Chapter 96

Teachings

An endless parade of questions.

Her personality was completely different from what it had been in my previous life, but her intellectual curiosity hadn't changed in the slightest.

"What methods could we use to minimize temporal variability when compressing or expanding space?!"

At this rate, it would never end. I had already exhausted my meager store of knowledge anyway. I wasn't confident I could answer a single one of those questions.

"I'm sorry, but would you mind if I asked a question as well?"

"O-oh...!"

Iliana started, her whole body jolting.

"I-I've been asking far too many questions, haven't I...?"

Her voice dwindled to a whisper, and she hung her head.

"I couldn't contain my curiosity and got carried away..."

She looked as crestfallen as a puppy whose walk had been canceled by rain. It made me look as though I'd been giving her a hard time.

Considering she had been my superior, the commander of Magic Command, I was the one left flustered. Just then—

"G-go ahead! My knowledge is paltry compared with yours, Lord Adrian, but I'll do my best to give you my thoughts!"

Iliana clenched her fists and exclaimed as though nothing had happened. Those two small fists held close to her chest conveyed her determination to do her very best.

"Then may I hear your thoughts on infinity?"

"Infinity...?"

"Yes."

She tilted her head at my answer.

"Are you perhaps researching infinity?"

"Research would be overstating it. Let's call it curiosity."

Her expression abruptly turned grave. Before I could wonder why, she spoke.

"You said you weren't a mage or a scholar of magic, correct?"

"Is there a problem?"

"Well... have you ever visited Langrid Mage Tower?"

"I haven't."

Even counting my previous life, I had never been there in person. By that time, Langrid Mage Tower had already fallen in the war.

"If you look at Langrid Mage Tower's main gate, you'll see an inscription. The first mage engraved it himself."

The first mage, Arcanis Rilsein. Arcanis had also been the original founder of Langrid Mage Tower.

"It's an ironclad rule that everyone at our tower must obey."

And Langrid Mage Tower was the cradle of mages. Which meant it was effectively an ironclad rule for every mage on the continent.

[Place no limits on your curiosity. Except when it comes to infinity.]

"Do you mean that exploring and researching infinity is forbidden?"

"Yes, that's right."

"May I ask why?"

"Um... for starters..."

Iliana briefly gathered her thoughts before continuing.

"Infinity is itself a paradox. The moment you try to define infinity in finite language, you've already strayed from its essence."

"Hmm."

"And actually, it's not as though no one has tried to explore infinity."

Of course. Knowing what mages were like, why would they give up on that? Iliana alone was proof enough.

They loved explaining and analyzing things more than anyone. Granted, she was an extreme case, but it was only a matter of degree. All mages shared that tendency.

Above all, being told not to do something only made people want to do it more.

"There have been countless attempts to explain and study infinity within the framework of magical studies. But..."

Lowering her gaze slightly, she continued.

"Regardless of whether they succeeded, they caused a great many problems."

"What sort of problems do you mean?"

"For a start, people have gone insane while researching infinity or died while experimenting with it."

There had been cases of uncontrollable dimensional gates opening. Catastrophes caused by runaway energy. Outbreaks of disease that destroyed the cycles and order of nature. The conception of unidentified beings, and more.

"Every mage and scholar of magic who explored infinity met a bad end. That gave rise to a saying."

—Infinity is a warning that you have taken a wrong turn on your journey toward truth.

"Strictly speaking, though, it's the study and exploration of actual infinity that's forbidden. Potential infinity is an essential component of spell formulas."

... I had no idea what she was talking about. What was potential infinity, and what on earth was actual infinity?

I wanted to plug my ears right then and there. But to improve my understanding of Infinity[M], I needed to force myself to listen.

"Could you explain that in a little more detail?"

"Hmm... Simply put, potential infinity is a 'property of numbers.'"

"You mean numbers like 1, 2, 3, 4, and 5?"

"Yes. Those natural numbers can keep increasing without end, right? However large a number N you imagine, you can naturally imagine N+1."

A state of endless expansion like that.

"That's potential infinity."

... Hmm?

"Isn't that just the concept of infinity?"

"It is. The concept of infinity people are generally familiar with is 'potential infinity.'"

"Then what is actual infinity?"

"Actual infinity is... hmm..."

After considerable thought, Iliana cautiously spoke.

"... I suppose you could call it 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's why most problems arise here. Not only is physical infinity difficult to grasp, it's a concept that the laws of this world don't permit."

She continued her explanation.

"Did you know that infinity can be counted?"

Infinity could be counted.

That was the very concept I had seen and heard in the vision I experienced while consuming Avarus with Predation[S+].

But I had only seen and heard it. I didn't understand it.

"If you don't mind, could you explain?"

"Of course. You'll need that concept to understand actual infinity anyway."

Iliana gave a small nod and continued.

"An infinity that can be counted is called countable infinity."

I listened as closely as I could as her explanation continued.

* * *

In my previous life, Iliana had taught me a wealth of knowledge, including evolutionary biology.

The reason I now fully understood my biological evolution ability, the foundation that had allowed me to create combination skills and evolved skills, and ultimately to develop the Predator's fighting style Ian had spoken of—all of it rested on her teachings.

Naturally, learning all that had been anything but easy. I had only reached my current level after pushing through countless moments when I nearly gave up.

"For example, let's suppose a large group of customers came to this restaurant."

Iliana looked around the Predator restaurant before continuing.

"How could we compare the number of tables here with the size of the group?"

"Couldn't we count the tables and the customers separately?"

"That works too, but we could make a very simple, immediate comparison by having each customer sit at a table."

"Hmm."

"If there are tables left over, there are more tables. If customers have nowhere to sit, there are more customers."

"Ah."

"We can compare the sizes of two sets like this by matching them one to one. Countable infinity means an infinity whose size can be compared through this 'one-to-one correspondence'—an infinity that can therefore be counted."

A bluish line of light emerged from her fingertip. As her hand moved smoothly through the air, writing appeared in its wake.

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 there are infinitely many odd numbers, even numbers, and natural numbers, which set has the most numbers?"

Natural numbers included both odd and even numbers. The whole was greater than its parts.

So obviously—

"Aren't there the most natural numbers?"

"No."

Iliana shook her head.

"They're all the same."

"They all have the same number of elements?"

"Yes. We can prove it using the one-to-one correspondence I mentioned."

She waved her hand again, and the numbers formed of magical power, softly twinkling in the air like stars, began to pair up.

1 ↔ 1

2 ↔ 3

3 ↔ 5

4 ↔ 7

5 ↔ 9

6 ↔ 11

.

.

.

"If we keep going, the natural number 10,000 will correspond to the odd number 19,999."

"..."

"The same holds for any natural number. Every single one, without exception, can be matched one to one with an odd number, infinitely."

However large the natural numbers became, however many there were, there would always be an equal number of corresponding odd numbers. Because numbers were infinite.

Thus, natural numbers, odd numbers, and even numbers all had the same number of elements: infinitely many.

In the realm of infinity, having a one-to-one correspondence like this...

"Means that different sets have the same number of elements and the same size. We call this an infinity that can be counted—countable infinity."

That was precisely the limit—

"And there are infinities larger than countable infinity. There are also 'uncountable infinities' that cannot be put into a one-to-one correspondence with the natural numbers. To explain a little further..."

...of what I could understand.

* * *

Iliana's explanation continued for a long time after that. I could safely say one thing.

... This was on another level.

Now I understood exactly why the first mage, Arcanis Rilsein, had left that maxim behind.

[Place no limits on your curiosity. Except when it comes to infinity.]

The more I absorbed the concept of infinity, the more I felt a pressure, as though something were bubbling deep inside my head.

The harder I tried to understand Infinity[M], the more it felt as though my entire head were swelling like a balloon on the verge of bursting.

◆Player's Will[EX] resists the anguish crushing your mind!!

... Thankfully, Player's Will[EX] at least kept my head from exploding.

That made her all the more astonishing. How did Iliana carry all this knowledge around in her head? The fact that she could remain perfectly fine without her head exploding proved she wasn't called the [Mage of Truth] for nothing.

"... And that's everything I know about the concept of infinity."

Somehow, I had managed to hear everything she knew about infinity. But frankly, I hadn't properly understood what she was saying. I had merely listened and memorized it blindly.

Still, didn't they say understanding began with memorization? There were some parts I could now vaguely grasp.

◆Your understanding of the Concept Skill, Infinity[M], increases.

After all that trouble, I had managed to improve my understanding of Infinity[M].

My head throbbed. Pressing both temples firmly with one hand, I tried applying my better-understood Infinity[M] to everything I could.

... And yet, it wouldn't combine with any concept. Not Strength, Agility, Stamina, mana, or anything else.

Then, just at that moment—

◆The Concept Skill, Infinity[M], combines with Player's Will[EX].

Unexpectedly, it began combining with Ian's ability, Player's Will[EX].

◆You have acquired the fusion skill, 'Successor's Will[EX].'

My aching mind suddenly snapped alert.

A fusion skill. A skill formed by merging two or more different things into one, with no distinction remaining between them. It was quite different from a combination skill, in which each component remained independent.

Unlike its earlier application to the Inventory, this was the first time Infinity[M] had combined with another skill.

Soon, the description of Successor's Will[EX] appeared before my eyes.

◆Successor's Will[EX]

: Infinitely expands the player's mental fortitude, granting complete mental autonomy against any form of mental interference (curses, illusions, brainwashing, hypnosis, suggestion, etc.).

<This is a fusion skill created by the fusion of Player's Will[EX] and Infinity[M].>

Its rank was [EX], short for Extra—beyond the standard. The same rank as before.

Apparently, any skill that fell outside the standards of the existing ranking system received an [EX] rank.

Even so, its effect had clearly been upgraded. Namely, the part about infinitely expanding mental fortitude, thereby granting complete mental autonomy.

'Could this mean...?'

Wondering if my suspicion was right, I checked 「Player Information」.

==「Player Information」==

[Name] = Adrian Whitewolf

[Title] = master of the snowy mountains

[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 Points +1>

I could see that my maximum [Sanity] had changed.

[Sanity] - 4/ℵ0

According to what Iliana had just taught me, ℵ0 was read as 'aleph-null' and represented countable infinity. The familiar infinity symbol, '∞,' represented potential infinity. In that sense, the infinity applied to the Infinite Inventory had been '∞.'

Either way, infinity was infinity. In other words, my maximum [Sanity]—the capacity of my mental fortitude—had been converted to infinity, ℵ0.

At first glance, it didn't mean much. Strictly speaking, Player's Will[EX] had effectively given me infinite mental fortitude too.

But there was an enormous difference between the two.

Player's Will[EX] worked by resetting my Sanity value. As a result, it had a fatal limitation when faced with mental attacks that eroded the mind continuously.

Successor's Will[EX], however, didn't reset anything. It granted complete mental autonomy, infinitely accommodating the rising Madness.

Which meant—

'I can fight the Sovereign of the Abyss.'

I no longer had to submit to The Inexplicable Terror of the Unknown. I could fight without being crushed by that endlessly rising fear.

On top of that...

'Berserk's limitation is gone.'

I could accumulate Sanity without limit. That meant I could infinitely expand Berserk[?]' s power as well.

'Then...'

Even Predation[S+] could now transcend its rank. In other words, my own potential had expanded to infinity.

And that wasn't even the end of it. Countable infinity wasn't the limit of what there was to understand about Infinity[M].

What if I raised my understanding of Infinity[M] even further?

I could obtain more absurd skills like the Infinite Inventory and Successor's Will[EX].

"So... was that helpful...?"

Iliana finally asked cautiously.

My face had been somewhat contorted with shock and pain. Perhaps that was why she was watching my reactions so nervously. I quickly composed my expression and answered.

"It was tremendously helpful."

Helpful didn't begin to cover it. With a little exaggeration, it was salvation.

That was Iliana for you. There was a reason she had said what she did in my previous life.

["If you ask me 'why' a phenomenon occurs, I cannot answer you."]

But.

["I can explain everything about 'how' a phenomenon occurs under a given set of conditions."]

Insight[L], which allowed her to intuitively grasp laws and phenomena. Peak Human Intelligence[A+], which allowed her to immediately understand the knowledge she took in.

Even the word genius couldn't encompass such overwhelming talent. It didn't merely rival a dragon's—it surpassed one.

"Really?! Was I really helpful?!"

Iliana was overjoyed to hear she had helped.

"Hehe...!"

She beamed at me, but then—

"Ah, um... well..."

As though embarrassed, she flushed and hastily lowered her head.

'I didn't know she could make that expression.'

It was an expression I had never seen in my previous life. I watched her quietly for a moment.

"On that note..."

I took a heavy pouch out of my Inventory.

"Subspace magic?!"

Iliana's eyes went wide.

"Didn't you say you weren't a mage?!"

"That's right."

"And yet you can use Subspace magic?!"

She looked ready to faint from shock. Understandably so, since Subspace magic was highly advanced magic.

"That's impossible unless you can implement the concepts of hyperspace and quantum tunneling!"

... Well, apparently so.

But the Inventory wasn't Subspace magic. It was classified as subspace, but it wasn't magic. So an explanation was impossible. Not that I was confident I could explain it anyway.

As though to cut off her questions, I handed her the pouch I'd taken out.

"What... is this?"

"Have a look."

Tilting her head, Iliana checked its contents.

"These are platinum coins."

"One hundred in all."

One platinum coin was worth a thousand gold.

"A hundred thousand gold?!"

She cried out in astonishment.

Provided they didn't indulge in extravagant luxuries, a person living alone could live off a hundred thousand gold for the rest of their life without working.

I took nine more identical money pouches out of my Inventory and placed them on the table.

"Each of these also contains a hundred platinum coins."

"A million gold?!"

Her small mouth fell wide open, but only for a moment.

"I'd like you to have all of it, Iliana."

"Whaaaat?!"

Her eyes opened so wide they looked ready to split. Her gaze quivered wildly, as though an earthquake had struck, silently asking why I was giving her a million gold.

"We at the Predator Merchant Company would like to sponsor you."

The instant I finished speaking—

"Whaaaaaaaaaat?!"

Iliana leaped into the air like a tree frog.