Bring Back Old 2A Above Baseline Standard

[RALFdoang]

Currently, we use the CH (Continuum Hypothesis) as our Invisible default standard to determine the boundary between 2A and Low 1-C.

For a little explanation, CH is an hypothesis which stating that there is no set between the set of Natural number and the set of Real number (no set between Aleph-null to Aleph-1). From "this" CRT, we treat CH as the default standard to determine the boundary between 2A and Low 1C, by simply saying: "there is no space between 2A and Low 1C , therefore any space that contain 2A become Low 1C structure, as how Continuum Hypothesis is." Since this standard has been applied, we don't use 2A above baseline system anymore unless a fiction specifically says so (which I'm sure it won't because of the supporters is trying to falsify their feats interpretation).



There is one thing I want to say here. Applying CH as our default standard like this and apply it to almost every single fiction in this wiki is not a good idea. This is because CH is a controversial problem in math due to its unprovable state. According to Gödel 2nd incompletness theorem, which state::

"For any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself "

Meaning, we can't construct a model of ZFC (A system that used as the base standard for Set Theory) while working in the ZFC, or simply if we prove a math system is correct within its own math system, then those math system is incorrect, and viceversa, making it inconsistent. Similiar to Halting problem. CH is independent from the ZFC, thus it is an axiomatic model (model that have self-contained proof), therefore making it unprovable whether it is actually true or false within ZFC system itself. The best solution to this problem is to seperate CH into two interpretations to work: an interpretation of a universe where CH is true (Gödel interpretation of Contrustible Universe), and an interpretation of a universe where CH is false (Cohen interpretation of Forcing Inconstructible Universe).

Something that has multiple interpretations is applied to become our default standard by choosing to apply only one of its interpretations? We have been an ignorant by ignoring the other interpretation of Continuum Hypothesis.

I already asking Ultima about this, and he said that he makes this standard due to its simplicity sake to understand for a new people. So i don't think that's a good reason to make this standard still stand in this wiki.

Conclusion? we have to stop using CH as default standard and revive the previous 2A above baseline system in order to make this wiki more consistent with the real world theorem. Therefore, any space that containing 2A is not automatically Low 1-C if there's no spesific stuff that suitable with our Higher Dimensional standard. This will not changing the Tiering System of Tier-1, its just returning the old 2A above baseline standard.

Also, i think we better waiting Ultima to give input here, althrough he seemingly agree with this.

----

So, proposal to remove invisible CH 2A to Low-1C standard.

Agree:

Neutral:

Disagree:

 

[LeylinFarlier01]

sheesh let's go, following this thread

 

[Logic]

Following

 

[Ren1999]

Following, waiting for the other members, then they can give arguments

 

[Tatsumi504]

Following though you're wrong somewhere. Simply containing 2-A is not enough for Low 1-C. A space could contain multiple 2-A structures and still have the same cardinality.
To gain Low 1-C from containing 2-A you need supporting context of being qualitatively bigger

 

[Aachintya31]

You all can stop with the Following shenanigans in a staff thread

 

[Reiner04]

Well a staff thread but Continuum hypothesis holding true or false is not needed, that basically is for 2^aleph null = aleph 1 or that real number is equals to aleph 1, ZFC and ZF both imply this w/o continuum hypothesis. So it's not reductant.

 

[KLOL506]

@Planck69 @Ultima_Reality @DontTalkDT @Executor_N0 @Theglassman12 @Maverick_Zero_X Have fun LOL

 

[Georredannea15]

You are wrong about having a larger infinite space Low1-C containing infinite 2-A. Just as a larger rational number containing a rational number between two integers is equal to an Integer.This seems illogical. (We can wait for DT and Ultima.)

 

[ImmortalDread]

Currently, we use the CH (Continuum Hypothesis) as our Invisible default standard to determine the boundary between 2A and Low 1-C.

The assertion is incorrect. Instead, we rely on precisely established principles governing infinite cardinal numbers.

For a little explanation, CH is an hypothesis which stating that there is no set between the set of Natural number and the set of Real number (no set between Aleph-null to Aleph-1).

It is incorrect to claim that CH entails a definite relationship between Aleph-0 and Aleph-1. However, it should be noted that the relationship between Aleph-0 and Aleph-1 is already established by definition.

To make it easier, the second statement, which is based on the total order of the class of cardinals in ZFC and the definition of Aleph-1 in ZF, differs entirely from the first statement.

From "this" CRT, we treat CH as the default standard to determine the boundary between 2A and Low 1C, by simply saying: "there is no space between 2A and Low 1C , therefore any space that contain 2A become Low 1C structure, as how Continuum Hypothesis is." Since this standard has been applied, we don't use 2A above baseline system anymore unless a fiction specifically says so (which I'm sure it won't because of the supporters is trying to falsify their feats interpretation).

Once again, this is unrelated to CH. The absence of space between 2-A and Low 1-C is due to the nature of infinite cardinals.

There is one thing I want to say here. Applying CH as our default standard like this and apply it to almost every single fiction in this wiki is not a good idea. This is because CH is a controversial problem in math due to its unprovable state. According to Gödel 2nd incompletness theorem, which state::

"For any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself "

Meaning, we can't construct a model of ZFC (A system that used as the base standard for Set Theory) while working in the ZFC, or simply if we prove a math system is correct within its own math system, then those math system is incorrect, and viceversa, making it inconsistent. Similiar to Halting problem. CH is independent from the ZFC, thus it is an axiomatic model (model that have self-contained proof), therefore making it unprovable whether it is actually true or false within ZFC system itself. The best solution to this problem is to seperate CH into two interpretations to work: an interpretation of a universe where CH is true (Gödel interpretation of Contrustible Universe), and an interpretation of a universe where CH is false (Cohen interpretation of Forcing Inconstructible Universe).

The incompleteness theorems do not offer direct proof of the undecidability of CH.

Something that has multiple interpretations is applied to become our default standard by choosing to apply only one of its interpretations? We have been an ignorant by ignoring the other interpretation of Continuum Hypothesis.

It is possible to create a hierarchy in which the continuum hypothesis is not true, and it would not present a significant issue.

I already asking Ultima about this, and he said that he makes this standard due to its simplicity sake to understand for a new people. So i don't think that's a good reason to make this standard still stand in this wiki.

Cardinal systems that satisfy CH, or even better, the generalized continuum hypothesis (GCH), are easier to comprehend due to the relationship between powersets and alephs. While it is possible to create a system in which GCH does not hold, doing so would be difficult for those who lack a solid understanding of basic set theory.

Conclusion? we have to stop using CH as default standard and revive the previous 2A above baseline system in order to make this wiki more consistent with the real world theorem. Therefore, any space that containing 2A is not automatically Low 1-C if there's no spesific stuff that suitable with our Higher Dimensional standard. This will not changing the Tiering System of Tier-1, its just returning the old 2A above baseline standard.

Also, i think we better waiting Ultima to give input here, althrough he seemingly agree with this.

----

So, proposal to remove invisible CH 2A to Low-1C standard.

Already answered above

 

[Georredannea15]

Once again, this is unrelated to CH. The absence of space between 2-A and Low 1-C is due to the nature of infinite cardinals.

More precisely, there is an "inaccessible" continuum between .2-A and Low 1-C.

 

[Reiner04]

Ghost post/ping?

 

[Reiner04]

OP seems to be misunderstanding smth, our standards don't care and are unrelated of CH holding true or false. We take uncountable infinite by default to be Tier 1 regardless of low 1-C or above and countable infinite by default to be 2-A (as in number of universes). Continuum hypothesis has no place here, it's just telling us there is not set btw the set of natural numbers and real numbers, it's not contradictory to uncountable infinite being Tier 1.

 

[RALFdoang]

Well a staff thread but Continuum hypothesis holding true or false is not needed, that basically is for 2^aleph null = aleph 1 or that real number is equals to aleph 1, ZFC and ZF both imply this w/o continuum hypothesis. So it's not reductant.

That's not my point, my point is we treating CH as a standard to deteremine the gap between 2A to Low 1C.

Althought we could still keep those 2^Aleph-null stuff for tiering purpose.

The assertion is incorrect. Instead, we rely on precisely established principles governing infinite cardinal numbers.

We do have those Invisible standard from the previous MG and Chrono threat. I do already dm Ultima about this, and it seems this standard come from the CH application to Space that containing 2A.

It is incorrect to claim that CH entails a definite relationship between Aleph-0 and Aleph-1. However, it should be noted that the relationship between Aleph-0 and Aleph-1 is already established by definition.

To make it easier, the second statement, which is based on the total order of the class of cardinals in ZFC and the definition of Aleph-1 in ZF, differs entirely from the first statement.

Can you quote the "definition of Aleph-1 from ZF"? I don't find that one.

Once again, this is unrelated to CH. The absence of space between 2-A and Low 1-C is due to the nature of infinite cardinals.

It doesn't make sense if it only use the nature of transfinite gap to define that. Imagine if there exist a higher layer of reality that 2A above baseline, and then it also exist a Higher dimensional realm, higher than that. The gap of those Higher Dimensional still counted as "Inacessible" to the Higher Reality, and this is also the same with the gap to baseline 2A. It could happen if the verse violating the first statement of CH and it doesn't contradict those nature.

The incompleteness theorems do not offer direct proof of the undecidability of CH.

Althought it doesn't give dirrect statement, the second theorem say that every axiom independent from the ZF is Inconsistent to be proven (including the ZF itself), this is the basis that seperating CH and make it independent from ZF by Cohen and other mathematician.

It is possible to create a hierarchy in which the continuum hypothesis is not true, and it would not present a significant issue.

Cardinal systems that satisfy CH, or even better, the generalized continuum hypothesis (GCH), are easier to comprehend due to the relationship between powersets and alephs. While it is possible to create a system in which GCH does not hold, doing so would be difficult for those who lack a solid understanding of basic set theory.

The same as my fisrt repply, this not my point of this threat. I don't mind with the formula that both the CH and GCH offered, what i trying to argue here is it relation to the gap between 2A and Low 1C (i.e That space containing 2A stuff).

 

[DontTalkDT]

Yeah, no.

First, it wouldn't even get you what you propose. The difference between 2-A and Low 1-C is measure theory based. Cardinality has no relevance.

Second, it's a terrible idea as it means there are unlimited levels of infinity between any cardinality level we assign. Instead of easier standards for getting above baseline 2-A, what you end up with are impossible standards for higher cardinality tier. As without the cotinuum hypothesis, if you wanna proof to go from aleph_0 to aleph_1, it doesn't suffice to show that you are on a proper higher infinity, but you would additionally either need to proof that either CH applies or that you are additionally above all the in-between infinities.

 

[Andika_CL_atmadja]

Yeah, no.

First, it wouldn't even get you what you propose. The difference between 2-A and Low 1-C is measure theory based. Cardinality has no relevance.

Second, it's a terrible idea as it means there are unlimited levels of infinity between any cardinality level we assign. Instead of easier standards for getting above baseline 2-A, what you end up with are impossible standards for higher cardinality tier. As without the cotinuum hypothesis, if you wanna proof to go from aleph_0 to aleph_1, it doesn't suffice to show that you are on a proper higher infinity, but you would additionally either need to proof that either CH applies or that you are additionally above all the in-between infinities.

Yep. Which it's also subset of mathematical analysis. Time to learn Calculus Spivak (If all of you guys have very strong brain)

https://vsbattles.com/threads/from-2-a-to-low-1c-what-is-mathematical-set-theory-expression-of-it.141873/#post-5071286

 

[RALFdoang]

Alright, it seem its my missunderstanding about the standard. I though the standard was come from CH.

Can some staff close this thread now?

 

[Fixxed]

Following though you're wrong somewhere. Simply containing 2-A is not enough for Low 1-C. A space could contain multiple 2-A structures and still have the same cardinality.
To gain Low 1-C from containing 2-A you need supporting context of being qualitatively bigger

Yeah this, containing 2A is not will make the space is low 1C

 

[Crabwhale]

Your thread is goner.