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surpassing aleph one universes.
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what tier would this be?
- Thread starter 1st_Virtue_of_Pure_Void
- Start date
- 5,304
- 3,211
this question is funny
Q: How do cardinal numbers relate to tiering?
A: Firstly, it should be highlighted that asking about the tier of a cardinal number is effectively a meaningless question when the quantity which it is denoting is not specified in the question as well, and makes as much sense as asking "What tier is the number 8?"
Let's take the smallest infinite cardinal (aleph-0, or ℵ0, the cardinality of countably infinite sets) as an example in this case: A set comprised of a countably infinite number of 0-dimensional points is itself a 0-dimensional space under the usual notions of dimensionality, being thus still infinitely small. Meanwhile, a countably infinite number of planets is High 3-A, a countably infinite number of universes 2-A, and countably infinite dimensions High 1-B.
We then move on to the power set of ℵ0, P(ℵ0), which is an uncountably infinite quantity and represents the set of all the ways in which you can arrange the elements of a set whose cardinality is the former, and is also equal to the size of the set of all real numbers. In terms of points, one can say that everything from 1-dimensional space to (countably) infinite-dimensional space falls under it, as all of these spaces have the same number of elements (coordinates, in this case), in spite of each being infinitely larger than the preceding one by the intuitive notions of size that we regularly utilize (Area, Volume, etc)
On the other hand, an P(ℵ0) number of universes is Low 1-C, and a similar number of spatial dimensions/layers of reality is Low 1-A
However, the same does not necessarily apply when approaching sets of higher cardinalities than this (Such as P(P(ℵ0)), the power set of the power set of aleph-0), as they would be strictly bigger than all of the spaces mentioned above, by all rigorous notions of size, regardless of what their elements are. From this point and onwards, all such sets are Low 1-A at minimum.
Do note, however, that these infinities must specifically refer to elements that physically exist within a verse's cosmology. Them existing as in-universe mathematical concepts is not sufficient for anything to scale to them, unless there is a direct comparision that allows scaling to be made.
Q: How do cardinal numbers relate to tiering?
A: Firstly, it should be highlighted that asking about the tier of a cardinal number is effectively a meaningless question when the quantity which it is denoting is not specified in the question as well, and makes as much sense as asking "What tier is the number 8?"
Let's take the smallest infinite cardinal (aleph-0, or ℵ0, the cardinality of countably infinite sets) as an example in this case: A set comprised of a countably infinite number of 0-dimensional points is itself a 0-dimensional space under the usual notions of dimensionality, being thus still infinitely small. Meanwhile, a countably infinite number of planets is High 3-A, a countably infinite number of universes 2-A, and countably infinite dimensions High 1-B.
We then move on to the power set of ℵ0, P(ℵ0), which is an uncountably infinite quantity and represents the set of all the ways in which you can arrange the elements of a set whose cardinality is the former, and is also equal to the size of the set of all real numbers. In terms of points, one can say that everything from 1-dimensional space to (countably) infinite-dimensional space falls under it, as all of these spaces have the same number of elements (coordinates, in this case), in spite of each being infinitely larger than the preceding one by the intuitive notions of size that we regularly utilize (Area, Volume, etc)
On the other hand, an P(ℵ0) number of universes is Low 1-C, and a similar number of spatial dimensions/layers of reality is Low 1-A
However, the same does not necessarily apply when approaching sets of higher cardinalities than this (Such as P(P(ℵ0)), the power set of the power set of aleph-0), as they would be strictly bigger than all of the spaces mentioned above, by all rigorous notions of size, regardless of what their elements are. From this point and onwards, all such sets are Low 1-A at minimum.
Do note, however, that these infinities must specifically refer to elements that physically exist within a verse's cosmology. Them existing as in-universe mathematical concepts is not sufficient for anything to scale to them, unless there is a direct comparision that allows scaling to be made.
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