOOOOOOOOOOOO. Minor error, major regrets. It all led up to helping me understand my HW question though so thanks for the good work.
Thanks for watching - but bad idea! If you really need more excitement with your set theory, check out my rap on naming sets! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-L68v_W40SYo.html
@Wrath of Math: I am a little confused. You said that every set is a subset of itself which actually makes sense to be but I was watching The Trev Tutor says it is not always the case (see his explanation at 12:05). I am confused. Which one is it? Please explain. Thank you ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-H5D6EAezsXQ.html
Thanks for watching Shubeg! I looked quickly at the video and timestamp you provided, and in that part of the video TrevTutor says that every set is a subset of itself. He says every set is an element of its power set, which means it is a subset of itself. On the other hand, he points out NOT every set is a subset of its power set - that is totally different. Does that make sense?