MC Creative Mode: Wholesale Perpetual Motion Machine

Chapter 222 Unmeasurable Sets

"Oh?" Fang Zheng picked up the furry little animal and stared into its eyes. "You actually said it's all of them?"

Fang Zheng asked with a hint of curiosity, "Speaking of which, in my memory, I, Fang Zheng, have also watched quite a few anime and read novels like magical girls, Kamen Rider, and super warriors."

“In these stories, there often appears mascots like you, who look harmless but can give special powers to teenagers.”

"Generally speaking, in this kind of setting, the mascot is either hiding some kind of conspiracy or is an individual from a highly advanced civilization."

"So..." Fang Zheng gently rubbed Qubi's round cheeks. "What's the name of the civilization behind you?"

Cupid tilted his head and calmly replied, "It's difficult to accurately describe our names using human language. If you absolutely must find a similar word, you can call us 'Incubators'."

"Kyubi?" Mami Tomoe, who was standing nearby, was stunned when she heard this. "You... are you an alien? Why didn't you tell me your name sooner... aren't we friends?"

Kyubey tilted his head as if it were perfectly normal: "Although it's not entirely accurate, you can think of us as aliens. As for why I didn't say? Mami, you didn't ask either."

"Wait!" Sakura Kyoko seemed somewhat shocked. Although she hadn't received much formal education due to family circumstances, she was still a member of modern society and had watched some television programs about aliens.

She gestured somewhat frantically: "Chubi, you... if you're an alien, where are your tentacles? Don't aliens all have tentacles?"

"Could it be," a chill ran down her spine, "that your furry skin is covered in tentacles?"

Just imagining that scene gave the girl goosebumps.

“Moreover,” Sakura Kyoko’s expression became even more uneasy. She subconsciously covered her chest and took two steps back, “You said you are an incubator. Are you one of those aliens who capture Earthlings and incubate their offspring?”

"You're making us magical girls, not like those tentacle monsters in the movies, so we can hatch your offspring, right?!"

Faced with Sakura Kyoko's somewhat impolite question, Kyubey was not angry, but calmly replied: "We don't need to find humans to incubate our offspring, nor do we need inefficient limbs like tentacles."

"To be precise, our Incubator Civilization does not have the kind of physical body that humans are aware of."

"Huh?" Sakura Kyoko's expression first showed relief, then she pointed to its small, animal-like body and asked, "Then... what is this thing?"

Mami Tomoe followed up with, "Kyubi? You mean, the way you appeared when you came into contact with us wasn't your true form?"

Kyubey obediently squatted on the ground and replied, "Just as a person born blind cannot see, and a human being cannot directly touch space, our true structure is something that the human mind cannot recognize in essence."

"As for this body, it's just an interactive interface we created to facilitate communication with humans."

……

"The Incubator Civilization, is it..." Fang Zheng reached out and continued to stroke its head, a silent symphony playing in his fingertips as he tried to observe its body structure, but the result was a complete black box.

This fluffy, cute appearance is just like Fangzheng itself—a mere shell with an empty exterior.

"If you are truly a superior civilization beyond human comprehension, you should be able to understand what I am saying."

The next moment, a sharp scream burst from Fang Zheng's mouth.

Almost simultaneously, the same scream came from Cupid.

Two almost overlapping shrieks rose and fell in succession; if there had been glass nearby, it would probably have shattered long ago.

However, the screams only lasted for a moment before they stopped abruptly.

"Hey!" Sakura Kyoko covered her ears tightly, her face showing discomfort. "You two, why did you suddenly shout like that in the middle of your conversation? You scared us!"

"Yeah, yeah, that was a real scare!" Young Fang Zheng chimed in.

In a brief shriek, Fang Zheng used the simplest binary code to compress and package the massive amount of data he possessed.

Originally, Fang Zheng attempted to use the Concerto for micro-management and to communicate with Cupid more efficiently, but he discovered that the other party's internal workings were a complete black box.

So he simply reversed the process of all the mathematical structures he had mastered and compressed them into an information package.

Just like a short derivation formula can derive an infinite number of digits of pi after the decimal point.

Conversely, starting with the endless sequence of pi itself, and combining it with infinite computational power, we can also deduce all the formulas that can produce this number.

Given certain initial conditions, the derivation formula for pi can be definitively determined. Similarly, since information is an infinite set of all mathematical structures, it can, of course, be compressed into a compressed file with an extremely limited amount of information, following a similar principle.

This compressed file can be decompressed using a simple algorithm.

The decompressed contents contain an even larger compressed file and a more detailed decompression algorithm.

Decompress again, loop again, and iterate indefinitely, with the amount of information increasing exponentially with each iteration.

After performing an infinite number of calculations and decompressions, the entire set of mathematical structures known to and calculated by Founder can be completely restored.

In other words, this compressed file itself is a "genesis formula" capable of expanding into infinite information.

If there truly is an advanced civilization behind Cupid, then this information will naturally be gradually revealed through continuous decompression.

There's no need for endless iterative decompression; after a certain number of decompressions, you can roughly determine the extent of the decompression from the relevant directories.

Qubi responded to Fangzheng's "scream" in the same way as Fangzheng.

After analyzing Cupid's scream, Fang Zheng discovered that the other party had completely encompassed the set of mathematical structures he had provided, added more unknown information, and then reverse-compressed it into a "genesis formula".

This means that it did not simply obtain rough information from the directory of the decompressed content through limited calculations, but actually performed an infinite number of calculations to arrive at the complete picture, add new set information, and then compress it in reverse again.

"Oh, really? You also have infinite computing power? That's higher than I thought." As the shriek subsided, Fang Zheng nodded calmly. "You've actually already touched upon unmeasurable sets?"

Generally speaking, if we want to define a reasonable "measure" for as many sets as possible in the real number line or other spaces, such as length, area, or volume, two basic requirements need to be met:
First, it is "translation invariant": when a set is moved, its "size" remains unchanged;
Second, it is "countable and additive": when an infinite number of disjoint small sets are combined, the total "size" should be the sum of the "sizes" of each small set.

In simple terms, if you break a stick, its length won't change out of thin air.

However, using the mathematical tool of the "choice axiom," it is possible to construct some very "strange" sets, such as Vitaly sets. Under conventional measure theory, these sets "cannot be measured in size."

If you try to assign a "length" to this strange set, whatever value you assign it, whether it's zero or a positive number.

Ultimately, both will violate one of the two fundamental requirements: translation invariance or countability and additivity.

Therefore, such strange sets are called "unmeasurable sets", meaning that under the premise that the measure must satisfy translation invariance and countability and additivity, it is impossible to assign a logical and self-consistent "size" value to it.

“However,” Fang Zheng continued, “the unmeasurable set is merely an existence that is difficult to fully define under conventional human logic; it does not mean that it has fundamentally violated the basis of human logic.”

"But the information you gave me contains things that go far beyond this scope."

"This is something that I cannot understand at all with my habitual thinking of 'human uprightness' even if I apply the axiom of choice. It is something that can only be understood with other types of personality patterns."

"This also means that your 'incubator' civilization does not need to make wishes to me."

Fang Zheng turned to the three people standing to the side, who were completely bewildered. "Since they don't need it, what about your wishes? Have you thought about them?"

"Let me ask you something first," the young man asked, raising his hand, "can my wish be temporarily postponed?"

Fang Zheng nodded. "Okay. At least for now, I will continue to stay in this world."

"Oh, that's good," the young Fang Zheng breathed a sigh of relief and waved the sword in his hand that was gleaming slightly. "Since you say that I am the copy of Fang Zheng, then I now also have superpowers. I plan to take some adventures in this other world first, and then slowly consider making a wish."

"What about you two?" Fang Zheng then looked at Mami Tomoe and Kyoko Sakura. "Although I can't provide you with Lament Seeds or more Witch Contract opportunities for the time being, I can provide you with as much wealth or health as humans would like, no matter how much you want."

“Wealth…” Sakura Kyoko lowered her head, her mood somewhat dejected. She waved her hand and said in a forlorn tone, “Heh, I don’t need it anymore. This kind of thing is completely useless to me now…”

Mami Tomoe also shook her head slightly: "As for money, I don't lack it. I have enough."

"Alright." Fang Zheng nodded. "Since that's the case, I'll just give you a little 'gift' at the end."

"Take some enchanted golden apples back with you..."

……

The scorching sun beat down on the ground. In a quiet alley in Takihara City, four figures and a Kyubey appeared out of nowhere.

The group exchanged glances. Mami Tomoe and Kyoko Sakura formed one group, while Fang Zheng and young Fang Zheng formed another. The two groups then headed in different directions.

(End of this chapter)