Is there a bigger number than this?
Sure. Just feed Aleph into the Ackerman function. Boom.
>>8018496
What about Aleph -> Ackerman function + 1?
what about [math]\frac{-1}{12}[/math]
>>8018484
Is this the /sci/ way of bickering kids claiming to always have "one more" of a thing than the other?
That being said I'll just bullshit a new operator which will stump your power tower and claim it as trump, or short '
>>8018517
what about −1/12 ^ ℵ
>>8018532
What if I define a logic in which my numbers are always bigger than your numbers?
>>8018484
What is this fuckness
>>8018484
>$50k a year to study Hebrew symbols
USA
>Is there a bigger number than this?
Yes. Just divide it by [math]0[/math].
>>8018583
How humble of our nosy merchant friends to reserve their own glyphs to denote infinite quantities, while leaving the lowly goyim symbols for the finite ones, isn't it?
>>8018602
kek
How does any of this shit produce something remotely meaningful?
Is this why Set-Theory is and will always be a meme philosophy?
>>8018667
No-one actually cares about things like OP's cardinal. It's just some random cardinal. Set theorists do not study things like that, at all.
>>8018791
It's the set that contains all sets, even itself, isnt it?
>>8018811
A cardinal number is not a set.
The fuck are you shitlords talking about?
The cardinal of an uncountable infinite set is the largest possible number.
Get over it.
>>8018667
>How does any of this shit produce something remotely meaningful?
It doesn't. That's the joke. You probably don't get the joke. I'm aleph sure you don't get the joke.
>>8018869
Not nearly so. There are infinitely many degrees of uncountability. That ride only starts with [math]\aleph_1[math]. For instance, [math]\aleph_2[/math] is the number of all possible curves that can exist in a plane.
>>8018532
That's presumably as long as you decide to keep playing the game. The last one alive in the counting game is the winner.
Here are some numbers/cardinals (or playfields) by size, and ordinals by order
The Kunen inconsistency
Berkeley cardinal
super Reinhardt cardinal, Reinhardt cardinal
j:L(Vλ+1)→L(Vλ+1)
rank+1 into rank+1 cardinal j:Vλ+1→Vλ+1
rank into rank cardinal j:Vλ→Vλ
The wholeness axiom
super n-huge cardinal
superhuge cardinal
huge cardinal
almost huge cardinal
Vopěnka cardinal, Woodin for supercompactness cardinal
Vopěnka's principle
extendible cardinal
grand reflection cardinal
supercompact cardinal
PFA cardinal
strongly compact cardinal
nearly supercompact and nearly strongly compact cardinals
indestructible weakly compact cardinal
subcompact cardinal
superstrong cardinal
Shelah cardinal
Woodin cardinal
strong cardinal and the θ
-strong and hypermeasurability hierarchy
tall cardinal
0†
Nontrivial Mitchell rank, o(k)=1, o(k)=k++
measurable cardinal
weakly measurable cardinal
strongly Ramsey cardinal
Ramsey cardinal
virtually Ramsey cardinal
Rowbottom cardinal
Jónsson cardinal
ω1
-Erdős cardinal and γ-Erdős cardinals for uncountable γ
0
Erdős cardinal, and the α-Erdős hierarchy for countable α
1-iterable cardinal, and the α-iterable cardinals hierarchy for 1≤α≤ω1
remarkable cardinal
completely ineffable cardinal
ineffable cardinal, and the n-ineffable cardinals hierarchy
weakly ineffable cardinal
subtle cardinal
ethereal cardinal
superstrongly unfoldable cardinal, strongly uplifting cardinal
weakly superstrong cardinal
strongly unfoldable cardinal
unfoldable cardinal
Totally indescribable cardinal
indescribable cardinal
weakly compact cardinal
hyper-Mahlo cardinals
the α-Mahlo hierarchy
1-Mahlo
Mahlo cardinal
uplifting cardinal
psuedo uplifting cardinal
ORD is Mahlo
Σ2-reflecting, Σn-reflecting and reflecting cardinals
1-inaccessible, the α-inaccessible hierarchy and hyper-inaccessible cardinals
Grothendieck universe axiom, equivalent to the existence of a proper class of inaccessible cardinals
inaccessible cardinal, also known as strongly inaccessible
weakly inaccessible cardinal
Kelly-Morse set theory
worldly cardinal and the α-wordly hierarchy, hyper-worldly cardinal
the transitive model universe axiom
Transitive ZFC model
the minimal transitive model
Con(ZFC) and Conα(ZFC), the iterated consistency hierarchy
...
correct cardinals, Vδ≺V and the Feferman theory
Σ2 correct and Σn-correct cardinals
0-extendible cardinal
Σn-extendible cardinal
ℶ-fixed point
the beth numbers and the ℶα hierarchy
ℶω and the strong limit cardinals
Θ the continuum
cardinal characteristics of the continuum
the bounding number b, the dominating number d, the covering numbers, additivity numbers and many more
the descriptive set-theoretic cardinals
ℵ-fixed point
the aleph numbers and the ℵα
hierarchy
ℵω
and singular cardinals
ℵ2, the second uncountable cardinal
uncountable, regular and successor cardinals
ℵ1, the first uncountable cardinal
cardinals, infinite cardinals
ℵ0
ω1, the first uncountable ordinal, and the other uncountable cardinals of the middle attic
stable ordinals
The ordinals of infinite time Turing machines, including
Σ = the supremum of the accidentally writable ordinals
ζ = the supremum of the eventually writable ordinals
λ = the supremum of the writable ordinals,
admissible ordinals and relativized Church-Kleene ωx1
Church-Kleene ωck1, the supremum of the computable ordinals
the Bachmann-Howard ordinal
the large Veblen ordinal
the small Veblen ordinal
the Feferman-Schütte ordinal Γ0
ϵ0 and the hierarchy of ϵα
numbers
the omega one of chess
ωCh∼1 = the supremum of the game values for white of all positions in infinite chess
ωCh,c1= the supremum of the game values for white of the computable positions in infinite chess
ωCh1= the supremum of the game values for white of the finite positions in infinite chess
indecomposable ordinal
the small countable ordinals, such as ω,ω+1,…,ω⋅2,…,ω2,…,ωω,…,ωωω,…
up to ϵ0
Hilbert's hotel and other toys
ω, the smallest infinity
limerick
PS: They also have mice and I think I've seen squirrels before
https://en.wikipedia.org/wiki/Mouse_%28set_theory%29
Hey does somebody know the -smallest- model of ZF(C) where all sets are measurable?
I know there are constructions - are the several and some which are more comprehensible than others?
I asked because a friendly loon on SE once discussed how forcing everything measurable would the the only sensible way to set up a good mathematical theories of path integrals
>>8019084
>The last one alive
THERE CAN BE ONLY ONE.
(This isn't actually a highlander reference, it's a joke about number counting.)
>>8018484
Yeah, the weight of your mother
>implying infinite sets exist
>>8019168
Then what is the largest natural number, if [math]\mathbb{N}[/math] is not infinite, i.e. finite?
Does this even make sense? Does [math]\aleph_{aleph_0}[/math] even make sense? Shouldn't you being saying things like
[math]\aleph_{\omega}[/math] instead?
Infinity - 1
biggest actual number since infinity isn't one
[math]\aleph^{\aleph^{\aleph^{\aleph}_{\aleph}}_{\aleph^{\aleph}_{\aleph}}}_{\aleph^{\aleph^{\aleph}_{\aleph}}_{\aleph^{\aleph}_{\aleph}}}[/math]
>>8020327
not this anon but let's try it again this way, I was dreaming of this, oddly:
[math] \displaystyle \aleph_{ \aleph_{ \aleph_{ \aleph_{ \aleph}^{ \aleph }}^{ \aleph_{ \aleph }^{ \aleph }}}^{ \aleph_{ \aleph_{ \aleph }^{ \aleph }}^{ \aleph_{ \aleph }^{ \aleph }}}}^{ \aleph_{ \aleph_{ \aleph_{ \aleph }^{ \aleph }}^{ \aleph_{ \aleph }^{ \aleph }}}^{ \aleph_{ \aleph_{\aleph }^{ \aleph }}^{ \aleph_{ \aleph }^{ \aleph }}}} [/math]
>>8020172
If "infinity" isn't a number (as you just said yourself), then how can "infinity - 1" be a well-defined denotation of a number? It's meaning less.
>>8020327
Now, the reason why mine worked and yours didn't is that 4chan's TeX implementation really hates it when the back-slashes that declare special symbols are{\right {\next {\to {\other ]\characters, in your originally formatted and posted version anyway (the tex code sometimes shows up as slightly different after posting, but you have to let the engine decide how it wants to represent what the code "was" after-the-fact). The best practice is { \to ] \always { \insert $ \a ] \space between two such objects. Don't ask me why but I know it works, and that you ignore this at your own peril.
It depends, is your mom a number?
>>8020372
[math]\displaystyle \bigwedge_{n \in \mathbb{N}} (\bigvee_{n} \implies \bigvee_{n+1})[/math]
There is isn't largest number, thus at least potential infinity (i.e. a concept representing a process which can be continued indefinitely) exists.
>>8020366
Isn't it just that you used "\displaystyle" and he didn't?
[math]\displaystyle \aleph^{\aleph^{\aleph^{\aleph}_{\aleph}}_{\aleph^{\aleph}_{\aleph}}}_{\aleph^{\aleph^{\aleph}_{\aleph}}_{\aleph^{\aleph}_{\aleph}}}[/math]
>>8020430
Yup, just as I thought.
(I copied verbatim his LaTeX that failed to render, only adding "\displaystyle" at the front, and voila, it rendered.)
>>8020436
That expression is meaningless, you know. Aleph symbols need to have some explicit index somewhere, just by themselves, however nested, they mean nothing.
>>8020445
So nest it with omega
>>8020439
Be that as it may, the thing that I mentioned is also a best practice on this board. I know for a fact that I have had math posts fail to format for want of that SINGLE switch-change. Using \displaystyle by default is another best practice, as it renders large operators legible.
So do both.
>>8018577
Is it consistent? Post your axioms.
>>8018602
u jelly?
How can the alephs be used as a subscript. What does that even mean? Shouldn't the subscripts be ordinals?
>>8018484
infinite
What about:
infinity-27
