The Super Zeroie Cardinal is a large macro-zeroid, defined using the Ie function as Ie(Ie(0)). It first appeared on September 26, 2021, on the video "(SNEAK PEAK) -0 to 1". The Ie function is introduced but not defined in the video, but some clues allow us to get a rough idea of it's meaning.
Official Ranking[]
It is listed after Ie(0) and before Largest Zeroie Cardinal, the latter of which does not have a proper known expression (it contains question marks implying uncertainty). It occurs after 0, but before the infinitesimals. This puts it in the class of Macro-Zeroids. Technically this places it in Class 0, since it is considered larger than 0. None the less it is given a special designation of Ie here.
Conjectured Properties[]
It is conjectured that the Ie function may only return large macro-zeroids which lie above and outside some 0-dimensional structure enveloping 0. Despite the impression this gives of their being a left and right side of this structure, in fact the numbers here are still too small to have "sides" and instead there is only "one side" outside of the structure. Ie(a) will always return a macro-zeroid of the Ie Class designation, which can be thought of as a subclass of Class 0.
The following properties are believed to hold:
Ie(a) * non-zero = Ie(a)
Ie(a) * le(a) = le(a)
Ie(a) * le(b) = Ie(min(a,b))
le(a) * 0 = 0
Ie(a) * hyper-zero = hyper-zero
Ie(a) <<> Ie(b) iff Ie(a)*le(b) = Ie
Ie is believed to have an unrestricted domain.
It appears that the creator of the Super Zeroie Cardinal assumed that Ie(Ie(0)) would be much larger, in much the same way that say e(e(0)) is much larger than e(0), or zeta(zeta(0)) is much larger than zeta(0). It might be assumed that Ie(Ie(0)) would be much larger than Ie(1). However, one has the remember that Ie(0) is not a large number, but rather a macro-zeroid by definition! This means Ie(0) is in a certain technical sense, not that much larger than 0. Thus Ie(Ie(0)) is not that much larger than Ie(0) since 0 <~ Ie(0). It appears that Ie(1) would actually be larger!
This means Ie is unique and different from ordinal functions. For example:
e(1) << e(e(0))
Ie(Ie(0)) << Ie(1)
In fact, since Ie(Ie(0)) is also a macro-zeroid it follows that it is also less than 1, and therefore Ie(Ie(Ie(0))) is less than Ie(1). In fact Ie(1) is larger than recursions on 0 with Ie. This is the first example of a zeroid function which itself can take zeroids as arguments, leading to all sorts of new possible insanity!
The key thing is ... due to this property, Ie(1) is not the immediately next largest macro-zeroid after Ie(0). Arguably the next largest would actually be Ie(_-1), assuming it can only take macro-zeroid tiers as arguments. It would be a very long time before we reached Ie(Ie(0)) let alone Ie(1). In that sense Ie(Ie(0)) would actually be much much larger, lending credence to the idea of existing above the macro-zeroid tiers.