Power Set of the Power Set of the Power Set of the Empty Set | Set Theory
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- เผยแพร่เมื่อ 5 ก.ย. 2024
- The power set of the power set of the power set of the empty set, we'll go over how to find just that in today's set theory video lesson! We'll also go over the power set of the empty set, the power set of the power set of the empty set, and we'll se the power set of the power set of the power set of the power set of the empty set (yes, really).
Watch me eat bugs and prove Pythagoras: • Eating BUGS and Provin...
Power set of the empty set: • What is the Power Set ...
Why the empty set is a subset of every set: • Why is the Empty Set a...
What is a power set: • What is a Power Set? |...
Cardinality of a set: • What is the Cardinalit...
Power set examples: • Finding Power Set Exam...
Finding the number of subsets of a set: • Finding the Number of ...
Formula for cardinality of power sets: • Formula for Cardinalit...
What is a subset: • What is a Subset?
How to identify the elements of a set: • How to Identify the El...
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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 so much! I am glad you have found the videos and insightful and be sure to let me know if you ever have any video requests!
11:10 "if we wanna be crazy... what would that bad boy be"😂😂😂😂😂😂😂
I love learning power sets even though I am 8 years old what is the set of set be though I know the set a but I don't know b or c
keep on learning kid, I can give you some pdf's about this stuff but they might be too dificult
Bruh I am being taught about this in school for the first time and I am double your age 💀
Slow down kid...
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
So glad it helped! Thanks a lot for watching and let me know if you ever have any questions!
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
Interesting video but also
What's Cardinality of P{P{1,2}}?
Iam from India cool teaching sir
Thanks a lot! Let me know if you ever have any video requests!
No sir
thank you very much
My pleasure, thanks for watching and let me know if you ever have any questions!
Thank you so much sir love from india 🇮🇳 .
That last one is hilarious. Great lesson! :)
You are good teacher
Thanks a lot!
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).
Nice question. One I never thought to ask myself.
Best kind of thumbnail too -- One that invites you to solve it before you even click.
Thank you so much! This was very helpful!!!!!
You're very welcome, I am glad it helped and thanks for watching!
Hello
From which video should we start to understand Sets subject from very beginning?
For the next iteration, run this on the Sage Cell Server:
list(powerset(powerset(powerset(powerset(powerset([]))))))
I don't know if I want to subject my eyes to such an abomination
@@WrathofMath lol
This was a huge help!
So glad to hear it, thanks for watching!
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.
thanks a lot buddy
Glad to help!
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?"
No you won't, because there is nothing weird or exceptional about a set with no Lambos in it!
@@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.
best explanation
Thanks Kabir, glad it was helpful!
I have a doubt in that 6th set of last question,,,how did u get that?
ALHAMDULILLAH! I solved it very well.
5:05 of this bad boy😂😂😂
Sir, what will the power set of a={φ,1,2}
1:58 Where can I find that video?
If you to a shot of vodka every time he said "set" you would be definitely dead now.
Sir, I have a doubt.
Never knew Logic was a math genius.
What's the difference between p(0) and p({0}) ?
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?
@@WrathofMath it just got interesting because p(p(0)) is also = {0, {0}}... now I'd like to know if p(p(0)) and p({0}) have the same definition
What about P(A) if A=( 1, (1,2), (1,2,3) ?
Starts at 1:20
For the chaos of Maths!! XD
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!
Can I share with you
It was precisely at 2:28 that I shit myself.
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.
Yo dawg, I hear you like the empty set
Who spilled the beans on that one??
solution in such a way that u write Pn(ø) in terms of Pn-1(ø)
Take a shot every time he says set.
Thanks for watching - but bad idea! If you really need more excitement with your set theory, check out my rap on naming sets! th-cam.com/video/L68v_W40SYo/w-d-xo.html
Ta
what if A=Ø ?
Thanks for watching, I am not sure what you mean by your question. This video was all about the empty set and its power sets.
5:58 what a joke😂😂😂
@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
th-cam.com/video/H5D6EAezsXQ/w-d-xo.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?
0:00 that intro caused disrespect..... bad intro. Are you dissing set theory
Nicki Minaj is the Queen of Rap
Thank you so much. It was really really helpful.
That's what I like to hear, thanks for watching!