Empty Set vs Set Containing Empty Set | Set Theory

What's the difference between the empty set and the set containing the empty set? We'll look at {} vs {{}} in today's set theory video lesson, discuss their cardinalities, and look at their power sets. As we'll see, the power set of the empty set is our friend { {} }! The river runs peacefully in the background as we enjoy the beauty of nature and set theory! #SetTheory #MathOutside

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[WrathofMath]

What stops me from hauling a chalkboard, a camera, a microphone, an easel, a tripod, chalk and an eraser into the woods to film math lectures? NOTHING, that's what! Please share if you enjoy!

[safa-ucmk]

THANK YOUUU, i was so stuck on this 😭
not to self:
it's basically --> { } VS { { } }
empty set vs set containing an empty set

[tomkerruish]

Here's an analogy I came across long ago. A set can be thought of as a box containing its elements. The empty set is an empty box. The set containing the empty set is a box containing an empty box, which is clearly different. (Like all analogies, this one breaks down if you push it too far. For example, we would need to consider all empty boxes to be one and the same empty box.)

[gradientO]

This is really useful, even though I'm studying CS

[davidshi]

I think it helps to think about how you might construct these sets, by removing elements. This is how I make sense of the null set being a subset of every set.

[randomthinkingindividual]

Thank you so much. The discrete structures course is no joke!

[davidshi]

Back to nature, I like it! Very calming. Maybe you should do a proof, Bob Ross style!

[jigarbhatiya]

Ohhh mmyyy gggod 😮 exactly I was searching for this from last 1 day ... Thanks so much 😇😇🙏🙏🙏

[VanshMehta-dvdf]

HEHE. I WAS LAUGHING THROUGH THE ENTIRE VIDEO. COOL. I LIKED THE EXPLANATION. MATH SURE IS INTERESTING.

[sagatparkes]

great explanation. trying to explain this to my kids, but I'll let you do it instead. :)

[philosophyversuslogic]

Thank you for all your videos! But I have to say, I still don't understand. Why ∅ is in every set, and at the same time we can write {}? Either not every set contains an empty set, or there are some sets that don't contain an empty set. Besides, there should be no difference between: {∅, {∅}} and {{∅}} then.

[akae]

But there is a confusing question which is : phi is subset or belong to the set containing empty set ?!

[nasanidgoirnightspring]

what's the difference?
me: letters

[kettle]

you are very charming and easy to listen to

[landback]

The real confusion comes from logic, computers and everyday common sense. If the empty set contains nothing. Then the set that contains the empty set also contains nothing. The container is supposed to be negligible. Stacking empty sets, then using numbers defined by empty sets (ZFC), is circular logic. Computer languages have long optimized this non-sense out; aka, simple graph theory. De-referencing the null pointer. {{{x=1;}}}gets optimized to x=1. So these students are right to be confused, because it's non-sense.

[ritik]

Who is Watching from India ??😉😉

[GTS_RAHU_iq]

Atleast give one example, my problem is not solved 😭

[tysonkoch]

So would {∅} ⊆ {{∅}} be false since ∅ is not an element of {{∅}}?