/sci/ - Science & Math

Like an infinite set that has a term in it in constant superposition.

>>9717687
Conjecturally (nobody has detected its existence experimentally) it looks very much like the "set of real numbers".

>>9717687
sets do not contain themselves

>>9717713
Well if it doesn't contain itself then shouldn't it be contained in the set of all sets that do not contain themselves?

Every set contains itself as a subset.

There, mystery solved: now go on to do something useful instead.

>>9717732
But wouldn't mean that all of set theory is wrong?

>>9717687

> But wouldn't mean that all of set theory is wrong?

Absolutely. Except for the obscure part of it that says that a set is a subset of itself.

>>9717687
A universe-sized box that contains a lot of boxes. Obviously it cannot itself because a box can't fit inside a box of the same size and shape

It looks like a proper class

>>9717732
>Every set contains itself as a subset.
This is classically false.

>>9717750
good pic!

>>9717775
You look like a proper git.

>>9717789
Every set except the empty set contains itself as a subset. That's well understood in set theory. Without it, CS majors couldn't use trees.

>>9717949
Counterexample: {1}. Notice it contains only 1, and not {1}.

Is the set that contains an empty set empty?
(if you can't answer this correctly you're a brainlet)

>>9718132
if you think of sets as independent objects, then yes, the set contains something, the empty set, and it's not empty

but to me it seems the empty set equals nothing. there being nothing is not a thing in and of itself. so, a set containing nothing remains empty as ever.

did I get it right senpai?

>>9718161
>but to me it seems the empty set equals nothing
no you didn't

>>9718163
well, what is a set? is it the "boundaries" and their contents? are the "{}" literally a part of a set? does every set come with an implicit identity attached to it? or rather, is a set merely its contents? to me it seems the latter option makes more sense. if so, an empty set equals nothing, and a set containing only the empty set, nothing, is an empty set.

Axiom:
There exists no set that isn't an element of a set

Russell BTFO

>>9717771
For you

>>9718166
okay brainlet let me explain it to you in sub 100 iq terms:
a set is like a sack which can contain anything
an empty sack (set) is empty
a sack containing an empty sack is not empty because it contains the empty sack. while there might not be anything "useful" in it, it's still not empty.

>>9718247
that's also why
5≠{5}

>>9718132
>Is the set that contains an empty set empty?
No, it contains the empty set

>>9718247
what a brainlet explanation. what mathematical property of a set actually corresponds it being a "sack"? it all depends on whether you wanna treat it associating an identity, "a sack" to a certain group of objects or not. so I guess the common way is the "sack" model, but by no means is anything preventing you from using the alternative.

>>9718606
Actually it was pretty elegant, maybe you need a sub 80 iq explanation

>>9718629
>proceeds to ignore that I have acknowledged my understanding of "le sack" view in two posts already
maybe it's you two being unable to consider alternate viewpoints who are the real brainlets

>>9718640
Scratch that sub 60 iq explanation is needed

>>9718655
is that the only one you're able to give? you're terrible at arguing, it's highly indicative of your IQ.

>>9718662
sub 40 iq. Anon you better stop replying youre running out of points

>>9718606
>preventing you from using the alternative
what "alternative", brainlet

>>9718759
holy shit, what's wrong with your reading comprehension? the alternative is not associating an identity to a set of objects, and instead treating sets as mere collections of objects with no further identity. then an empty set is equal to nothing.

>>9717730
You can't create a set of all sets that don't contain themselves.
It's the grammatical equivalence to saying "a box which doesn't contain itself that contains itself".

>>9718132
A set which contains an empty set would have one element, therefore not empty. Math is useless.

>>9718764
>a collection is a set
every time you post your iq drops by 20 points in our eyes
>what is cantor's paradox
>what is literally OP's post

>>9718785
a set is a collection, brainlet. maybe try arguing if you actually wanna demonstrate that you're not a retard parroting what you've heard

>>9718857
if a set is a collection then show me a set with the greatest cardinal number

>>9717687
It would look like something which doesn't exist, perhaps like [math]\sqrt{2}[/math]