Extended Universe Size Index

The Extended Universe Size Index (EUSI) is a number, which indicates the deepest nestation of verses within a specific verse.

An example of the EUSI.

It can be used to tell the size of a universe, without needing to say its size, due to most verses having beyond infinite sizes, or ordinals/cardinals that aren't named yet.

EUSIs aren't confined to just verses either, they can be applied to other containers, boxes, structures (artifical or not), etc.

Definition

We define a function

$\psi (\alpha )=\alpha +1$

$\psi (\alpha ,\beta ,\gamma \cdots \delta )=\psi (\alpha -1,\psi (\alpha ,\beta ,\gamma \cdots \delta ),\gamma \cdots \delta )$

$\psi (0,\beta ,\gamma \cdots \delta )=\psi (\beta ,\gamma \cdots \delta )$

$\psi (0,0,\gamma \cdots \delta )=\psi (1,\gamma \cdots \delta )$

After this, we can create another extention, by borrowing some things from other functions, such as the veblen function, by asserting:

$\psi (\Omega ^{\alpha })=\psi (\overbrace {1,0,0\cdots 0,0} ^{\alpha })$

$\psi (\Omega ^{\Omega })=\psi (\Omega ^{\psi (\Omega ^{\psi (\Omega ^{\cdots })})})$

$\psi (\Omega ^{\Omega ^{\Omega }})=\psi (\Omega ^{\Omega ^{\psi (\Omega ^{\Omega ^{\cdots }})}})$

EUSI in number form

EUSIs can obviously be broken down into ordinals / cardinals after they've been fully decomposed. The article of these is here.

Examples

• Protoverse = $0$
• Our Universe = $\psi (0)$
• Hyperverse = $\psi (4)$
• Berryverse = $\psi (1,0)$
• Omniverse = $\psi (1,0)$
• The Pentagonal Hexacontahedron = $\psi (2,0)+\psi (540)$ (according to TOH)
• The Box = $\psi (2,0)$
• Absoverse = $\psi (1,0,0)$
• Cloudverse = $\psi (2,0,0)$
• Nvgngyu = $\psi (3,0,0)$