Senior Goose's Temple!

The mountain the Goose stood on grew countless times larger. The entire mountain range transformed into a paradise, towering above everything with gorgeous cliffs where one could bask in the godlike scenery.

Lush, multi-coloured plantlife grew along the mountains, creating a vibrant yet harmonic scene. The presence of Qi here was thousands of times greater than anywhere else in the Five Mythical Worlds, making this mountain range a true paradise for cultivators.

The mountains were surrounded by countless amounts of bright multi-coloured planets, each one being the size of the Ten Thousand Worlds. The Ten Thousand Worlds is the lowest layer of existence, below the Five Mythical Worlds. It is a massive collection of realms with uncountably infinite layers of existence and universes.

New sets of universes and layers are created in every single one of the uncountably infinite amount of instances at any interval of time with the cardinality of the new universes and layers being greater than the cardinality of the previous set, akin to that of the axiom schema of replacement.

The axiom schema of replacement is defined as follows: x is a set and f is a function, then {f(y): y ∈ x} is also a set. The name of this axiom stems from the fact that the set {f(y): y ∈ x} can be thought of as being formed by replacing each member y of x by its image f(y).

For example, one could take the set of all the natural numbers, (0, 1, 2, 3, ...), denoted as aleph null, and replace each element with a corresponding aleph number to create the set (ℵ0, ℵ1, ℵ2, ℵ3...) denoted with aleph omega.

And it doesn't stop there, one could go further by taking a set whose cardinality was the first uncountable infinity, (0, 1, 2, ... ω, ... ω + ω, ... ∈0, ... α, ...), known as aleph 1, and repeat the operation above of replacing each member with a corresponding value to create the set (ℵ0, ℵ1, ℵ2, ... ℵω, ... ℵω + ω, ... ℵ∈0, ... ℵα, ...); and so on from there.

It was with this axiom that the Ten Thousand Worlds increased its size, instant 1 would see aleph null layers of existence and universes created, instant 2 would have aleph omega layers of existence and universes made, and so on from there. Hence, the Ten Thousand Worlds grew exponentially to larger and larger infinities with no end in sight to this relentless self-expansion.

At the base of the highest mountain, filled with Qi in quantities millions of times higher than the rest of the mountain range. The same would be said for its quality and purity.

A mesmerizing stone path surrounded by glowing gold plants led its way up to the peak of the mountain as golden clouds were present along the way.

The higher one went up, the purer the Qi one would find. At the peak of the mountain stood a massive white temple that spanned quadrillions of miles with its shiny golden roofs oozing off endless glory. Stood before the gate on each side was a marble statue of Senior Goose, giving off boundless glory and majestu.

Inside the palace were dozens of areas for different purposes. There is a blacksmithery, herb shops, areas for fighting and tournaments, vast fields for training, majestic houses within where one could reside. There is also a massive training ground where people can gather situated on the peak's cliff.

It was truly a majestic place to be in. The beautiful jade plants scattered around made the sight even more beautiful. At the center of the temple stood a massive pagoda going up tens of thousands of floors.

At the peak of temple stood the great Senior Goose, looking down on the mountain ranges. It stroked its beak with its right wing as it spoke, "Mhm. Very nice. Those planets could do a little work though."

And so the Goose waved its wing, the movements of which seemed to flow harmoniously with the Dao itself. The planets then exponentially increased their size to hyper-inaccessible.

The cardinal number θ is recognized as being an inaccessible cardinal if it is regular (a cardinal is considered regular if it cannot be written as a sum of cardinal numbers less than itself) and whenever a number, x, is less than θ, then the first cardinal number greater than x, denoted as x+, is less than θ as well.

An example of an inaccessible cardinal would be aleph null, since it is regular and is not a successor cardinal (if y is less than aleph null the first cardinal number greater than y, y+, would still be finite and hence still be smaller than aleph null); thus aleph null is generally called 0-inaccessible, with 1-inaccessible being the first inaccessible cardinal greater than aleph null.

In short, it was very hard to reach θ as it couldn't be attained by taking the limit of the cardinal to any number less than θ itself, nor can it be reached by jumping from cardinal to cardinal which are lesser than θ.

The cardinal number v is hyper-inaccessible if it is a regular cardinal, and has the property that whenever x is lesser than it x+ is also lesser than it, and whenever y is lesser than v the first inaccessble cardinal greater than y is also smaller than v.

In short, v cannot be reached from below by taking the sum of cardinal numbers less than itself, nor can it be reached from jumping from cardinal to cardinal (as it is a limit cardinal), or jumping from inaccessible cardinal to inaccessible cardinal as it is the limit of inaccessible cardinals.

The Goose quacked in satisfaction, its bright golden eyes shining with endless golden light. The Goose then proceeded to speak, sending a message throughout the entire Five Mythical Worlds.

"The Soaring Dragon Peaks shall now be my property! The greatest cultivators shall be the ones that can qualify for my great sect, the Immortal Temple of the Great Venerated Holy Divine Immemorial One Who Basks In His Supreme Everlasting Light, Who Has Come To Save The World And Offer His Infinite Mercy! "

And so the Five Mythical Worlds exploded with vitality.