Googological regions are huge spherical regions of our infinite universe proposed by Denis Maksudov as addition for his naming system of large numbers (i.e. of numbers generated using functions of fast-growing hierarchy and such ordinal notations as Cantor normal form, Veblen's function and Buchholz's function).
Googological regions defined as follows:
Ra is spherical region of the universe bounded by imaginary sphere with center at the Earth's center and with radius of meters, where is a name of number, which was created according this system of names (if name of number begins with a vowel, then don't write "a" in "Ra").[1][2]
Example: The Octinommwil is equal to using fast-growing hierarchy and Buchholz's function. Then the Roctinommwil is spherical region of the universe bounded by imaginary sphere with center at the Earth's center and with radius of meters.
![{\displaystyle f_{\underbrace {\psi _{0}(\Omega _{\Omega _{\cdots _{\Omega }}})} _{8\quad \Omega 's}}(10)=f_{\psi _{0}(\Lambda [9])}(10)}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/43f76d377b4e8c8ffa248a54a93f43d10ae930f4)
![{\displaystyle f_{\psi _{0}(\Lambda [9])}(10)}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/bc1b1e5b509daaa04cfb9d27e6ae0d5039098665)
Bounders of those regions are not connected with existing real structures of the universe or with some inhomogeneities in the distribution of matter since we don't know anything about structures or inhomogeneities on so huge scales, but nevertheless any googological region can be defined at simple assumption that the space-time is infinite.
Note: instead light-years or parsecs for measure of astronomical distances the meter was chosen since it is base unit of the International System of Units (SI) but numbers mentioned above are so large that as a rule expressions don't change after convertion for light-years or gigaparsecs.
Gallery[]
The galaxy Milky Way in the sky of planet of a binary star in a Globular cluster of the Large Magellanic Cloud. We can say that Milky Way and Large Magellanic Cloud as well as the whole observable universe belong, for example, to the Ratralum - googological region with radius of Tralum meters.
Picture was generated using Space Engine