Hermaeus Mora, Jyggalag, and the different types of infinities.

In mathematics there's the concept of differing infinities. A countable infinity (referred to as Aleph-Naught/Zero/Null| ℵ0) and an uncountable infinity that is simply infinite with no linear gauge of size. These apply to quite literally everything we can measure. The universe is infinite, ever expanding, but it has a limit, therefor it can be counted. That's a countable infinity, ℵ0. The number of universes? ℵ1? ℵ2? Nope, entirely uncountable, uncountably infinite.

With that established in what limited terms I personally understand it with, I've come to this question regarding the two Daedric princes whose spheres encompass knowledge. Hermaeus Mora and Jyggalag.

Mora's realm of Apocrypha is said to contain all knowledge that is knowable > It is an endless library consisting of untitled books with black covers, where all forbidden knowledge can be found.

The supposed caveat is that it's forbidden knowledge but that doesn't really matter when you take into account the art of making sweetroll icing is probably forbidden by some family somewhere, so it stands to reason Apocrypha would contain all knowledge knowable.

Let that sink in for a second, all knowledge knowable. That's the location of every grain of sand in the Niben bay, every loose rock on the throat of the world, every hair on everyone's heads in all of time straight back to the dawn era! A library would need to be endless to contain that infinite amount of information.

And how far back and/or forward does this knowledge progress? We already know Daedra aren't quite bound by linear time so it makes sense Apocrypha could contain information from previous and future Kalpas, it could contain exactly what happens during and how to cause a dragon break, the mastery of Pankratosword and the achievement or at least the path to CHIM.

SO I ask, is Herma Mora's knowledge truly infinite? Or is it countably infinite? Can we know all that Mora knows? Or is there too much for all of every mortal born and yet to be born on Nirn?

Onto Jyggalag.

Jyggalag was reviled by the Daedra for being a being which promoted logic and stasis to unseen levels, prime exmaples are the crystalline Knights of Order, crystalline substances are some of the most stable currently known. Jyggalag is said to have formulae and algorithms so perfect and applicable they can predict with supposedly 100% accuracy what has been, what is, and what will be.

> Using the formulae once contained in the Great Library, Dyus can predict all events before they happen, save the Prophecies of the Elder Scrolls.

It's worth noting here that not even Apocrypha contains the knowledge of the elder scrolls so there's that.

Jyggalag's Great Library, referenced there by Dyus (speaking of, where the hell is Mytheria anyway?) was probably on par with Apocrypha during the height of Jyggalag's power.

If Jyggalag had forumlae to predict everything, and therefor know everything with mathematical certainty, could Jyggalag have known the entire contents of Apocrypha? The likelihood of of the ascension of Talos? The rate at which entropy occurs in the Mundus?

I posit that Hermaues Mora had an ℵ0 set of information stored in Apocrypha, that is countably infinite, but that Jyggalag had an ℵ1+ or potentially uncountably information in potentia but had not and potentially could not come into being.

OR

Maybe I'm overcomplicating things applying vague mathematical principles to a high-fantasy world where the sun is literally just a hole in the sky to another plane of existence.