Chapter 96. Teachings
The endless barrage of questions continued.
Although her personality was completely different from her previous-life self, her intellectual curiosity had not changed in the slightest.
“When compressing or expanding space, what methods could be used to minimize temporal fluctuations?!!”
This would never end.
I had already exhausted all my knowledge anyway. I was not confident that I could answer even one of her questions.
“I apologize, but may I ask you a question as well?”
“Ah!”
Iliana flinched violently in surprise.
“I-I’ve been asking far too many questions by myself, haven’t I....?”
She lowered her head, her voice growing exceedingly quiet.
“I became too excited because I couldn’t contain my curiosity....”
She looked as dejected as a puppy that could not go for a walk because of the rain.
It made it seem as though I had reprimanded her.
Since she had been my superior as the Commander of Mage Command, I was the one who became flustered.
“P-Please ask! My knowledge is insignificant compared to yours, Lord Adrian, but I’ll do my best to offer my opinion!!”
As though her dejection had never existed, Iliana clenched her fists and shouted.
Her two small fists were gathered before her chest. They contained her determination to do her very best.
“Then may I hear your thoughts regarding Infinity?”
“Infinity....?”
“That’s correct.”
Iliana tilted her head at my answer.
“Are you perhaps researching Infinity?”
“I wouldn’t go so far as to call it research. Let’s merely call it curiosity.”
Iliana’s expression suddenly became serious.
I briefly wondered why.
“You said that you were neither a mage nor an Arcane Scholar, correct?”
“Is there a problem?”
“Well.... Have you ever visited the Langrid Mage Tower?”
“I have not.”
Even including my experiences from my previous life, I had never visited it personally.
By that time, the Langrid Mage Tower had already collapsed during the war.
“If you look at the main entrance of the Langrid Mage Tower, you’ll see an inscription. It was engraved there by the First Mage—”
The First Mage, Arcanis Rilsein.
Arcanis had also been the original founder of the Langrid Mage Tower.
“It is an inviolable rule that everyone in the Langrid Mage Tower must obey.”
The Langrid Mage Tower was the Cradle of Mages.
Therefore, the inscription could also be considered an inviolable rule for every mage on the continent.
[Place no limits upon your curiosity. Infinity is the sole exception.]
“Does that mean researching and studying Infinity is forbidden?”
“Yes, that’s correct.”
“May I ask why?”
“Um.... To begin with—”
Iliana briefly organized her thoughts before speaking.
“Infinity is inherently paradoxical. The moment you attempt to define Infinity using finite language, you have already departed from its essence.”
“Hmm.”
“And truthfully, it isn’t as though no one has ever attempted to study Infinity.”
Then again, how could mages possibly give up on something like that?
Iliana alone was enough to prove it.
Mages loved explaining and analyzing things more than anyone else.
Of course, Iliana was particularly extreme, but it was merely a difference in degree.
Every mage possessed similar tendencies.
More importantly, human nature made people want something even more when they were told not to pursue it.
“There have been countless attempts to explain and study Infinity through the framework of Arcane Studies. However....”
Iliana lowered her gaze slightly before continuing.
“Regardless of whether those attempts succeeded, they caused numerous problems.”
“What kind of problems?”
“There were cases of people losing their minds while researching Infinity or dying while experimenting with it.”
Some had opened uncontrollable dimensional portals. There had been catastrophic incidents caused by runaway energy. Plagues that destroyed nature’s cycles and order had broken out.
Unidentifiable entities had been conceived. And many other things had occurred.
“None of the mages or Arcane Scholars who investigated Infinity met a good end. That led to the creation of a certain maxim—”
—Infinity is a warning that you have strayed onto the wrong path during your journey toward truth.
“Strictly speaking, however, only the study and investigation of Actual Infinity are forbidden. Potential Infinity is still used as an essential component of magical formulas.”
I could not understand a word she was saying.
What was Potential Infinity, and what was Actual Infinity?
I wanted to cover my ears immediately.
However, if I wanted to improve my understanding of Infinity [M], I needed to listen even if I had to force myself.
“Could you explain that in greater detail?”
“Hmm.... Simply put, Potential Infinity is a ‘property possessed by numbers’.”
“Do you mean numbers such as one, two, three, four, and five?”
“Yes. Natural numbers like those can be extended endlessly, can’t they? No matter how large a number N you imagine, you can naturally conceive of N+1.”
A state that could be extended without end—
“That is Potential Infinity.”
....Hmm?
“Isn’t that simply the concept of infinity?”
“That’s right. The concept of infinity most people are familiar with is ‘Potential Infinity’.”
“Then what is Actual Infinity?”
“Actual Infinity is, um....”
Iliana appeared to think deeply before answering carefully.
“....Perhaps it could be described as infinity that actually exists in a complete form.”
“......”
“Or perhaps....physical infinity.”
“......”
“It’s difficult to understand, isn’t it....?”
“To be honest, yes.”
“That is where most problems arise. The existence of physical infinity is difficult to comprehend, and it is not a concept recognized by the laws of this world.”
Iliana continued explaining.
“Are you aware that infinity can be counted?”
Infinity could be counted.
It was the very concept I had seen and heard within the vision that appeared when I used Predation [S+] on Avarus.
However, I had only seen and heard about it. I did not understand it.
“If you don’t mind, could you explain it?”
“Of course. It is a concept you need to understand Actual Infinity anyway.”
Iliana nodded lightly before continuing.
“An infinity that can be counted is called Countable Infinity.”
I listened as attentively as possible to Iliana’s continuing explanation.
In my previous life, I had learned Evolutionary Biology and countless other subjects from Iliana.
It was why I could now understand biological Evolution Abilities completely.
It was the foundation that allowed me to create Combination Skills and Evolution Skills.
It was also what had allowed me to establish the Predator’s method of combat that Ian had described.
Iliana’s teachings lay at the foundation of all those things.
Naturally, learning them had never been easy. I had nearly given up countless times before finally reaching my current level.
“For example, let’s suppose a large group of customers entered this restaurant.”
Iliana looked around the Predator Restaurant before continuing.
“How could we compare the number of tables in this restaurant with the size of the group?”
“Couldn’t we count the tables and customers separately?”
“That would work, but there is an even simpler method. We could have the customers sit at the tables one by one.”
“Hmm.”
“If there are empty seats remaining, there are more seats than customers. If some customers have nowhere to sit, there are more customers than seats.”
“Ah.”
“In this manner, the sizes of two sets can be compared through a one-to-one correspondence. Countable Infinity refers to an infinity whose size can be compared through this kind of ‘one-to-one correspondence’, making it ‘countable’.”
At that moment, a bluish thread of light emerged from Iliana’s fingertip.
Following the smooth path traced by her hand, something appeared in the air.
Odd numbers such as [1, 3, 5, 7, 9....].
Even numbers such as [2, 4, 6, 8, 10....].
Natural numbers such as [1, 2, 3, 4, 5, 6, 7, 8, 9, 10....].
“If the odd numbers, even numbers, and natural numbers are all Infinity, which set contains the most numbers?”
Natural numbers included both even and odd numbers.
The whole was greater than any of its parts.
Naturally—
“Wouldn’t the natural numbers contain the most?”
“No.”
Iliana shook her head.
“They all contain the same number.”
“They all have the same cardinality?”
“Yes. It can be proven through the one-to-one correspondence I mentioned earlier.”
When Iliana waved her hand again, the Mana Force numbers shimmering faintly like stars began pairing with one another in the air.
1 ← 1
2 ← 3
3 ← 5
4 ← 7
5 ← 9
6 ← 11
It was because numbers were Infinite.
Therefore, the quantities of natural numbers, odd numbers, and even numbers were all equally “Infinite”.
In the world of infinity, establishing a one-to-one correspondence—
“Means that different sets possess the same cardinality. This is called an infinity that can be counted—Countable Infinity.”
That was—
“And there are infinities larger than Countable Infinity. There are also ‘uncountable infinities’ that cannot be placed into a one-to-one correspondence with the natural numbers. To explain further—”
....The absolute limit of what I could understand.
“If you continue the sequence, the odd number corresponding to the natural number 10,000 would be 19,999.”
“......”
“The same applies to every natural number. Without exception, each one can be paired ‘Infinitely’ with an odd number through a one-to-one correspondence.”
No matter how large the natural number became and no matter how many natural numbers there were, an equal number of corresponding odd numbers would always exist.
Iliana’s explanation continued for a long time afterward.
I could say one thing with certainty.
....This was on an entirely different level.
I immediately understood why the First Mage, Arcanis Rilsein, had left behind that maxim.
[Place no limits upon your curiosity. Infinity is the sole exception.]
The more I attempted to accept the concept of Infinity—
The more I felt an oppressive sensation, as though something were bubbling deep within my head.
The more I attempted to understand Infinity [M]—
The more my entire head felt like a balloon expanding until it was about to burst.
In that sense, Iliana was astonishing.
How could she carry all this knowledge inside her head?
The fact that her head remained intact instead of exploding proved that she was not called the [Mage of Truth] for nothing.
“....That is everything I know about the concept of Infinity.”
Somehow, I managed to hear every concept of Infinity that Iliana knew. To be honest, however, I had not properly understood what she said.
I had merely listened and memorized it indiscriminately.
Still, did they not say that understanding began with memorization?
Some parts had begun to make vague sense.
◆Understanding of the Concept Skill Infinity [M] has increased.
After considerable difficulty, I succeeded in increasing my understanding of Infinity [M].
My head throbbed.
Pressing both temples firmly with one hand, I attempted to apply my improved understanding of Infinity [M] to everything possible.
....However, it did not integrate with any existing concept.
It did not integrate with Strength, Agility, Stamina, Mana, or any other concept.
At that moment—
Fusion Skill.
A skill in which two or more distinct things merged into one until no distinction remained between them.
It was quite different from a Combination Skill, in which each element retained its independence.
Unlike what had happened with my Inventory previously, this was the first time Infinity [M] had integrated with another skill.
A message concerning Successor’s Will [EX] appeared before my eyes.
◆The Concept Skill Infinity [M] is integrating with Player’s Will [EX].
Unexpectedly, it began integrating with Ian’s ability, Player’s Will [EX].
◆Successor’s Will [EX] : Infinitely expands the Player’s mental capacity, granting complete mental autonomy against every form of mental interference, including curses, illusions, brainwashing, hypnosis, suggestion, and more.
<This skill is a Fusion Skill created through the fusion of Player’s Will [EX] and Infinity [M].>
◆You have acquired the Fusion Skill ‘Successor’s Will [EX]’.
My throbbing mind instantly became clear.
The [EX] represented the Extra Rank.
The rank had remained the same.
Apparently, every “Extra Rank Skill” that could not be evaluated using the existing ranking system received the [EX] Rank.
Nevertheless, the skill’s ability had clearly been enhanced.
Most importantly, it now “Infinitely expanded the Player’s mental capacity.”
Through that, it granted complete mental autonomy.
‘Could this possibly....?’
Wondering if my suspicion was correct, I checked my Player Information.
== 「Player Information」 ==
[Name] = Adrian White Wolf
[Title] = Master of the Snowy Mountains
[Level] = Level 76
[HP] = 9,185
[MP] = 0
[Sanity] = 4/ℵ₀
[Stats] = Strength: 81 (+5), Agility: 110.8 (+18.8), Stamina: 90.85 (+11.85), Mana: 11 (+5)
[Experience] = 9.33%
<Additional Stat +1>
I confirmed that the maximum value of [Sanity] had changed.
[Sanity] = 4/ℵ₀
According to what I had just learned from Iliana, ℵ₀ was read as “aleph-null” and represented Countable Infinity.
The familiar infinity symbol, ∞, represented the concept of Potential Infinity.
In that sense, the infinity applied to Infinity Inventory had been ∞.
Regardless, infinity was still infinity.
In other words, the maximum value of [Sanity]—the limit of my mental capacity—had changed to “infinity”, or ℵ₀.
At first glance—
It did not appear particularly meaningful.
Strictly speaking, Player’s Will [EX] had also provided something equivalent to Infinity mental strength.
However—
There was an enormous difference between the two.
Player’s Will [EX] worked by “resetting” the Sanity value.
Therefore, it had the fatal limitation of being vulnerable to mental attacks that caused continuous corruption.
Successor’s Will [EX], however, did not reset it.
By granting complete mental autonomy, it allowed me to contain endlessly rising madness within infinity.
That meant—
‘I can fight the Monarch of the Abyss.’
I no longer needed to submit before An Unknowable Terror Beyond Explanation.
I could fight without being overwhelmed by endlessly accumulating fear.
Furthermore—
‘The limit on Berserk has disappeared.’
I could accumulate an infinite amount of Sanity. As a result, the power of Berserk [?] could also expand infinitely.
‘If that’s the case....’
Even Predation [S+] could transcend its rank.
In other words—
My potential had also expanded infinitely.
Moreover, that was not the end.
Countable Infinity was not the limit of my understanding of Infinity [M].
What would happen if I increased my understanding of Infinity [M] even further?
I could obtain more absurd skills like Infinite Inventory and Successor’s Will [EX].
“Did that....help you....?”
Iliana eventually asked me cautiously.
My expression had become somewhat distorted by shock and pain. Perhaps because of that, Iliana was carefully watching my reaction.
I quickly composed my expression before answering.
“It was extraordinarily helpful.”
Merely calling it helpful was an understatement.
With only slight exaggeration, it had practically been salvation.
As expected of Iliana.
There was a reason why Iliana had said those words in my previous life.
—If you ask me “why” a phenomenon occurs, I cannot give you an answer.
However—
—Under the given conditions, I can explain everything about “how” that phenomenon occurs.
Insight [L] allowed her to intuitively comprehend laws and phenomena.
Peak Human Intelligence [A+] allowed her to understand acquired knowledge immediately.
Her overwhelming talent could not be adequately described with the word “genius”.
It did not merely rival a Dragon’s talent.
It surpassed it.
“Really?! Was I truly helpful?!!”
Iliana became overjoyed when she heard that she had helped me.
“Hehe....!”
She smiled brightly at me, but then—
“Ah, um.... Well....”
Perhaps embarrassed, she blushed and hurriedly lowered her head.
‘She was capable of making an expression like that?’
It was an expression I had never once seen in my previous life. I silently watched Iliana for a moment before speaking.
“That being the case—”
I retrieved a heavy pouch from my Inventory.
“Subspace magic?!”
Iliana’s eyes widened.
“Didn’t you say you weren’t a mage?!”
“That’s correct.”
“Yet you can still use subspace magic?!?!!”
Iliana looked as though she might faint from shock.
That was understandable because subspace magic was extremely difficult.
“It should be impossible without realizing the concepts of hyperspace and quantum tunneling!!”
Apparently, that was how it worked.
However, Inventory was not subspace magic. It was merely classified as a subspace. It was not magic.
Therefore, I could not explain it. Nor was I confident that I could.
As though blocking Iliana’s questions in advance, I handed her the pouch I had retrieved.
“What....is this?”
“Why don’t you check?”
Iliana tilted her head and examined the pouch’s contents.
“These are platinum coins.”
“There are one hundred in total.”
One platinum coin was worth one thousand gold.
“One hundred thousand gold?!”
Iliana cried out in shock.
Assuming one did not indulge in tremendous luxuries, one hundred thousand gold was enough for a single-person household to live without working for an entire lifetime.
I retrieved nine more identical pouches from my Inventory and placed them on the table.
“Each pouch likewise contains one hundred platinum coins.”
“One million gold?!?!!”
Iliana’s small mouth fell wide open.
“I will give all of it to you, Lady Iliana.”
“Whaaaat?!”
Iliana’s eyes widened as though they might split apart.
Her gaze shook violently as if caught in an earthquake, silently asking why I was giving her one million gold.
“Our Predator Merchant Company would like to sponsor you, Lady Iliana.”
The moment I finished speaking—
“Whaaaaaaaaaaaaaat?!?!!”
Iliana sprang into the air like a startled frog.
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