/sci/ - Science & Math » Thread #13692657

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Anonymous Tue 28 Sep 14:00:04 2021 No.13692657 View Reply Original Report

Quoted By: >>13692755 >>13692804 >>13692841 >>13692850 >>13692882 >>13693266 >>13693737 >>13693795 >>13693829 >>13694163 >>13694187

I dont' get it, why can't the set of all sets exist?

Anonymous

Anonymous Tue 28 Sep 2021 14:25:46 No.13692755 Report

Quoted By: >>13693090

>>13692657
It's poorly defined because you can always find a bigger set.

Anonymous

Anonymous Tue 28 Sep 2021 14:37:25 No.13692804 Report

Quoted By: >>13693089 >>13693090

>>13692657
Who fucks the top? So there's a collective of gays right and they agree that they 'belong' to whomever does them in the butt. the bottoms belong to the top? You with me so far?
So they all belong to the top, because he fucks them in the butt. But who fucks the top in his butt? Well he ceases to be a top now, he belongs to someone else... but then who fucks that guy in the butt...

Anonymous

Anonymous Tue 28 Sep 2021 14:46:18 No.13692841 Report

Quoted By: >>13692854 >>13693090

>>13692657
A set of all sets can exist, no problem.
However, in contemporary set theory, it is a theorem that such a set does not exist.
It is not an axiom, so such a set would a priori be allowed. It just happens to be a
consequence of the axioms that there isn't any such set.

Anonymous

Anonymous Tue 28 Sep 2021 14:47:54 No.13692850 Report

Quoted By: >>13694010

>>13692657
why cant the liquid solid exist
why cant the black white exist
why cant the hot cold exist

Anonymous

Anonymous Tue 28 Sep 2021 14:49:00 No.13692854 Report

Quoted By: >>13692863 >>13692922

>>13692841
Wouldn't it need to include itself

Anonymous

Anonymous Tue 28 Sep 2021 14:51:44 No.13692863 Report

Quoted By:

>>13692854
It would indeed. Like the famous example of the concept of all abstract concepts.

Anonymous

Anonymous Tue 28 Sep 2021 14:58:15 No.13692882 Report

Quoted By: >>13693090

>>13692657
Judges should be impartial right? And theoretically everybody is equal before the law. So let's imagine there's a little village called 'Set' where there is one judge who treats everyone equally in his court.
But what happens if the judge is charged with doing something illegal - who judges the judge?
He can't judge himself because he'd be partial. So we need a super-judge to judge the judge of all Set...
oops but our super judge of the judge of all set has been accused of doing something illegal, so we need a super-super-judge...

Anonymous

Anonymous Tue 28 Sep 2021 15:16:11 No.13692922 Report

Quoted By: >>13693001

>>13692854
This right

Anonymous

Anonymous Tue 28 Sep 2021 15:41:56 No.13693001 Report

Quoted By: >>13693452

>>13692922
Yes. And?

Anonymous

Anonymous Tue 28 Sep 2021 15:47:40 No.13693027 Report

Quoted By:

Some infinities are bigger than others.

Anonymous

Anonymous Tue 28 Sep 2021 16:01:52 No.13693089 Report

Quoted By:

>>13692804
We're all arranged in a circle so everyone is simultaneously fucked and fucking at once.

Anonymous

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Anonymous Tue 28 Sep 2021 16:01:55 No.13693090 Report

Quoted By: >>13693316

>>13692755
>you can always find a bigger set
Define "bigger"

>>13692804
>But who fucks the top in his butt?
He fucks himself (provided he has a long and flexible enough cock)

>>13692841
>It just happens to be a
consequence of the axioms that there isn't any such set.
What axioms in particular?

>>13692882
>He can't judge himself because he'd be partial.
Then replace him with a robo-judge that's programmed to be impartial

Anonymous

Anonymous Tue 28 Sep 2021 16:38:01 No.13693266 Report

Quoted By: >>13693358

>>13692657
The set containing all sets would need to contain itself. Suppose there are n sets. The set containing all sets would contain those n-many sets. But that would also be a set, so there'd be n+1 sets. So the set containing all sets would contain n+1 sets, but that'd also be a set... So on and so forth. If you cannot follow this, then /pol/ would be more your speed.

Anonymous

Anonymous Tue 28 Sep 2021 16:50:06 No.13693316 Report

Quoted By: >>13693358

>>13693090
>What axioms in particular
In ZF it is mainly the axiom of regularity of course.

Anonymous

Anonymous Tue 28 Sep 2021 17:03:26 No.13693358 Report

Quoted By: >>13693429 >>13693458 >>13693731

>>13693266
>The set containing all sets would need to contain itself.
Yep

>Suppose there are n sets. The set containing all sets would contain those n-many sets. But that would also be a set, so there'd be n+1 sets.
No, why? If there are n sets, then the set containing them all is one among those n.

>>13693316
>In ZF it is mainly the axiom of regularity of course.
Then why don't we get rid of it?

Anonymous

Anonymous Tue 28 Sep 2021 17:25:11 No.13693429 Report

Quoted By:

>>13693358
You could just say you don't understand set theory and save everyone a lot of time.

Anonymous

Anonymous Tue 28 Sep 2021 17:31:05 No.13693452 Report

Quoted By:

>>13693001
Now construct the set that contains all sets that don't contain themselves

Anonymous

Anonymous Tue 28 Sep 2021 17:33:05 No.13693458 Report

Quoted By:

>>13693358
>why don't we get rid of the axiom of regularity?
That is an excellent question.
In Categorical Set Theory, there is no such axiom. You can check out a paper
Steve Awodey, Carsten Butz, Alex Simpson, Thomas Streicher: Relating first-order set
theories, toposes and categories of classes. Annals of Pure and Applied Logic, Volume 165,
Issue 2, February 2014, Pages 428-502.
The axiom is mostly practical, since e.g. it allows you to assume that vectors provably exist,
instead of having to assume that they exist.

Anonymous

Anonymous Tue 28 Sep 2021 18:45:26 No.13693731 Report

Quoted By: >>13693773 >>13693908

>>13693358
>>Suppose there are n sets. The set containing all sets would contain those n-many sets. But that would also be a set, so there'd be n+1 sets.
>No, why? If there are n sets, then the set containing them all is one among those n.

That's a great point, you're almost there anon! The point the other guy was trying to make is that you're right to be suspicious about that: there cannot be n and n+1 sets simultaneously. The assumption that there are n sets leads to the conclusion that there are n+1 sets, both of which are mutually contradictory. Since we cannot abide by contradictions, we conclude that the premise that the set of all sets exists is false. That is, the set of all sets does not exist.

Anonymous

Anonymous Tue 28 Sep 2021 18:46:56 No.13693737 Report

Quoted By:

>>13692657
for the same reason that the set of natural numbers does not exist

Anonymous

Anonymous Tue 28 Sep 2021 18:58:05 No.13693773 Report

Quoted By:

>>13693731
This seems more like a proof that there isn't a finite amount of sets.

Anonymous

Anonymous Tue 28 Sep 2021 19:04:11 No.13693795 Report

Quoted By:

>>13692657
Because no sets exist at all.

Anonymous

Anonymous Tue 28 Sep 2021 19:14:00 No.13693829 Report

Quoted By: >>13693908

>>13692657
if the set of all sets exists, then this set contains itself. therefore it's possible for a set to contain itself in principle. consider the subset of the set of all sets consisting of sets which do not contain themselves. this subset does and does not contain itself at the same time which is a logical contradiction.

Anonymous

Anonymous Tue 28 Sep 2021 19:46:56 No.13693908 Report

Quoted By: >>13693936

>>13693731
>there cannot be n and n+1 sets simultaneously
And that's precisely why we assume that the set of all sets is among those n: so we don't need that "+1"

>The assumption that there are n sets leads to the conclusion that there are n+1 sets
No, it doesn't, see above.

>>13693829
>consider the subset of the set of all sets consisting of sets which do not contain themselves. this subset does and does not contain itself at the same time which is a logical contradiction.
This just means that there is no such thing as "the set of all sets which do not contain themselves", but it says nothing about "the set of all sets"

Anonymous

Anonymous Tue 28 Sep 2021 19:58:11 No.13693936 Report

Quoted By: >>13694027

>>13693908
>And that's precisely why we assume that the set of all sets is among those n: so we don't need that "+1"
Let's suppose there are three sets, and they are the only sets which exist: {A}, {B}, {C}. Okay, the set of all sets is {{A}, {B}, {C}}, which then implies all the sets which exist are: {A}, {B}, {C}, {{A}, {B}, {C}}. But this implies that the set of all sets is: {{A}, {B}, {C}, {{A}, {B}, {C}}}. So on and so forth.

Anonymous

Anonymous Tue 28 Sep 2021 20:19:06 No.13694010 Report

Quoted By:

>>13692850
A black white can exist...it's called a wigger

Anonymous

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Anonymous Tue 28 Sep 2021 20:22:19 No.13694027 Report

Quoted By: >>13694118

>>13693936
>which then implies all the sets which exist are: {A}, {B}, {C}, {{A}, {B}, {C}}
Not if {{A}, {B}, {C}} = {A}

Anonymous

Anonymous Tue 28 Sep 2021 20:51:11 No.13694118 Report

Quoted By:

>>13694027
{A} = {{A},{B},{C}}
Take the power set of {A}...
P({A}) = {{A}, {{A}, {B}}, {{A},{C}}, {{B},{C}}}
Those sure look like sets not contained within {A}.

Wisdom clown

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Wisdom clown Tue 28 Sep 2021 21:08:16 No.13694163 Report

Quoted By:

>>13692657
Why can't one thought or abstraction contain all thought and abstraction?

OR

How would you get a box to fit itself inside itself? How would you close a box trying to contain itself.

Anonymous

Anonymous Tue 28 Sep 2021 21:16:58 No.13694187 Report

Quoted By:

>>13692657
A structure that contains all sets absolutely can exist, but the issue is that it violates some of the basic assumptions we have about sets - so the resolution is that the object that contains all sets isn't a set.
There are a lot of articles / writeups on this. Take your pic and read a few.

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