Power Set of the Power Set of the Power Set of the Empty Set | Set Theory

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).

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+

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[Arcvx]

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.

[migfed]

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.

[paulkline]

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

[garvitjain]

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

[subhashchouhan]

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

[TrueSpeak-TS]

11:10 "if we wanna be crazy... what would that bad boy be"😂😂😂😂😂😂😂

[jdbsksnb]

Thank you so much sir love from india 🇮🇳 .

[mike_the_tutor]

For the next iteration, run this on the Sage Cell Server:

[yhiuics]

Interesting video but also
What's Cardinality of P{P{1, 2}}?

[Daetelus]

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.

[anon]

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.

[rohankaramel]

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).

[ser]

Hello
From which video should we start to understand Sets subject from very beginning?

[-by-_Publishing_LLC]

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?"

[brandonzappanti]

That last one is hilarious. Great lesson! :)

[norbertk.]

If you to a shot of vodka every time he said "set" you would be definitely dead now.

[bhartisubodh]

I have a doubt in that 6th set of last question, , , how did u get that?

[ahmedhomoeoclinic]

Sir, what will the power set of a={φ, 1, 2}

[montshoomosweu]

What's the difference between p(0) and p({0}) ?

[enochofori]

What about P(A) if A=( 1, (1, 2), (1, 2, 3) ?