Dimensionality

Miscellaneous, Standards and Guidelines

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Dimensionality is one of our hierarchical classification standards, based on the concept of dimension in physics and geometry. In geometry, each dimension is an imaginary directional axis in space. In the case of multiple dimensions, each axis is always perpendicular to the other.

This concept has been present in geometry since Euclid, where the Euclidean space is established, which encompasses any dimensional finite space. Euclid worked with the second and third dimensions, which is the limit that our perception can comprehend. Centuries later, the mathematician David Hilbert created the concept of Hilbert space, which is a generalization of Euclidean space that is not restricted to a finite number of dimensions.

In the theory of relativity, time is considered the fourth dimension of our universe.

The Book Flatland: A Romance of Many Dimensions, of Edwin A. Abbott, clarifies how this works.

Usage

Most of the time the dimensionality of a given character will not necessarily affect his power (mostly characters from 1D to 3D), but it is worth remembering that to have a dimensional level it is necessary for the franchise to work with higher infinities of the spatial axes. That is, a higher-dimensional "bulk" space which embeds lower-dimensional ones (Such as our universe) as subsets of itself, whose dimensions are not microscopic/compactified. Only in this way can this character be seen as infinitely larger than the lower dimension.

Regardless of the limiting number of dimensions that each theory addresses, we will express each dimension by its proper ordinal number among all finite numbers. Therefore we can express the set of all natural numbers as Countably ∞D, mathematically this would be expressed as;

ω = {0, 1, 2, 3, 4, 5...}, where ω is the first infinite ordinal number, and thus all natural numbers of dimensions.

Regarding Non Dimensional beings, we rate these characters' dimensionality as Inapplicable, due to this concept being unable to be used to describe them.

However it is important to know that dimensionality in itself is simply an additional axis of movement, and being a higher dimensional being and/or existing in a higher dimension won't warrant a higher tier. See here for more information.