Question about the Tiering System™️

[Dolphinsipslean]

If I'm understanding it correctly, this should be the system right?
11-C = 0
11-B = aleph 0
11-A = aleph 1
10-C = aleph 2
10-B ~~ 3-A = finite
high 3-A = aleph 0
Low 2-C ~~ 2-A = aleph 1
Low 1-C = aleph 2 ~~ aleph 3
1-C = aleph 4 ~~ aleph 6
High 1-C = aleph 7 ~~ aleph 8
1-B = aleph 9 ~~ cardinal below aleph omega
High 1-B = aleph omega
Low 1-A = aleph 2
1-A = aleph 3 ~~ cardinal below aleph omega
1-A+ = aleph omega ~~ cardinal below inaccessible
High 1-A = inaccessible cardinal ~~ cardinal below mahlo
0 = mahlo and higher

 

[Dolphinsipslean]

Bump.

@Ultima_Reality @Agnaa @AKM sama

 

[Planck69]

Regular members can't ping others, only staff can. You need to manually message them.

@Ultima_Reality

Your help would be appreciated.

 

[Dolphinsipslean]

Regular members can't ping others, only staff can. You need to manually message them.

@Ultima_Reality

Your help would be appreciated.

Thanks for the help.

 

[Ultima_Reality]

In summary: No. The tiers from 11-C to High 1-B can be defined as being, more or less, just several levels of uncountably infinite differences in power (Low 2-C is uncountably infinitely superior to 3-A, Low 1-C is uncountably infinitely superior to Low 2-C, and so on and so forth), which is just equivalent to the difference between a given n-dimensional object and something of one dimension lower (Although you should keep in mind that higher-dimensional things are not necessarily infinitely greater in power than lower-dimensional ones, for reasons that are explained in a bit more detail here).

In any case, the issue of defining tiers below Low 1-A in terms of cardinality is that spaces with any number of dimensions (From 1 to aleph-0) have the exact same number of points (2^aleph-0, the power set of aleph-0), and, while this obviously doesn't impact on whether or not they are bigger or smaller than each other in terms of volume, it does mean that going solely by cardinality will not get you any useful answers in regards to how large they actually are. Given that, cardinality doesn't really play any significant role in the Tiering System until Low 1-A and up, where it becomes the primary measuring stick (Low 1-A being 2^2^aleph-0, 1-A being 2^2^2^aleph-0, and so on)

 

[Dolphinsipslean]

Low 1-C is uncountably infinitely superior to Low 2-C, and so on and so forth)

Correct me if I'm mistaken but are you saying that uncountable infinity x uncountable infinity > uncountable infinity?

 

[SagaTheLegend]

In summary: No. The tiers from 11-C to High 1-B can be defined as being, more or less, just several levels of uncountably infinite differences in power.

This enlightened me. So this basically means that 1D, 2D, and 3D are uncountable infinities, every character that can control that dimensional level ***** on Aleph Null and above hooray /s

Also you claim cardinality has no significant role in the tiering system until Low 1A but you also define all tiers below by differences of uncountable infinities, I am really confused here.

 

[Tago238]

Correct me if I'm mistaken but are you saying that uncountable infinity x uncountable infinity > uncountable infinity?

Yes, in the sense that a higher aleph number is greater than the previous aleph number squared, since the former has a greater cardinality.

 

[Ultima_Reality]

Also you claim cardinality has no significant role in the tiering system until Low 1A but you also define all tiers below by differences of uncountable infinities, I am really confused here.

When I say "cardinality," I specifically refer to the difference between any two cardinal numbers, which doesn't really apply to these tiers, since, as I've said, everything from 11-B to High 1-B actually falls under the same cardinal (2^aleph-0)

 

[Dolphinsipslean]

Yes, in the sense that a higher aleph number is greater than the previous aleph number squared, since the former has a greater cardinality.

I doubt you would be able to get a higher cardinality this way unless you know something I don't. If so, what is it?

 

[Ultima_Reality]

Correct me if I'm mistaken but are you saying that uncountable infinity x uncountable infinity > uncountable infinity

To elaborate a bit more on Tago's answer: It wouldn't give a greater cardinality, no, but it would indeed produce an object with a larger volume.

 

[Tago238]

I doubt you would be able to get a higher cardinality this way unless you know something I don't. If so, what is it?

You do not get a higher cardinality from squaring an uncountable infinity, yes. That is literally my point. Operations like that would result in something larger by another metric of measuring size, but not through cardinality since infinity doesn't work like that.

 

[SagaTheLegend]

When I say "cardinality," I specifically refer to the difference between any two cardinal numbers, which doesn't really apply to these tiers, since, as I've said, everything from 11-B to High 1-B actually falls under the same cardinal (2^aleph-0)

Huh? So what are the "levels of infinity" and the "uncountably infinite differences" between Tiers 11-C and High 1B all about if you consider they the same cardinality.

 

[Dolphinsipslean]

You do not get a higher cardinality from squaring an uncountable infinity, yes. That is literally my point. Operations like that would result in something larger by another metric of measuring size, but not through cardinality since infinity doesn't work like that.

Why would the size increase? All you're doing is multiplying the uncountable infinity by itself. If you're talking about size in measure theory, isn't infinity still infinity?

 

[Tago238]

Why would the size increase? All you're doing is multiplying the uncountable infinity by itself. If you're talking about size in measure theory, isn't infinity still infinity?

Tell me if I answered your previous question and you are moving onto a new one or if you are trying to debate me.

As for what I meant by a certain type of size increasing, refer to what Ultima said above my comment.

 

[Dolphinsipslean]

Tell me if I answered your previous question and you are moving onto a new one or if you are trying to debate me.

As for what I meant by a certain type of size increasing, refer to what Ultima said above my comment.

My question was for both of you I suppose, since Ultima said "volume" but size in measure theory is just infinity. If you have evidence for "higher infinity" of volume in measurement theory I'm interested in seeing it.

 

[SagaTheLegend]

Honestly screw this transfinite and pseudo math bullshit, I could care less at this point. Unfollowing.

 

[Ultima_Reality]

My question was for both of you I suppose, since Ultima said "volume" but size in measure theory is just infinity. If you have evidence for "higher infinity" of volume in measurement theory I'm interested in seeing it.

There isn't really a universal notion of "size" in measure theory, and any given dimensional space has a separate notion of size that applies only to it in particular, with the word "measure" in itself being just a very broad label that generalizes all of these notions (So, length is a 1-dimensional measure, area is a 2-dimensional measure, and so on).

For example, 0-dimensional sets are evaluated through the Counting Measure, which is just the number of points in a set (Which can be any natural number if it's finite, and +∞ if it's infinite), but, for instance, given a countably infinite set of such points, it would still be a set of zero measure in a higher dimension, and you'd need uncountably-many points to form even a 1-dimensional object.

And this generalizes to objects of higher dimensions, too, since any object of n dimensions can be seen as a multiplication of sets which themselves have uncountably infinite points, so, for instance, the construction of the unit square, denoted as [0,1]² (or [0,1] x [0,1]), is intuitively speaking nothing but the act of taking "copies" of the later interval and associating each of them to every point of the former interval, and the amount of points between 0 and 1 is uncountably infinite: Thus, by doing that, you are basically stacking uncountably infinite line segments along the y-axis to form a square.

There are a lot more factors as to how this relates to practical tiering, and all of them are explained in the FAQ page I linked above, so, should probably give that a read.