Issue 1: Otto's statements are unreliable
One of the two sources for the "absolute infinity" scaling is that Otto himself boasts that "the power that cannot be renormalized is absolutely infinite" (which either refers to the Imaginary tree, his particular Imaginary Space, or Otto's power). The issue here is that Otto is not a reliable source of information whatsoever. Otto had
claimed to have transcended Herrscher entirely, becoming a god in comparison to them; yet, he
obviously got killed by a Herrscher anyways. That particular boast of his regarding the "absolutely infinite"
was in the middle of him claiming that relying on the Herrscher of the Void's power would not be enough to kill him... and then immediately getting killed by the Herrscher of the Void's power seconds later anyways (and my goodness, Otto's voice is grating to listen to).
As demonstrated, Otto has been shown repeatedly to be full of shit. As a result, his boasts of his own power being "absolutely infinite" are not reliable. But there is still a quote from a book claiming that Otto's imaginary space is absolutely infinite. This should be reliable on paper, but there are problems with even that which I will go over below. In light of those problems, this one solitary statement from the book which could've been reliable should be discarded.
Otto as the False God is stated to
have his energy to be in pair with the Herrscher of Finality, said Herrscher is
stated to stronger than any other Herrscher (Consistent) Otto didn't get killed,
only his power was turned into finite or
destroyed (?) and then it vanished, by that time
he already had lost his powers, so anything after this timestamp no longer applies to FG Otto, but rather his Kolosten key, and even then he actually didn't die,
he is alive as he walks to the Imaginary Tree and only dies to Shamash flames. (
Starts here, and he dies
here to Shamash)
As I said before, Otto's statements are backed up
by the entity that was providing him this energy, by
other characters and
by the book (Will get into the book soon). Another thing is that even if Otto were unrealible here, just because a character was once, doesn't mean he will be every time, especially when there is extra statements supporting him.
Issue 2: Otto's power is limited, and by extension, so is his imaginary space despite it supposedly being "absolute infinity"
Otto's power
was stated to be limited (even Shiroiyo seems to accept that), yet
he was still able to use that limited power to distort the his entire imaginary space to the point where the entirety of it was resonating with his energy. This indicates that the space itself is limited; otherwise it would be too big for Otto to perform this feat. Since this Imaginary Space in particular, which has been demonstrated to be limited, was described as being 绝对的 "无限" this also indicates that something which is 绝对的 "无限" can still be limited, which speaks against 绝对的 "无限" strictly meaning "absolute infinity" in the Cantorian sense (since Cantor's Absolute Infinite is NOT limited).
I agreed that Otto was inferior in relation to the Tree due to the
"slave" and "close" statements, as you can
see here. I will repeat my a bit of my previous point, Nagamitsu is very likely to be out-stated here since if Otto couldn't use all that power at once, it wouldn't make sense for the plot to require that power/energy to be transformed into finite, Otto would at least have to have a downscaling of that infinite value for that infinite to be transformed into finite, since any % of something infinite is still infinite, or else renormalization would be transforming finite into finite.
The Imaginary Space was called
infinite here and
here. Again, I will argue that Nagamitsu is contradicted by the fact that Otto actually showed to be able to create the space, and was never (visually at least) showed to be limited.
I would give in for the on screen feat/narration here. Imagine person X was robbed by person Y, person X denouces Y for theft, but Y denies it... but in this case we have a camera that recorded the event and we have visual evidence that Y actually stole from X, in which case X is favored due to visual evidence. We also have Kalpas and Elysia busting Imaginary Spaces (Kalpas was stopped before doing it, but Elysia actually did it on one go) for consistency sake.
Issue 3: The Imaginary Tree is transfinite; thus, it is not "absolutely infinite" in the Cantorian sense nor is it Low 1-A.
The Imaginary Tree
is stated to have a transfinite scale and can be described using the concept of transfinite numbers. This is a problem because
"transfinite" is literally a word coined by Cantor specifically to refer to infinities that are NOT absolute. Additionally, this is a problem because Low 1-A
is beyond transfinite numbers as a whole (the Von Neumann universe is beyond transfinite numbers). Since the Imaginary Tree is transfinite and has a scale that can be described using the concept of transfinite numbers, it cannot be Low 1-A.
As for this, there was a discussion about the statement during the firsts upgrades threads and after checking the raws, it actually says that the Tree is
infinite in scale even in a transfinite sense, and it currently what we use now. Without the 'even' here, the localization still implies that anyway, as if the Honkai on Earth already makes up for a transfine cardinal, the Tree was still far from and was stated to infinite even in a relation to it, it is
consistent. But you like you said in your point 5, it would be good to get some translation members here just to double check.
Issue 4: Cantor's Absolute Infinite just has a lot of baggage to it that simply does not fit with Honkai's descriptions of "absolute infinity."
Cantor didn't treat numbers as quantitative extensions
of strength like in our tiering system does below 1-A, but rather
treated them in a Platonic sense and viewed numbers as representing reality itself, including the very relationships and processes that govern both the external and mental world. These numbers encompass both "quantitative superiority" and "qualitative superiority." Already, Cantor's theories go beyond Low 1-A and into 1-A and above
Cantor also viewed the Absolute Infinite as not just beyond numbers, but
fundamentally beyond mathematics as a whole. Cantor viewed the "set of all alephs" as something that could not be considered a mathematical object at all (unlike V) due to the Burali-Forti paradox. Instead, he viewed the Absolute as an
unique, completely individual unity in which everything is, which contains everything (this already clearly doesn't apply to Otto's "absolutely infinite" imaginary space since it doesn't contain everything in the verse); a metaphysical entity
without determination whatsoever in the Hegelian sense ;
completely unincreasable (unlike Low 1-A which is treated as increasable on our Tiering System);
unable to be conceived as an abstract or mathematical magnitude, number, or order type; and
beyond the intellect's ability to define, determine, or distinguish due to the Absolute's sheer immensity.
I'd argue this actually proves it's Tier 0 which absolutely does not apply to Otto or the Imaginary Space, but I want to hear what Ultima thinks of that first. Either way, Cantor's Absolute Infinite does NOT work at all for Otto's imaginary space and thus should not be used to scale here.
Absolute Infinity is capped at low 1-A, it is how treat it as of now, unless that changes,
it is just baseline low 1-A, we treat it as a quantity (This thread here even has inputs of 3 staffs). If you think that Absolute Infinity should be 1-A or tier 0, you are free to make a thread to upgrade it to these tiers, but as of now it isn't how we treat it. Regardless, it is not how Honkai treats it, Honkai treats it just like our tiering system and most definitions does, something quantitative.
ssue 5: The Chinese referring to "absolute infinity" is iffy (should probably get a translation member here though)
In Chinese, Cantor's Absolute Infinite is usually written out as "绝对无限." However, in the actual statement our scaling is based off of,
it is written out as 绝对的 "无限". In addition to it being spelled differently, notice the quotation marks. Quotation marks are often used to denote proper nouns (ie names) and metaphorical language, meaning that the "infinity" is likely either just a name/buzzword or figurative language rather than a literal basis for scaling.
Like covered before, Otto actually states without any
quotation mark here, the renormalize
here refers to the Imaginary space btw, and even
googling the CN is going to take you there. Other than that, we dont know what the " " even means here and assuming it is hyperbolic when the same is stated more directly in the game is baseless imo.