Chapter Seventy-Three: Gödel's Completeness Theorem
The destruction of Wang Qi began.
"...... for the simplest first-order predicate logic"
The mana in Wang Qi's whole body seemed to sense the impending breakthrough, and he became agitated.
One after another acupuncture points are washed away, and new yin and yang patterns are being generated in batches.
"Performing Logical Calculus ......"
When Wang Qi wrote this sentence, all the yin and yang in his body began to run at full capacity.
“...... All logically valid formulas can be proved......"
Wang Qi's hand holding the pen turned white from excessive force, and his black eyes became dark.
An answer is on the horizon.
"Therefore ......"
The moment Wang Qi put down his pen, all the yin and yang in his body were instantly shattered, and the explosive mana filled his body in an instant.
However, the teenager did not perceive it. Or maybe he sensed it, but didn't pay attention to it.
I got it! I got it!
He had a vague premonition that what he was going to write next would be the greatest glory of his life.
"It can be considered that the first-order predicate calculus is complete. ”
At this moment, the Yin and Yang Diagram began to re-condense in the Great Acupoints, but the number was twice as large as before!
Wang Qi didn't bother to check the condition in his body, because he had fallen into great joy.
"Whoahaha, I know!
A finger tapped twice on his desk: "Can you explain first, what do you know?"
When Wang Qi saw Chenfeng, he was a little strange: "Dongjia, why did you chase down Wanfa Gate? We said that we would ...... tomorrow Ahh
As he spoke, Wang Qi actually let out a scream.
"I'll go to you......" Chen Feng's ears hurt, and he said helplessly: "You also know that you missed the appointment." ”
Wang Qi suddenly clasped Chenfeng's shoulder. The great god asked, "To be honest, how many days have I missed the appointment?"
Chen Feng was confused: "How many days, I found here after you missed the appointment for a day, and if you don't come for a few days, I may have to change my clothes to arrest you." ”
"One day?" Wang Qi was in a trance: "What time is it?"
"...... the time"
Isn't that right? It's less than a day? Isn't that scientific?
Wang Qi grabbed the top draft on the table, the one he had just written, and asked, "This, really I wrote it?"
Chen Feng's face changed: "Have you gone mad and your brain has been injured?: Do you want me to check it on you?"
"You sue me first, aren't you!" Wang Qi's voice became more and more anxious: "Old man, you also saw it, sue me, aren't you?"
"Yes, it's true that you wrote it. ”
Chen Feng was shocked: "You don't remember what you wrote? ”
Another "old man" Liu Yunxiang also walked in: "I saw it with my own eyes, and you wrote it." Kid, what the hell are you writing about?"
Wang Qi seemed to be drained of all his strength, sat down on the ground, and said, "This is unrealistic......
The entire Wanfa Gate garrison was awakened. Everyone gathered around curiously. Seeing Wang Qi's stunned appearance, Liyue, who had suffered a loss before, was very unhappy: "Pretending to be a ghost." ”
Wang Qi suddenly snorted: "I'm sorry everyone, can you go out for a while?" I need to be alone and quiet." ”
Liu Yunxiang wanted to take a look at Wang Qi's paper, but Wang Qi held down the paper: "I'm sorry...... I can't show this yet...... Uncle Liu, please go out for a while, I really need to be alone and be quiet. ”
Wang Qi's words made several disciples of the Wanfa Sect change color slightly, and Li Yue said angrily: "You dare to be rude to Uncle Liu?"
Liu Yunxiang stopped the accusations of the disciples of the Ten Thousand Methods Sect and said, "Let's go out and wait for a while." ”
Chen Feng came outside with a group of Ten Thousand Fa Sect disciples. Regarding Wang Qi's abnormal appearance, everyone has a lot of discussions.
Mo Zhenzhen sighed: "It turns out that the legend that a genius can go all the way up by writing a thesis is true. ”
The sigh of the people around was slightly envious.
"That's it, it turns out that Senior Brother Wang is actually ......"
"He's definitely not an outer disciple...... right?"
Hearing the surrounding discussions, Ritsuki, who had already fallen below the table for Wang Qi's favorability, snorted: "There is such a thing as writing an essay to increase cultivation, but it is not that simple. The reason why cultivation grows is because the process of thinking drives the soul, and as long as you really think, even if what you think about is wrong, you can also grow your cultivation. ”
Someone asked curiously, "What happens if the conclusion is wrong?"
Huangfu Lian said in a deep voice: "It will deviate from the Fa-rectification, and if you insist on making mistakes, it will even be difficult to return." In general, don't be tempting. ”
A disciple who was close to Wang Qi nervously asked Liu Yunxiang: "Senior Uncle, Senior Brother Wang's conclusion shouldn't be wrong, right?"
Liu Yunxiang shook his head with a smile: "This ...... I don't know?"
This conclusion is very correct, and Wang Qi is very confident in this.
Because, this conclusion was not drawn by himself, but by a mathematician of the earth.
Gödel's completeness theorem.
Compared to Gödel's incompleteness theorem, this theorem is not well known. It is derived from Kurt Gödel's doctoral dissertation. It proves that in the formal system, the first-order arithmetic is complete, and all logically valid formulas in the first-order logical calculus can be proved.
However, the first-order predicate calculus is a relatively weak mathematical system, and if you just apply it, you can't even define natural numbers, let alone arithmetic.
For Hilbert's plan, Gödel's completeness theorem is a heavy breakthrough, but it is far from having the final effect of the incompleteness theorem. Moreover, the completeness theorem is only a step forward on the basis of von Neumann along Hilbert's line of thought, and is not a genius leap like the incompleteness theorem.
But......
"That's really an unscientific speed. Wang Qi muttered to himself.
For a god-level mathematician like Gödel, this paper may only be a doctoral thesis, but most mathematicians in the world cannot write such a paper.
In other words, ordinary mathematicians may not understand it.
"Although I knew the general idea and the conclusion in advance, I ...... I actually launched it in one day?"
Wang Qi was stunned.
Knowing the general idea and conclusion does not mean that it is completely uneasy. This is equivalent to everyone going to a new map to hunt for treasure, ordinary people don't know if there is a treasure, Wang Qi knew that there was from the beginning, and saw a guiding sign.
But the specific way still needs to be found by himself
At first, he didn't even think to push out Gödel's complete theorem in one go, but just follow von Neumann's idea and find a special subsystem of the arithmetic system to demonstrate.
"Am I so high?"