As we all know, there is a set of theories in set theory specifically used to measure the size of various types of [infinite sets] called [infinite cardinal numbers].

The basic concept of this set of theories is that if all the elements in the two sets can establish a one-to-one correspondence, or establish a bijective relationship.

Then, it can be considered that the two sets are equal in size and have the same ‘cardinality’.

Based on this concept, a basic theory can be derived: that is, the set of natural numbers is the smallest infinite cardinal number, which can be called a countable set or ?? (Aleph zero).

The next infinite cardinal number that is greater than the set of natural numbers, that is, greater than Alev zero, is the set of real numbers, which can also be called the uncountable set, and ?? (Alev one).

If we understand this simply and crudely, it is between infinity and infinity, and we can perform the operation of 'comparing sizes'.

Although they are both infinite, Alev One is bigger than Aleph Zero, and it is bigger with reason and evidence and irrefutable.

But there is also a very serious problem in this.

This is the problem.

If we only use the [infinite cardinality] theory to 'measure' the size of many [infinite sets], it will be too rough and not detailed enough.

Imagine a ‘ruler’ named [infinite base number].

The smallest scale is Alev Zero, and the second scale... is Alev One.

This... suddenly jumped from countable infinity to uncountable infinity.

This kind of jump amplitude is so huge that there is no way to conduct more detailed 'measurements' on many infinite sets.

And according to the famous [Continuum Hypothesis], the authenticity of which can never be judged within the Zermelo-Frankl axiom system.

No one can ever know whether there are other infinite cardinal numbers between ?? and ??.

From this, a theory called "Infinite Ordinal Numbers" was born.

A new, more refined 'ruler' that can be used to 'measure' all kinds of infinite sets.

This 'ruler', or the basic idea of ​​the theory, is to add an attribute called [order] to all elements of various collections.

As for the definition of [sequence], to put it simply and crudely, it means that the various elements in the set can be arranged in a series.

This too 'strong' definition instantly limits the set to countable sets.

If the definition of "order" is more detailed, then it can be said that any two elements in the set can be compared in some way.

This relationship of ratio is called "order relationship".

The comparison operation on sets is called "total order relationship".

Therefore, when a set has a certain total order relationship and any non-empty set has the smallest element, the set is a [well-ordered set] with excellent properties.

For example, the natural numbers are well-ordered sets.

Because zero is the smallest natural number among them, and there is always a smallest number in any subset of natural numbers.

But integers are not a well-ordered set.

Because there is no smallest integer, its properties are not good.

Ordinal numbers are well-ordered sets.

If a well-ordered set can establish a one-to-one correspondence with this ordinal number, and the corresponding result also maintains its own well-ordered relationship, then the two sets can be called the same ordinal number.

Then all the natural numbers are a well-ordered set, which is an infinite ordinal number or a transfinite ordinal number with the same size as w (omega).

The word "transfinite" is used to describe the concept of cardinal numbers or ordinal numbers that are larger than all finite numbers, but do not have to be "absolutely infinite".

Therefore, although w is indeed infinite, do not think that w is the so-called "absolute infinity".

These two concepts must not be confused together.

And it starts from ?? (countable infinity) and ends with ?? (uncountable infinity).

Within this vast and boundless ‘interval’, there are apparently infinite kinds of transfinite ordinal numbers with infinite ‘gaps’ from each other.

These infinite kinds of transfinite ordinal numbers all fall within the category of Aleph zero.

Then w is the first initial sequence of ??.

Mu Cang guessed that the Manhai goddess was probably a terrifying creature that resided on a certain transfinite ordinal level far beyond w.

I just don’t know what level he is at and what kind of transfinite ordinal it is.

"Whether it is recursive ordinal numbers or non-recursive ordinal numbers, they are not within my reach at the moment. Forget it, it is useless to think about it."

After Mu Cang thought quietly for a moment, he decided not to think about it anymore.

Because what Mu Cang needs to do now is to deduce the eighth realm of "Haoyang Xuanqiong Law" and advance the supreme divinity to the same realm as the supreme god Aleister, so as to improve his

The natal miracle [Dong Seize the Great Thousand] will completely transform you into a higher level.

Only then would he have a slight possibility to fight against Aleister.

In the past, Mu Cang might not have been able to do this.

But after collecting a large amount of information about the divine path to the realm of enlightenment, he already had some insights into the deduction of the eighth realm of Haoyang Dharma.

In Mu Cang's imagination, after entering the eighth realm, his supreme divinity will transform into a wonderful phenomenon between finite numbers and real infinity, between divinity and '?'

Mysterious things.

In order to distinguish it from the term "divine nature", Mu Cang named this phenomenon and thing that is above the highest level of divinity... [Void and Real Source Seed].
Chapter completed!