[Discrete Mathematics] Subsets and Power Sets

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Today we look at subsets and power sets. This includes the empty set, and the power set of the empty set.

[cosmickitty]

Seriously thank you for making all of these. Its really hard to find good help with discreet math and you are the best!

[sizzxrk]

Thanks mate, I've got an exam tomorrow and I think you might have saved my life! Keep these tutorials going! Thanks again!

[JustSipBrewsRS]

At 16:20, A is in fact a subset of the powerset of A, since the only element of A, the empty set, is an element of the powerset of A.

[sgibby]

I just started watching your videos a week or two ago. It had helped me in my class tremendously!!! Thank you!

[JonathanD]

2^6 begins with a 6, 2^5 is 32 ->3+2. Those two are the only two I can remember most of the time. Enjoying your videos as I ready for a final. Thanks for putting them together.

[TheRobel]

Your videos are great for review before an examination. Keep up the good work!

[Aycore]

I enjoy your teaching style and pace bro, you are the raddest

Note: The empty set is a subset of every set because: Let P be some set which the empty set is a subset of, then for All Q such that Q is a member of the empty set implies Q is a member of P. Which is false regardless of what Q is, Q is not a member of the empty set. So the left hand side of the hypothesis is False which means the whole implication is True.

[multicultures]

My professor has a strong accent so I can only understand 10% of what he says. If it wasn't for these videos I would be in deep water. Thanks a lot.

[FrancisHala]

Great tutorials especially for those just starting out, cheers.

[td]

At 15:43, the example you gave of A is *definitely* a subset of its power set. The only element of A, namely the empty set, is certainly a subset of A, and hence in the power set by definition. In general, A is transitive and power sets of transitive sets are transitive as well.

[hfysrrh]

Math Dunce - best explanation for using "2"! Thanks

[AbooddHamdan]

Thank you so much you cleared a lot of confusion, I used to think A is the same as {A}  lol  :|

[grigoriefimovic]

Hey Trev....just an observation in your example of P(P(0)). Does this have any meaning? Since 0 is not a Set, how can we work outward from part is confusing me, thanks

[MegaBdboy]

Is this math taught in university ? Is this good for CS ugrads?I have a course called Discrete Mathematics in my software engineering bachelor.Should this be similar ?

[jaygupta]

I am a tiny bit confused by something. In an earlier video, you said the set A = {1, 2, 3, 1} = {1, 2, 3}.

So, if I have B = {1, 1, 1, ..., 1, 1, 1}, is B a subset of A = {1, 2, 3} or not? Is |B| > |A|, or, because it's redundant, do we discard everything, and end up with B = {1}?

[blakef.]

I need clarification on something. With the set {6, 9, 2, milk}, we could say that the cardinality of the set is 4, correct? But if the empty set is a subset of the set, then couldn't the set be rewritten as {∅, 6, 9, 2, milk}, which would make the cardinality 5 right?

[maxew]

Why is there a power set of a number? (in this case P(0)) ...shouldn't it be P({0})?

[iftekhar]

It says old video, is there a remastered one ? or this will suffice ?

[NigatsuNeko]

Thanks for the video! I have a question. I didn't know a number can be a set. Say, 0. I know that 0 is not the same as {0}. But shouldn't it be possible to represent any set with curly brackets and by showing what's inside? Is there a way to express 0 with curly brackets as a set, if 0 and {0} are not the same? I hope that was clear.

[Elzelgator]

Does Last Question state that we can take power set of a integer or natural numbers? P(S) S--->N ?