List of lists

[Matt-EUC]

Does a list of all lists that do not contain themselves, contain itself?

Discuss.

[Littlepeahead]

Have you been eating all the orange Smarties again?

[shiftin_gear98]

and I thought my day was dragging

[shiftin_gear98]

Baby due any day, just waiting for the phone to go.

[Spank86]

There are two lists of lists that do not contain themselves, the only difference between them is that they both contain the other.

[Matt-EUC]

I'm talking one list.

This list cannot exist. It only contains itself when it doesn't, and doesn't only when it does.

[aarond]

Depends on what you means by exists.

I think such a think would fall into the category of possibly a clopen space

[Dave20046]

And when you've answered that:
http://4.bp.blogspot.com/-5fjyQ54DPFQ/TrA39Ks_bJI/AAAAAAAAEzI/u4yU77EGwiM/s1600/Best+math+question+chalkboard.jpg

[Mark_h]

And when you've answered that:
http://4.bp.blogspot.com/-5fjyQ54DPFQ/TrA39Ks_bJI/AAAAAAAAEzI/u4yU77EGwiM/s1600/Best+math+question+chalkboard.jpg

Tuesday

[Grant66]

Not C

[JulesW]

nor A

[Matt-EUC]

Err, I'm am idiot... B

[The Idle Biker]

Correct answer :-)

[DJFridge]

What are you talking about? Actually I've just had a thought. If it's a list that contains itself then it must be a continuous loop of listiness, sort of a mobius list

[Spank86]

And when you've answered that:
http://4.bp.blogspot.com/-5fjyQ54DPFQ/TrA39Ks_bJI/AAAAAAAAEzI/u4yU77EGwiM/s1600/Best+math+question+chalkboard.jpg

0%

[CharleyFarley]

A


"Gas it w###a".........

[CharleyFarley]

B


"Gas it w###a".........

[CharleyFarley]

C


"Gas it w###a".........

[CharleyFarley]

D


"Gas it w###a".........

[Shawthing]

Mental torture for the ones who stuck sticky tape to the blackboard.

[thulfi]

visual aid
http://www.storyofmathematics.com/images2/russell_paradox.gif

Russell's paradox on a motorcycle forum! Whatever next?

[davepreston]

if matt was to go to a bar and drink 9 pints
how many times would he crash on the way there
and if any how many would be caused by grass

[Matt-EUC]

I've had approximately 0 grass crashes. That's Tomor's speciality.

I have, however, crashed sideways into the front of a car (whilst travelling forwards), into the back of a lorry (whilst I was stationary) and lowsided on the approach to a junction. Oh, and not forgetting the front end tuck on a moped on track during a charity event which coincidently did more damage to me and my kit than the others put together.


Beat that!

[Matt-EUC]

visual aid
http://www.storyofmathematics.com/images2/russell_paradox.gif

Russell's paradox on a motorcycle forum! Whatever next?

To this we can apply Schroedinger's theory. If we don't look at it, it's both at once, yet simultaneously neither.

So, forget the cat, let the ****er die... Or did it?

[Mrs_giggles]

I've had approximately 0 grass crashes. That's Tomor's speciality.

I have, however, crashed sideways into the front of a car (whilst travelling forwards), into the back of a lorry (whilst I was stationary) and lowsided on the approach to a junction. Oh, and not forgetting the front end tuck on a moped on track during a charity event which coincidently did more damage to me and my kit than the others put together.


Beat that!

DP here on the OCs account

beat that lmfao
I shall sit and wait for my top ten to be regailed by the org on mass


but all of mine put together dont compare to SCOOBS

[andreis]

To this we can apply Schroedinger's theory. If we don't look at it, it's both at once, yet simultaneously neither.

So, forget the cat, let the ****er die... Or did it?

You just want to wind people up, don't you?
Just like Russell did back at the beginning of 1900.

Russell's paradox prompted a whole redesign of set theory (and therefore, of everything, as set theory is the basis for cardinals and numerals theory, which is then used in pretty much anything that does sciency stuff).
In the redesigned set theory, you have to state the universe of discourse when declaring sets via a property. Pertaining to your example, you would have to say the Lists of Objects from set A (where A is a set you have already defined).

First of all, before continuing, let me warn you that it has been proven under the set axioms that there can be no set A such that: A is a member of itself.

Now, suppose that you already have a set of objects, A, which was declared using the set axioms. Let P(A) be the set of parts of A (all the possible lists you can make using objects from A). Let B = {x \in P(A) | x \notIn x}. Let's analyse now the construction of Russell's paradox. It asks whether B \in B. Because you have to define the universe of discussion (in this case, P(A)) and B is not originally a part of P(A), the question becomes mute as B itself is not a list constructed by this process. You can only argue that B was already in P(A), but then this would require the ability to build a set S such that S \in S.

You can follow the arguments in the (Zermelo-Fraenkel + Axiom of Choice) set of axioms and see that this is impossible.
(see wiki here for an introduction: http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory)

[Matt-EUC]

I have literally no idea what you just said. I have, at best, a very fleeting knowledge of the most basic logic.

[PyroUK]

To this we can apply Schroedinger's theory. If we don't look at it, it's both at once, yet simultaneously neither.



So, forget the cat, let the ****er die... Or did it?


I think what you mean is you can apply the Copenhagen theory.

[Spank86]

I have literally no idea what you just said. I have, at best, a very fleeting knowledge of the most basic logic.
Take a box, for simplicities sake we shall call this box, 'box A'.

Now put it in 'box A'.

you can't.


I think what you mean is you can apply the Copenhagen theory.
Indeed, Schrödinger didn't propose a theory, he was making a criticism.

A fairly valid one.

[PyroUK]

Take a box, for simplicities sake we shall call this box, 'box A'.

Now put it in 'box A'.

you can't.


Better yet, make box a airtight and unable to be opened from the inside. Get in box a and close it.