Vol 3 Chapter 826: Zhen Jie Zi's Root-seeking Journey

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The first of Hilbert's twenty-three questions is the continuum cardinality question.
The continuum problem, that is, "there is no other cardinality between the cardinality of the countable set and the cardinality of the real number set".
The so-called "cardinality" refers to the "absolute measure" of the set. There is one element in a set, then the cardinality of this set is one, and if there are two elements, the cardinality is two. And so on.
The cardinality of the infinitely countable set of "all integers" and "all natural numbers" is recorded as "Alev zero"-the smallest infinite integer that China calls it "the zero number of Dao yuan"
The ancients in Shenzhou used to think that the total number and the infinite number are the numbers.
Alev zero plus one is still Alev zero. Alev zero plus Alev zero or Alev zero. Alev zero times Alev zero or Alev zero.
Infinite and infinite. Ordinary methods of operation are completely meaningless for this number.
So, is there a number bigger than this infinite number in the world?
Actually there is.
That is the cardinality of "power set".
If a set has an element of "1", then there are two power sets-"1" and an empty set ?.
If a set has two elements "1, 2", then it has four power sets-empty set ?, set {1}, set {2}, set {1, 2}.
By analogy, when a set has three elements, then it has eight power sets. When the set elements increase by four, the power set increases to sixteen.
The power set of a set is always more than the elements of this set. If a set has N elements, then it has a power set of 2 to the Nth power.
The power set of an infinitely countable set, the Alev zeroth power of two, is the second infinite number discovered by mankind-bass one.
In addition to being the power set of the integer set, this "beth1" is also the base of all real number sets.
The continuum problem can also be summarized as "Are there any other cardinal numbers between Alev zero and bass one?".
Is there a cardinality of a set that is definitely greater than one infinity and less than another infinity?
This is the first of the twenty-three questions.
Among the twenty-three questions, the second and tenth questions are related to the foundation of mathematics and are considered extremely important. It is precisely because of the operator's idea of ​​"completeness, consistency, and decidability" that these two questions have been compared. But from the perspective of the "questioner", the relationship between the first question and the second question is closer. The first question and the second question, continuity and completeness, are basically connected.
The first question leads to the second question, and the answer to the second question inspires the answer to the tenth question.
These problems can be regarded as a system.
Of course, each of the twenty-three questions of Jimen is more or less related to the other twenty-three questions. The entire twenty-three questions are implicitly a whole. And this whole, covering most aspects of mathematics, once solved, the whole mathematics will show a huge progress. And each of the mathematicians' research is more or less related to one of the twenty-three questions.
There has never been a fortune-teller who can do this, not before, and unlikely in the future. For the history of mathematics, the twenty-three questions are a huge leap.
And Wang Qi is also fancy with this. He has solved the second and tenth questions. Now throwing the solution to the first question, it is actually not particularly shocking.
In addition, the continuum hypothesis is similar to the proof of completeness and decidability, both of which are extremely important but relatively independent. They are like the first piece of a domino, which is not very much in itself, but when it falls, it will trigger a chain reaction.
If you want to solve these problems, you don't need much accumulation. These questions are all about "ingenuity".
On the earth, the answerers to the second and tenth questions are quite young talented scholars. The answerer of the first question, even strictly speaking, does not understand mathematical logic-P.J. Cohen's professional field is analysis, he is just attracted to this question, nothing more.
The answerer of the first question, P.J. Cohen, could not even understand the application of the proof method he invented in the field of logic.
In other words, this achievement can also be pushed into the "flash of genius inspiration".
However, the biggest problem is ...
"I didn't seem to have taken this thing back in my life in particular ..." Wang Qi felt a headache again.
The solution to the binary linear equation is now a middle school student. But how many people know how to prove that solution?
The distance between "knowing" and "proving" is roughly equivalent to "cultivating the supreme mind" and "creating the supreme mind". The latter is more difficult than the former.
What's more, Wang Qi didn't even remember the solution of the first question, the "force method", but only a general direction.
"How long does it take me now to be able to put the first question's proof process on my own?"
Uncontrollably, Wang Qi began to think about this issue.
Until Zhen Jiezi came to remind: "Hey, kid."
"Think about it, don't bother."
"I want to remind you that you are here." Zhen Jiezi sighed: "If you don't land, you will fly over."
"Oh." Wang Qi looked down. It was an endless plain. The flat ground extends all the way to the skyline, and only the west is faintly shaded by the mountains. That is the northern section of Kunlun Mountain. On the south side of Wang Qi, there is a river, satin-like flat on the ground, almost straight. That is the second largest river in China. There are private houses gathered, with Dajiang as the center, all the way to the north and south. Outside the town, there are fields like parcels. Now the new season of wheat has just sprouted, looking green and fluffy from above.
Green and brown are the colors of this ground.
"Jiangbei City, here." Wang Qi sighed.
This scene is not so easy to see north of Kunlun. The dragon clan nailed the West Sea plate, which also made the movement of the Shenzhou West Land plate strange. The terrain to the west of Kunlun was far more complicated than the east to Kunlun.
Wang Qi flew all the way from the west of Kunlun, and I've already seen you the scenery of the mountains. Now that I see this plain, I feel relaxed and happy, and the trace of depression brought about by the problem just now disappears completely.
Speaking of this, although he has cultivated immortals for more than ten years, he has been unable to find time to look at this world. In the first few years, he concentrated on his studies in Xianyuan, and later was "under house arrest" in Shenjing because of the suspicion of "Xianxian". Except that he once went to Xiaodong with Chen Feng, and Chen Feng, who once went to Tianling Mountain, he never went out. After arriving at Leiyang, he stayed at sea again, hardly seeing the side of the world where he lives in this life.
The universe is infinitely large, but only the planet at this moment is special to him.
Zhen Zhenzi also sighed: "The blood of the Luo family, should ... should it be here?"
Liwu Luoshi, where the descendants of the true eldest son's family may exist.
Wang Qi heard the words and patted his ring: "Well, I flew for more than half a month just to help you find the root!"
Really explain her anger: "Why does this sound so dead like a dead man?" And why is it so nasty? "
"No, no, other people are looking for roots for ancestors. You are looking for roots for future generations." Wang Qi looked innocent: "As for the sloppy ... am I not helping you find blood roots? Is there anything else here?" the meaning of?"
On that day, after bidding farewell to Chen Feng, Wang Qi also began his "journey to help the old man of the ring find roots." He first went to Mao Zimiao, which was regarded as an early year. After eating a light meal, Wang Qi first went all the way north and entered the category of Split Peak Island.
Chiding Island is very small, no match for Fuso mainland. It is located at the junction of the West Sea and the North Sea. There is no overly large biome here, and the number of demons is much smaller than that of the Xihai. After the Kraken had lost the most terrible amount, it was not a cause for concern. On the other hand, there is also an unusual place. The first practitioner of Jinfa was born on this island, and he realized that for the general practitioner of Jinfa, Split Peak Island can even be regarded as a holy place. The mortals near Split Peak Island can also be regarded as living and living.
When Wang Qi came to Split Peak Island, it was New Year's Day. There was heavy snow on the Split Island, wrapped in silver, and the scenery of the Northern Kingdom. After enjoying the snow scene, Wang Qi also visited Ai Changyuan who returned home for the New Year.
Wang Qi and Ai Changyuan had a friendship when they were young. It's just that Wang Qi has a cheating device, which leads Ai Changyuan about three or four years in practice. Before breaking through the realm, Ai Changyuan in the foundation period could not beat Wang Qi, who had already become a knot. This makes the young master of the Ai family quite depressed.
After leaving Liding Island, Wang Qi turned against Luojiang and went all the way to the west foot of Kunlun. Then, at the foot of Kunlun Mountain, Wang Qi abandoned the method of flying and escaped, and he didn't even need to protect his body.
This is not "experience" or "increasing difficulty". Even if Wang Qi does not need the method of flying escape and does not need to protect his body, he is also a monk of Jindan, whose physiological function is far superior to any common creature. With only his hands and feet, he can easily browse this mountain.
It's just that the feeling of letting the strong wind blow across your face and the feeling of wide and sharp vision at the moment of summiting are really interesting.
At the top of Kunlun Mountain, Wang Qi changed his direction, found the upper reaches of the river north, and then went all the way down.
He is now a monk of Jindan. In the absence of enemies, you can fly around the world in more than ten hours-of course, the environment of the West Sea where enemies are everywhere is discussed separately. Along the way, he spent much more time playing than Fei Dun but time.
"Let's see ... Um, this Jiangbei local specialty food ... Um, bran rice cake, and noodle tea ... and then places of interest ... There is no of meditation, the most famous scenery is only spring and autumn." Wang Qi held a travel book in his hand and seemed to be thinking about playing first.
However, Zhen Jiezi broke into an unimaginable stubbornness: "Show the old man to Luojia Village in Chengbei first!"
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