What are Cardinal Sets Of Infinity?

[Cryso Agori]

I know we use this to quantify cosmologies and stuff. However, I have no actual idea how they work.

And searching it up on Google gives me a bunch of scientific shit I don't understand.

So someone dumb down what cardinal sets of infinity are.

 

[Cryso Agori]

@Dead Lock Why'd you delete your post?

 

[Maddie]

1. They're used to prove that yes, "My infinity is higher than yours" is a legitimate thing in versus debating

2. Basically it starts on the premise that if you count a matrix of numbers diagonally it will net a larger set of numbers than a horizontal row, which in turn if infinite will mean the diagonal set is a larger set than the horizontal set.

3. The premise is expanded with all real numbers being larger than all natural numbers. Natural numbers: 1,2,3,4,5,6.. you can count all the way to infinity. Uncountable infinity is counting every decimal between 1 and 2, which is impossible. So the set of all real numbers is larger than the set of integers.

4. You can use further manipulations of pure mathematics, abstract algebra, and set theory to create larger sets.

5. Cardinalities are how large a set is.

Aleph-Null is all countably infinite numbers

Aleph-One is equivalent to all real numnbers

Aleph-Two is equivalent to Aleph-One ^ Aleph-One, or Aleph-One ^^ 2

.
.
.
Aleph Omega is Aleph-One ^ Aleph-One a countably infinite number of times, this would be megaversal+

However you can then have alephs of alephs, like aleph-aleph-one

This goes all the way to Aleph-Fixed Point

Beyond that inacessibles which have their own hierarchy through advanced manipulation of math, this would be omniversal and above

 

[Cryso Agori]

snip

I see, so each aleph is exponential right? So Aleph-Aleph-One is Aleph-One^Aleph-One^Aleph-One^Aleph-One?

 

[Maddie]

I see, so each aleph is exponential right? So Aleph-Aleph-One is Aleph-One^Aleph-One^Aleph-One^Aleph-One?

That's only Aleph-Four

Aleph-Omega is Aleph-One ^ Aleph-One ^ Aleph One ^ ...

 

[Stocking Anarchy]

From what I understand of it, it's the same logic of how an infinite multiverse is bigger than an infinite universe, an infinite megaverse is bigger than an infinite multiverse, an infinite omniverse is bigger than an infinite megaverse, an even bigger omniverse is bigger and so on. It's not infinity X infinity, but more the same logic as infinity > zero (aleph null is to aleph one what zero is to aleph null).

 

[Irradiance]

From what I understand of it, it's the same logic of how an infinite multiverse is bigger than an infinite universe, an infinite megaverse is bigger than an infinite multiverse, an infinite omniverse is bigger than an infinite megaverse, an even bigger omniverse is bigger and so on. It's not infinity X infinity, but more the same logic as infinity > zero (aleph null is to aleph one what zero is to aleph null).

Isn't in terms of cardinality an infinite multiverse and infinite megaverse are the same size? You know, because an infinite megaverse is only infinite x infinite, which is just the same cardinality again? It's gotta be something like power set size to be larger, no?

 

[Maddie]

Isn't in terms of cardinality an infinite multiverse and infinite megaverse are the same size? You know, because an infinite megaverse is only infinite x infinite, which is just the same cardinality again? It's gotta be something like power set size to be larger, no?

yes, an infinite megaverse would remain in the same cardinality, which is why mega+ is a massive range. It is basically Aleph-Two to Aleph-Fixed Point