Metafinities

When your verse is just too large, you need something beyond infinities. Ω, ∞, ω, they’ve all become… too small. And you can’t multiply them, that just results in themselves. So, Metafinities are numbers describing the sizes of verses in Meta-Class 4 or above.
== Power of Infinities (POI) ==
Not to be confused with ‘Powers of Infinity’, which as we know, just results in infinity, Power of Infinity is the ‘power’ an infinity has. How much bigger. This can’t be quantified, but we can operate on it. We do this with ΩIP. We can’t have ΩIP+, as IP cannot be quantified. So, we create ΩIP×. ΩIP×1 is just Ω. It is 1x the ‘power’ of Ω. ΩIP×2 is Ω, with double the power. At the surface level, ΩIP×2 is basically Ω… to Ω. Like Ω, if Ω was 0 or something (not actually, as that would still result in Ω). ΩIP×3 is 3 times the power. So ΩIP×∞ is INFINITE times the power. So, is ΩIP×Ω would just be ΩIP↑2 right? Why that’s exactly WRONG! It don’t work like that. ΩIP↑2 is even larger than ΩIP×ΩIP×ΩIP×Ω… forever! Just like how Ω×Ω won’t give you a larger number. Nay, ΩIP↑2 is basically, completely surpassing ΩIP×! So, ΩIP↑3 would be… triple the power. Like ΩIP↑2… to ΩIP↑2. And ΩIP↑4 would be ΩIP↑3 to ΩIP↑3, and so on. Like you may or may not have guessed, ΩIP↑↑2 is Ω> than ΩIP↑ΩIP↑ΩIP↑... forever. Also, new terminology, Ω> means surpassing, not just 'greater'.
=== Uparrow Mania ===
As we get ΩIP↑↑↑...↑↑↑ with more and more arrows, we need to symbolise all these arrows. ΩIP↑n will be created. N will be the number of arrows. But eventually, we will get to ΩIP↑ΩIP↑... and more. So, what about a new notation. ΩIP↑↑n, where N is now the number of layers. Still too many layers? ΩIP↑↑↑n is how many layers of ΩIP↑↑n, and so on. But what about when there are too many ↑'s, again? ΩIP↑2n. Now, N is the number of ↑s, again. ΩIP↑3n? N is the number of layers, and so on, just like perviously. And ΩIP↑↑2n = ΩIP↑nn.
So, in a nutshell...
*ΩIP↑x = ΩIP↑↑↑...x...↑↑↑
**ΩIP↑↑x = ΩIP↑ΩIP↑... x times
**ΩIP↑↑↑x = ΩIP↑↑ΩIP↑↑... x times
**ΩIP↑↑↑↑x = ΩIP↑↑↑ΩIP↑↑↑... x times
*ΩIP↑2x = ΩIP↑↑↑... x ...↑↑↑x
**ΩIP↑↑2x = ΩIP↑2ΩIP↑2... x times
**ΩIP↑↑↑2x = ΩIP↑↑2ΩIP↑↑2... x times
*ΩIP↑3x = ΩIP↑↑↑... x ...↑↑↑2x
**ΩIP↑4x = ΩIP↑↑↑... x ...↑↑↑3x
*ΩIP↑↑2x = ΩIP↑xx
**ΩIP↑2↑2x = ΩIP↑↑2ΩIP↑↑2... x times
**ΩIP↑↑↑2x = ΩIP↑x↑2x
**ΩIP↑2↑↑2x = ΩIP↑↑↑2ΩIP↑↑↑2... x times
*ΩIP↑↑3x = ΩIP↑↑↑↑... x ...↑↑↑2x
**The same goes for ΩIP↑↑3x, as it did for ΩIP↑↑2x. 
**Likewise, ΩIP↑↑↑2x. would be ΩIP↑↑xx. This goes on until you have ΩIP↑↑↑↑...x.
After all this, it looks like this notation is bursting at the seams. So, let's define a new notation ~ 
ΩIP↑xL2. L means layer. So, L2 (layer 2) would be surpassing (Ω>) Layer 1, which would be everything else so far. We go L2, L3, L4, and in fact follow the exact same timeline as ↑, except ↑... would be L. We would have LL, LL, and finally, when we have LL, we'll introduce ML(1). Meta-Layer One, the layer of the layer, surpassing LLLL..., forever. Surpassing an infinite sequence of MLs, Meta-Layer Two, Meta-Layer Three, and then we'd have Meta-Meta-Layer One, which is larger than ML(ΩIP↑xML(ΩIP↑xML(...))))ML(ΩIP↑xML(...))ML(ΩIP↑xML(...))ML(ΩIP↑xML(...))...... forever, and, well, you know what's gonna happen. After an infinite amount of Metas and whatever, IP is obsolete. It's time for HFP.
=== Hyperfinite Power ===
"Too much powah!" 
For the truly massive verses, Hyperfinite Power (ΩHFP=y) is here. When IP is exhausted fully (no matter how many notations you make) HFP is way beyond that. Ж is the first hyperfinite ordinal. It has a HFP of Ω, and is also called Ω0. So its HFP is unquantifiable. A HFP of 1 is beyond IP. 2 is if HFP was IP (in which case it would be utterly devastating), it would break IP. 3 is likewise, but with 2. So, A HPF of Ω is... hyper. After this, you have Level 2 HFP (ΩH2FP=y), then Level 3 HFP (ΩH3FP=y), etc. After all that, you have Level x/2 Hyperfinite Power. (ΩHx2FP=y), then Level x/y/2 HFP (ΩHxy2FP=y) so on, and so forth. After all that, you have Ultrafinite Power (ΩUFP=x), the last notable notation before the Hebrewfinites. This notation transcends Hyperfinite Power to an unfathomable degree.
==Hebrewfinities==
What is a Hebrewfinity? Completely disconnected from HFP, Hebrewfinities are basically, beyond. There are two Hebrewfinite Chains - Alephfinities and Memfinities ~ which are used by Meta-Class 10 objects, such as the Terminality of All Verses. 
===Alephifinite Power===
Alephifinite Power is a notation unable to be reached in any way other than going straight to Alephifinite Power. Alephifinite Power is calculated using the notation ΩאFPx. The x in the ΩאFPx symbolizes how far in you are into Alephifinite Power. ΩאFP1 symbolizes regular Alephifinite Power, this can be represented as 𐌰1. At ΩאFP2 (𐌰2), 𐌰1 is basically True Nothing in compared to it. You can repeat this process until you get to ΩאFPΩ (𐌰Ω) at which point you can start using the Power of Infinities numbers. The largest possible using Alephifinite Power is ΩאFP𐌰𐌰... (𐌰𐌰𐌰... or 𐌰𐌰), with there being 𐌰𐌰 𐌰's! After this, you have Bethifinite Power, with an Alephipower Rating of 2. Alephifinite Power has an Alephipower Rating of 1. The notation for Bethifinite Power is ΩבFPx. ΩבFP1 can be represented as 𐌱1. You can repeat this process until you reach Gimelifinite Power that has an Alephipower Rating of 3. Then repeat that until you reach Shinifinite Power (ΩשFPx) with an Alephipower Rating of 22. The notation for Post-Shinifinite Power is Ω𐌿23FPx, which can be applied to previous notations (i.e. Ω𐌿1FPx = ΩאFPx). Ω𐌿23FP1 can be represented as 𐌿231. After all possible previous numbers have been exhausted, you get Tavifinite Power (ΩתFPx), which has an Alephipower Rating that cannot be written with finite space, or even infinite space! ΩתFP1 can be represented as 𐍄1. The largest number possible using Tavifinite Power is ΩאFP𐍄𐍄... (𐍄𐍄𐍄...), with the stack of 𐍄's going downwards forever!
===Memfinites===
Memfinities (Not to be confused Memifinite Power) with are categorised as Ωמ. The first Memfinity is Ωמin. Then comes Ωמin1, which is 1 tier above Ωמin. Fun fact - Ωמax is also completely inaccessible from Ωמin. In Memfinities, a tier is basically where that number is completely inaccessible to the tier below it, and can only be accessed by the Tier+1 function. It is thereby impossible to travel tiers, unless with Tier+1. And since Ωמax is inaccessible by the Tier+1 function, you cannot reach it even with a tier breacher. And, well, there's not really much to it.
This is pretty much the end. For more transfinities, metafinities and gendials, see my page on Fictional Googology Wiki.
Category:Number
Category:Meta-Class 4
Category:Fish's pages
Category:Fish’s Early Pages