There's been a misuse of the idea of the "no-limit fallacy." The no-limit fallacy has and ALWAYS has been used to say "Just because it is stated that a property has no limits, does not mean it has no limits." The NLF has never meant "Everything in fiction is a limit." Some people really do act like everything in fiction has a limit even when we can see examples of traits being absolute, or truly having no limit, that are commonly used.
The classic example to me is intangibility, or non-corporeality. Let's take Casper, the friendly ghost. He is a ghost. He lacks any physical body. He is not made of matter and energy. Then let's take a hypothetical character with a magic sword that can hurt primordial deities which created the a multiverse of infinite dimensions but does not have the ability to hit intangible entities. No one, or at least I would think no one, would say "Well Casper's intangibility has never been shown to work on characters that strong." Presumably it's clear that without the ability to hit intangible entities, you can't hit intangible entities with a physical attack because the very definition of intangible means they don't have a physical body to physically attack. However when you say that a character can't be transcended in power based on definition, then people think it's an NLF. Allow me to present three hypothetical scenarios.
1: Character states Demon is invulnerable to everything except a specific holy sword: Pretty Textbook example of NLF here. The character could be lying or mistaken. There's no reason at all to think they could survive attacks from characters vastly stronger than any feat shown in the verse. At best, this means that the Demon can't be killed by anything the character knows about.
2: The Narrator states Demon is invulnerable to everything except a specific holy sword. Once again the narrator is not expected to have knowledge or authority on things in other continuities. This one is a stronger statement in that unless it's contradicted, you can probably safely scale the Demon to being unkillable by everything in the verse itself, as the Author/Narrator is expected to have full authority and knowledge on their own continuity.
3: There exists a realm containing all concepts and ideas, however beyond that lies the highest transcendental plane of being transcending all concepts including things like power, infinity, duality, and hierarchy. This is a consistent non-contradicted part of the verse's lore, referenced from several different points by different sources. The Demon's existence is a part of this realm, transcending all concepts. At that point saying that a character would beat them because they are "infinitely stronger than them" is meaningless because their existence is above concepts like infinity, power, and hierarchy. I'm fine with the standards for this being as high as wanted, but I strongly object with people saying that this is a NLF because it's not. It's literally just seriously applying the information a fictional verse is trying to present. If a character transcends the concept of power, than the concept of power is no longer meaningful to talk about relative to them.
On VS wiki there is a general principle that with 1-A fights, that power is all that matters and hax doesn't matter. Respectfully, this seems inverted to me. Power to me just seems like one more concept like any other, and I see no reason it should have more conceptual "weight" than other concepts characters transcend like space and time. To me it seems the only thing that matters in fights of that nature is hax, or in particular what abilities are had that CAN even affect each other.
I'd like to give my thoughts on three types of infinity, and how they apply to vs debating, giving some general basic vs information on them for people who may not know; infinity as a concept, higher infinities as a concept, and the absolute.
Infinity:
Starting with a basic point. Infinity is NOT a number. Infinity is a concept. There are a set of numbers called "infinite" numbers. The definition in Mathematics of an infinite number is that it's a number larger than any "natural number" which are the positive integers [1, 2, 3...] That's it. You can do mathematics with infinite numbers but you have to understand that the results can be highly unintuitive. To talk about infinite sets, a branch of mathematics is used called set theory.
Set Theory is the theory about sets of things. A recurring term used in it is "Cardinality." Cardinality just means the number of elements in a set. For instance if you have a set of 3 apples, that set has a Cardinality of 3. If you have a set of 5 bananas, that set has a Cardinality of 5. Sets are compared in size if elements from one can match onto the elements of another. If you have a set of 5 apples and another set of 5 bananas, you can match the apples and bananas one to one and see they are the same size. For finite cardinalities, it is so intuitive it's basically common sense. However with infinite cardinalities, it gets a bit more complicated.
Let's say you have Aleph-Null, the smallest infinite set, the set of all the natural numbers. Let's say you also have the set of Aleph-Null and 0. Which set is larger? The truth is that they are identical in size. This is because you can match the elements in them one to one by simply subtracting one from every element in the first set. 1-1=0, 2-1=1, 3-2=1, and so on. What you get is the second set exactly. Aleph-Null + 1 =Aleph-Null.
Let's say you have the set of all natural numbers [1, 2, 3...] and you have the set of all positive even numbers [2, 4, 6...] These too are the same size. You can multiply every element in the first set by two and get the second set exactly. Without changing the number of elements, they have become the same set. Aleph-Null * 2 = Aleph-Null.
With this same logic you can also demonstrate Aleph-Null * Aleph-Null or Aleph-Null^2 = Aleph-Null. Let's say you have the set of all natural numbers [1, 2, 3...] and a set of every two-digit coordinate combinations [1,1 and 1,2 and 2,1 and 2,2 and 3,1 and 3,2...] Because every integer has a unique prime factorization you can take the X and Y coordinates presented in the second set and perform the operation X^2*Y^3 and you will get a unique coordinate in the first set. Aleph-Null squared is still equal to Aleph-Null. This is my main objection to dimensional tiering, which itself seems to be falling out of favor. An infinite two-dimensional plane is not larger than an infinite one-dimensional line. They are the same type of infinity. Squaring an infinite set does not increase it's cardinality.
This can be generalized as "multiplication between two numbers in which one is an infinite number and the other is not zero will lead to a product (result) equal to the cardinality of the greater value." Aleph-Null * 3 = Aleph-Null. Aleph-Null * Aleph-Null = Aleph-Null. Aleph-Null * Aleph-1 = Aleph-1. Not "basically" or "approximately" the ending value, EXACTLY the value. Zero is the odd one because an infinite set multiplied by zero is indeterminate, in the same way that dividing by zero is indeterminate.
One of the ideas that can be harder to understand about infinite numbers is that they can be different but have the same cardinality. For instance if you have a set of Aleph-Null apples, and a set of Aleph-Null apples and a banana those two have the same cardinality but don't have the same elements. Recall how there are the same number of even numbers and even AND odd numbers. Those sets have different elements but the same cardinality. You CAN have things outside an infinite set, it just isn't MORE things.
In VS debating there are several axioms to be taken about infinity if you wish to quantify a verse using the real world idea of an infinite set. You can say infinity "works differently" in a verse if you want. That's fine, but the problem is we can't quantify it then as our mathematics wouldn't apply and it becomes unquantifiable.
1: Characters can't be finitely stronger or weaker than a character with infinite power. This is objectively self-contradictory. They also can't be infinitely stronger or weaker when it's the same "type" of infinity.
2: Characters that scale to an infinite value either scale to it exactly, scale infinitely above it, or do not scale to it. This is a necessary consequence of the above. One can not be quantifiably finitely above or below an infinite value. Such is like being "0" above or below a finite number and somehow being a greater or lesser value.
3: A space can be any size that can be understood and quantified by the author and doesn't need to encompass a cosmology to do so. However destruction of more elements that is not a higher type of infinity does not increase the value at all if an infinite set is being destroyed. Destruction of a multiverse with infinite, infinite-sized dimensions is not a feat of greater cardinality than destruction of a single one of those dimensions, though it does indeed contain different elements.
I have deliberately left out things I think are my opinions or interpretations from these axioms. These are, to my knowledge, things that are simply logically necessary with an infinite number, where stating the opposite causes a contradiction.
Higher Infinities:
How are higher infinities reached? The mathematics for some of them is beyond the reach of myself or anyone who isn't significantly devoted to mathematics but I can go a bit further.
As mentioned Aleph-Null is the set of all counting numbers (among other things). Adding, Multiplying, or Raising Aleph-Null to the power of any finite number or Aleph-Null itself won't increase the value. Well there exists a set of numbers called Ordinals. Ordinals like Omega + 1 or Omega * 2 describe the way things are arranged. If you have Aleph-Null bananas and an apple, you would have Omega + 1 fruit, and if you have Aleph-Null bananas AND apples, you would have Omega * 2 fruit. These aren't bigger than Aleph-Null, they just describe the way Aleph-Null things are arranged.
The ordinal number describing the set of all the countable ordinal numbers if Omega-1. Omega-1's cardinality is Aleph-1. This might be the same thing as all the continuum, all the numbers on a number line, all finite numbers given Aleph-Null decimal points.
From there you can get bigger and bigger Alephs via a similar process.
One can also assert axiomatically that there exists higher cardinalities that can not be reached from below. These are called "Inaccessible Cardinals." Aleph-Null is sometimes considered one, as you can't reach Aleph-Null from below, it's asserted axiomatically as being beyond all counting numbers.
The Absolute:
The Absolute isn't really a mathematical concept, though it does have a mathematical component "Absolute Infinity." Absolute Infinity is the possibly paradoxical idea of a hypothetical largest number, so large that no mathematical operation can change its value. While in the real world it is debated if this idea is self-contradictory, because it is still in contention, and its meaning can be understood, if used in fiction it should be interpreted as it is rather then denying it with the NLF claim.
Absolute Infinity is tied to the philosophical idea of the Absolute or the Ultimate, that which is beyond all other forms of being. By definition there can only be one Absolute, though a verse can have different characters or objects experience or interact with it from a different lower perspective. What's exciting about this to me is that this is actually how most of the top tier series in fiction already describe the top of their cosmology, an absolute existence transcending concepts which various powers or beings participate with or perceive in different ways. It is inherently transcendent of all forms of being so concepts like "power", "infinity" and "hierarchy" don't apply to it and it can't be scaled in a direct quantification way, though different powers can participate in the absolute. The Mathematical "Absolute Infinity' idea is basically Infinity reaching and participating with the Absolute.
To give an example: DC Comics:
Outside Creation is the Void where infinite creations each filled with their own concepts and hyper-concepts like DC Comics all are zero in comparison. It consistently transcends all concepts, and is beyond thought. It is the Absolute in DC Comics, and it explicitly referred to as such. Powers that can affect the Void itself, or its other selves are absolute, which are actually relatively rare in DC Comics. Even powers that affect all of Creation or ALL the creations in the Void amount to nothing in comparison to the Overvoid.
For how this would apply to another god tier verse, take the Cthulhu Mythos:
There is infinite dimensional space before the First Gate, then Infinite Gates before one reaches the Ultimate Void inhabited by the Ultimate Mystery, which is what I would define as the Absolute, as it is where Carter realized individuality is an illusion, and it is referred to as the final sweep of existence outreaching fancy (thoughts, concepts) and mathematics (the hierarchies of infinities) alike. That which participates in it is absolute.
I believe this is the proper VS analysis as it is the information the series tries to present which can be meaningfully understood.
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