Definition: Russell's paradox

Russell's paradox is a standard way to show naïve set theory is flawed.
Naïve set theory uses the comprehension principle. This states that 'given any property there exists a set containing all objects that have that property'.
Russell's paradox demonstrates the looseness of this definition leads to a contradiction.
Consider the set defined by the property:

'The set of all sets which don't contain themselves.'
You will see in the video that this leads to a contradiction.

[drfpslegend]

this is actually one of the few videos that understandably explains the motivation behind Russel's paradox. I applaud you :D

[LittleMissChicGeek]

Thanks for this. A quick, simple explanation of the Paradox. Really helped my understanding!

[Lorncat]

I get it now. Thank you!
I was thinking about it too philosophically. It is much easier to see the point when I figured "okay, it either contains itself or it doesn't, let's try both, oh wait, none work, this is bullshit."

[wprandall]

it is not a member of itself; therefore, it is a member of itself. This is the paradox. What Russel is doing is trying to have it both ways. This is the solution to the problem. But what Is the statement of the solution? See if you can state it adequately.

[furiousfajitaa]

Thanks, a very clear defenition. I didn't understand the paradox until watching this but now I do. Brilliant made my day

[MGHOoL]

S does not belong to S? Isn't that just saying "1=/1"? It is defying the identity-principle, so of course it will be wacky. Not because set theory is flawed but because this statement defies logic.

[mEiKiSaKi]

Negate the claim in the principle, use the same set of axioms to approach the problem, and discover an antinomy.

[Math_oma]

How do you know that ZFC is consistent? (Enter Godel)

[aznwabbit]

In my final exam, my professor asked me to prove the Russell's paradox, but my professor just gave the statement like this "There is a set of all sets". Can we prove it wrong if Russell just stated that.

[Starr]

Thank you so much! Finally I got the idea!

[saikatkarmakar]

Every possible set is a subset of itself. So, set of those sets which does not belong to itself must be a null set since there is no such possible set.. if you think it is possible, give me an example..

[aakashverma]

sir video hindi languages avaliable ?