Generally speaking, Aleph 1 can be equated with the set R of real numbers.
In other words, the potential of the entire set of real numbers is equivalent to Alev one.
But in fact, what is truly equal to the real number set R is beth_1.
Only under the premise that the continuum hypothesis is established, since ??=beth_1, the result ??=R is obtained.
In short, within the ZFC background axiom system and when the continuum hypothesis is established, the smallest uncountable singular cardinal number is ?w.
This base number seems huge, but in the entire category of Aleph numbers, it is just a small 'beginning'.
On top of it, there are still more huge bases that are uncountable, immeasurable and immeasurable.
For example? (eee0) base,
…?(w?) base.
Note that since w? is the first ordinal number with the same potential as ??, ?(w?) can also be called...Alev Aleph one in a popular sense.
Of course, this name is still not rigorous.
However, for the sake of convenience, it does not hurt to use this type of title.
To sum up, since there is Aleph Aleph one?(w?).
Then it can be deduced by analogy, along the new road, all the way to Alef Alev Two? (w?), Aleph Alev Three? (w?), Alev Alev One Hundred? (
w???), Aleph Aleph ten thousand? (w??????), and even reach the so-called...Alev Aleph infinite? (w_w).
In short, as long as this uninterrupted Aleph Aleph Aleph goes on and on endlessly and countless times, it will eventually reach the so-called... Aleph fixed point.
If this fixed point is described in mathematical language, it is in the Alev function?(x), let x be a specific value.
And the value of x is so huge that it is equal to?(x)=?(?(x))=?(?(?(x)))=?(?(?(?(x))))...=?
(?(?(…?(x)))…), totaling infinite, countless, and endless layers of brackets.
So this?(x) is the first Aleph fixed point.
Since there is the first one, by analogy, there will naturally be the second one, the third one, the fourth one... there are Ge Liheng's number... there are SCG(3)'s... there are zero Alev's
...There are infinite Di'Alev's...There are infinite Di'Alev's...and many, many more.
So, is this the limit of Alev number?
No, far from it.
At that extremely high peak 'position' that all fixed points can never reach and all Aleph iterations can never reach, there is still... a power-admissible cardinal number.
Abbreviation: pow or pa.
The first pa is a point that cannot be reached by all Aleph iterations, and can be written as pa_1.
Since there is pa_1, then there will naturally be pa_2, which is another fixed point that pa_1 cannot reach even if it undergoes infinite iterations.
In the same way, pa_3 is also a fixed point that pa_2 cannot reach no matter what, even if it is iterated.
By analogy, we go through pa_4, pa_40, pa_400, pa_40000... and finally reach a fixed point that is so far away that even the word fixed point cannot be used to describe it - pa_pa_1.
On top of this, there are pa_pa_pa_1, pa_pa_pa_pa_1, pa_pa_pa_pa_pa_1...and so on, countless infinite-order pa fixed points.
So in the end, a fixed point like pa_pa_pa_pa_pa... never ending is power recursive inaccessible.
Abbreviation: PA base or PA fixed point.
At this moment, Mu Cang and the master of the Tao, Yun Zun, were in the realm of the entity corresponding to the PA fixed point, fighting fiercely.
In fact, after the two had a verbal confrontation in the field of ?(eee0) before, they fought without hesitation.
And after the entire ?(eee0) realm collapsed in an instant, Mu Cang and Yun Zun continued to use their own methods to 'ascend' all the way, going crazy through all the realms, realms, and levels.
So after penetrating and tearing apart the countless layers of countless realms, all the way through the (ζζζ?) realm...?(ηηη?) realm...?(φ(1,0,0,)) realm...?(φ(
1@33))Field…?(φ(1@w))…?(w?)Field…?(w????)Field…?(w_w)Field…and the first Alev fixed point bound
After the layer... and the 10,000th Aleph fixed point boundary layer... and the infinite Aleph fixed points... and the infinite layer pa fixed points, the two finally arrived and stopped there.
Among PA cardinal fields.
At this point, Mu Cang's life level and strength level have also completely stopped at the power-recursive-inaccessible base (PA) after this crazy journey of climbing the world, through the heaven-defying power of "I can get it when I see it"
Above the rank.
For this indescribably terrifying basic magnitude, its true power cannot even be described directly or indirectly using any natural language.
But Mu Cang didn't care about this at this moment.
His attention now has all been focused on the strange figure in the distance that is so far away that it cannot be described using words such as "endless" or "fixed point" or even "endless fixed point" -
On the body of Yun Zun, the master of Taoism.
Mu Cang could clearly feel that this guy named Yun Zun was actually not very interested in this battle.
The reason why He continues to 'ascend' towards higher levels of realm is more like... looking for something.
'When I see it, I get it...'
Mu Cang thought deeply in his heart, 'It can't actually have an effect on this master named Yun Zun? It's really... strange.'
Yes, Mu Cang had countless fierce battles with the Fortune Lord along the way, but [See and I Get] was as unresponsive as if he was dead, unable to replicate any of the opponent's abilities and strength.
Mu Cang relied entirely on [Ling Yue Feifu] to keep up with the rhythm of Yun Zun's 'ascension' and the intensity of the battle. He also relied on the external environment to stimulate the activation of [See is I Get], and finally reached the goal step by step.
The level of status He currently occupies.
The danger during this period is beyond description.
At the same time, Mu Cang also discovered that the Fortune Master seemed to have a similar ability as "I get it when I see it".
The reason why he said this was because he could clearly 'see' that whenever the opponent reached a certain realm, he would instantly possess the same level of strength as the other realm.
This level of improvement method and performance are almost exactly the same as Mu Cang's.
In this regard, Mu Cang extremely doubted that this method of increasing strength or ability was probably the same as the opponent's teleportation ability that could travel freely across all realms. It was some kind of innate talent of the Taoist clan.
'But looking at it on the other hand, if this Fortune Master still needs to go through 'growth' and 'progress' to become strong, then how did he break out of the prison before?'
Mu Cang was confused, 'According to normal logic, this Yun Zun should be extremely powerful to be qualified to see the operational loopholes of the prison and escape from it.
Could it be that... He had suffered severe injuries before being imprisoned in the prison and his strength declined, or... was it that some of his talents were blocked?'
Obviously, Mu Cang does not know the exact answers to these questions yet.
At the same time, Mu Cang has actually tried many times to kill Yun Zun through [Ling Yue Feifu], but he has never succeeded.
Therefore, this unknown creature named Yun Zun obviously has the ability to be immune to the power of the two heaven-defying skills [Ling Yue Fei Fu] and [See and I Get].
As for what this ability is specifically, you have to completely capture this guy and then search your memory to find out.
As for when we can defeat the opponent, we can only say... it will be soon, it will be soon.
'I have felt that after reaching this PA fixed point field, [Ling Yue Fei Fu] will soon leave the semi-awakening state and enter the true mature state, so I only need to wait for it to fully mature before proceeding.
...'
Mu Cang said to himself, 'The final victory is over.'
Buzz——
In the long secret words in his heart, [Ling Yue Feifu] suddenly began to undergo a mysterious transformation.
It seems to be about to break out of the cocoon and become a butterfly.
"Mu Cang."
Yun Zun in the distance suddenly said coldly, "You are probably not a creature from this territory."
"oh?"
Mu Cang said indifferently, "Why do you say that?"
"Your level growth ability is very powerful, so powerful that you can easily break through the allowable point."
Yun Zun said coldly, "Any living being here cannot have this ability anyway, so... you must come from outside this territory."
"maybe."
Mu Cang neither admitted nor denied, just chuckled, and then asked, "What about you? Where are you from? And why are you being imprisoned here?"
"Hey hey hey~"
Yun Zun suddenly changed his face and sneered, "Do you think I will tell you?"
"I guess……"
Ignoring Yun Zun's sarcastic words, Mu Cang said to himself, "You should be the so-called family of Taoists according to members of the Aleph family."
"Oh~ so what."
Yun Zun smiled solemnly, "Besides this, what else do you know?"
"It doesn't matter."
Mu Cang smiled calmly and said, "After I beat you to death, I will naturally know everything."
"really."
Yun Zun also said calmly, "As long as you can kill me, you can get everything, but... you have no chance."
Wow——
Suddenly, an aura that made Mu Cang feel extremely strange and illusory suddenly erupted with Yun Zun as the center.
At the same time, the moment this aura appeared, the entire realm where the two of them were located suddenly became illusory and blurred, as if it would disappear in the next moment.
"Mu Cang, I have to admit that you are indeed an interesting little ant."
The figure of Yun Zun began to become inexplicably hazy and false, like an illusion.
"It's a pity...I have to leave here."
Yun Zun, whose figure became more and more illusory and empty and seemed to be about to disappear, said with a relaxed smile, "Just wait slowly in this area, and wait until I have completely recovered to the perfect state... and then I will come back and take good care of you."
When the time comes, I will knock you down into a humble mortal, and then have fun with you again, hahahahaha!"
While he was laughing wildly, a 'portal' that was neither real nor false appeared out of thin air and enveloped the laughing Yun Zun, as if to transport him to an unknown realm.
And at this moment, Mu Cang's [Ling Yue Feifu] finally matured and entered a truly fully awakened state.
then--
"Hmph~"
Mu Cang raised his eyes to look at Yun Zun, who was about to disappear, and sneered coldly, "Want to escape? It's not that easy."
[Ling Yue Feifu], start!
Activating effect——
(Yun Zun has the ability to leave this territory ≠ Yun Zun can successfully leave this territory)
([See it, I get it] All the gifts and abilities of Yun Zun cannot be reproduced at this moment ≠ [See it and I get it] All the gifts and abilities of Yun Zun cannot be reproduced at the next moment)
(Mu Cang does not know all of Yun Zun’s memories at this moment ≠ Mu Cang does not know all of Yun Zun’s memories at the next moment)
(Yun Zun is a member of the Taoist clan at this moment ≠ Yun Zun is a Taoist clan at the next moment)
This chapter is not over, please click on the next page to continue reading! (Yun Zun is a PA fixed point level at this moment ≠ Yun Zun is not a carbon-based mortal in the three-dimensional universe in the next moment)
(Yun Zun can continue to grow and progress in this moment ≠ Yun Zun can continue to grow and progress in the next moment)
(Yun Zun will have basic attack ability from now on at this moment ≠ Yun Zun will have basic attack ability from now on at this moment)
(From this moment onwards, Yun Zun...)
(From this moment onwards, Yun Zun...)
…
Buzz!!!
In an instant, the illusory door collapsed without a trace, revealing the confused Yun Zun.
"What love..."
As soon as Yun Zun burst out a sentence from his mouth, all his abilities, talents, and memory information were instantly perfectly reproduced by Mu Cang.
At the same time, Yun Zun's PA fixed-point strength and his mysterious master essence also suddenly dissipated, and began to 'fall' crazily, almost without any process.
So in just a moment, Yun Zun 'falls' all the way through the infinite layer pa fixed point realm, endless layer? fixed point realm, endless layer? cardinal realm.
Finally, he fell into... a dirty corner of Aleph's realm - the recursive world - the three-dimensional universe - the Milky Way - the Earth - the Tianzhu slums.
"Ouch!!"
Yun Zun, who had transformed into a frail and frail transvestite, a white-faced Tianzhu man, appeared out of thin air and fell heavily into the shabby swamp on the bank of the Ganges River where feces and urine were flowing and sewage was everywhere.
"Ah~ it hurts so much! Ah~ it smells so bad! What's going on?! What the hell is this place?!"
Yun Zun, who was covered in mud and grinning, struggled to stand up from the stinky mud, one foot deep and one shallow, and walked desperately towards the not far away.
Although Yun Zun didn't know what happened, the harsh environment around him forced him not to stop.
At this moment, at the corner of the road not far from Yun Zun, a group of drunken, fat Indian men with dark skin and body odor suddenly walked up.
As if guided by fate, this group of Tianzhu drunkards actually saw the handsome Yun Zun not far away who looked like a beautiful girl.
"Lord Shiva! Is that a movie star?!"
This group of drunkards howled in excitement and immediately started chasing Yun Zun, who was dozens of meters away and completely unaware of all this, with a lewd smile.