„I knew! I knew!” The Su Jun yu inspired voice spread over the place of entire training. His rave, is excited to break with the supernatural power front manuscript paper, tosses in the air, several like flowers showered on the earth below by a goddess of the sky. “我知道了！我知道了！”苏君宇振奋的声音传遍了整个集训之地。他狂吼着,激动得将自己面前的稿纸用法力震碎,抛洒到空中,几如天女散花。 On several th, the place of this training was recently spiritless. One crowd of faith the calculation family/home that is doomed to be overruled are studying the exchange together, seems like one group of people condemned to death to warm up in sticking together. 最近几日,这个集训之地都是死气沉沉的。一群信念注定要被否决的算家在一起学习交流,就好像是一群死囚在抱团取暖。 Su Jun yu this, without doubt to other person of huge inspirations. 苏君宇这一声,无疑是给其他人一个巨大的鼓舞。 thin Xiaofeng the tiger body shakes. He knows that Su Jun yu is pondering anything. Although all sorts of signs showed, perhaps some seniors had proven that „is incomplete”, even if not, at least still denied calculated the Lord mentality. 薄笑风虎躯一震。他知道苏君宇正在思考什么。虽然种种迹象都表明,或许已经有前辈证明了那“不完备”就算不是,至少也是否定了算主的思路。 But when, this result really presents before him, he somewhat cannot believe. 可是,当这个结果真的呈现在他面前的时候,他又有几分不敢相信了。 Su Jun yu appearance, drew the attention of others. These, his strange thought had been known by many people on. Heard that he at pondering „is incomplete” the matter, many people are staring in secret. Perhaps the waiting looks at the joke, waits for his success. 苏君宇的样子,也引来了其他人的注意。这几日,他那古怪的思想已经被不少人知晓了。听说他在思考“不完备”的事儿,很多人都在暗中盯着。或是等待看笑话,或是等待他的成功。 But now, did he succeed? 而现在,他成功了？ More people encircled to Su Jun yu. thin Xiaofeng first said reluctantly: „Su Jun yu...... congratulates...... congratulates......” 更多的人围向了苏君宇。薄笑风最先勉强道:“苏君宇……恭喜……恭喜啊……” Su Jun yu beckons with the hand: „Also congratulates. During I felt me to have no intention to find a significant direction...... if successful, a Yuan god was hopeful.” 苏君宇摆摆手:“还不到恭喜的时候啊。我感觉我无意当中找到了一个重大的方向……如果成功的话,元神有望。” The member who another knows Su Jun yu asked: „Yuan god...... you now just gold/metal pill 34 years?” 另一个认识苏君宇的修士问道:“元神……你现在刚刚金丹三四年吧？” „The path of Yuan god. No, if I really solved this problem, perhaps besides the Yuan god, refining up the empty Nirvana continually is the things of fait accompli.” Su Jun yu expression is extremely stimulated: „This may be the achievement of free and unfettered rank!” “元神的道路啊。不,如果我真的解决了这个问题,说不定除了元神之外,连炼虚涅槃都是铁板钉钉的事情。”苏君宇表情极度亢奋:“这有可能是逍遥级别的成果！” The people held breath cold air. 众人倒吸了一口凉气。 In Yuan god day pass/test around makes the free and unfettered period the achievement, then the steady promotion rambles. Such member are many. Too a day reveres is the typical example. The talent member who many becomes famous young is this. 在元神天关的前后做出逍遥期的成果,然后一路平平稳稳晋升逍遥。这样的修士很多。太一天尊就是典型的例子。很多年少成名的天才修士就是这样的。 The people look to Su Jun yu look, is immediately different. The achievement of free level, means the infinite bright future. Even toward this direction was actually defeated diligently, that still denies a wrong path. But in this „denial” middle, the member who launches the impact can gain the huge advantage similarly. 众人看向苏君宇的眼神,立刻就不同了。逍遥级的成果,就意味着无限光明的未来。就算是朝着这个方向努力却失败了,那也是否定一条错误的道路。而在这个“否定”当中,发起冲击的修士同样可以获得巨大的好处。 Moreover, the free level achievement that at this time can present, except for 23 asked during second asked „complete proof” outside. What can also be? 而且,这个时候能够出现的逍遥级成果,除了二十三问当中的第二问“完备性证明”外。还能是什么？ „Did you find the mentality?” tall Jiyang quickly closely examines. Although he had transformed the thought that but had not actually found to the incomplete mentality. “你找到思路了？”高继扬急忙追问。虽然他已经转变了思维,但是却还没有找到通往不完备的思路。 Su Jun yu nods, said: „Ok. However beforehand stated that this mentality you cannot snatch.” 苏君宇点点头,道:“行啊。不过事先声明啊,这个思路你们可不能抢去。” „Senior Brother Su. So many people look that I do not believe some people is not really concerned about face.” thin Xiaoya said loudly. To that incomplete proof, she has been unbearably anxious, waited to look at the proof. “苏师兄。这么多人看着呢,我就不信还有人真个不要脸了。”薄筱雅大声说道。对那不完备的证明,她早就是急不可耐,就等着看证明了。 thin Xiaofeng also said: „Yes. old Su, if this people will plagiarize your mentality. I...... have my family member, very you.” 薄笑风也道:“就是。老苏,要是这会有人剽窃你的思路。我……还有我家里人,都会挺你。” thin Xiaofeng said „family member”, that is includes many are the free and unfettered member entire Bo. No one can disregard this warning. 薄笑风说的“家里人”,那可是包括多为逍遥修士在内的整个薄家。没人能够无视这个警告。 But more people said loudly: „Perhaps had been proven by that senior the thing, as for does cover-up? Said a bit faster! Said a bit faster!” 而更多的人则大声道:“说不定是已经被那个前辈证明了的东西,至于这么藏着掖着吗？快点说！快点说！” The disciples' of these ten thousand methods to the answer of this issue have waited for 这些万法门的弟子对这个问题的答案早就翘首以盼了 Su Jun yu nods: „Good, I say. The continual series do you know?” 苏君宇点点头:“好,那我就说一说好了。连续统你们知道吧？” „Continual series?” tall Jiyang detects immediately not to: Did the question that „second asked also involve the continual series? First asked that with second asked that in fact is both sides of issue?” “连续统？”高继扬立刻察觉出不对来:“第二问的问题还涉及连续统吗？第一问和第二问,实际上是一个问题的两面？” Su Jun yu also gawked: „Asked both sides? Has this view?” 苏君宇也愣了:“一问两面？有这种说法吗？” Immediately, he also realized anything, saying of knowing whether to laugh or cry: „That...... does not do right by everyone, my inspiration, was first asks. With second asked there is nothing to do with.” 随即,他也意识到了什么,哭笑不得的说道:“那个……对不住各位,我刚才的灵感,就是第一问的。与第二问无干。” „Did first ask?” thin Xiaofeng stared in a big way the eye: „You were not pondering that second did ask? How to run up to first to ask?” “第一问？”薄笑风瞪大了眼睛:“你不是在思考第二问吗？怎么又跑到第一问去了？” „Bumps into.” Su Jun yu laughs: „For the negative completeness, I recently in each corner that the ponder arithmetic can ponder, particularly in set theory system. Then, I pondered that ‚set axiom’ above, from that axiom, I found the inspiration......” “误打误撞罢了。”苏君宇大笑:“为了否定完备性,我最近在思考算学能够思考的每一个角落,尤其是集合论这个体系里面。然后,我就思考到了那个‘集合公理’上面,就从那个公理,我找到了灵感……” „Stops!” tall Jiyang stopped Su Jun yu, then drew a circle with the finger in the middle of the midair. The world spiritual energy gathers in this ring following his will, turns into a mature law. This spirit light halo encircled around Su Jun yu the person like this. “停一下！”高继扬制止了苏君宇,然后用手指在半空当中画了一个圆。天地灵气顺着他的意志汇聚到这个圆环之内,化成一个成熟的法度。这个灵光圈就这样圈住了苏君宇周围的这一圈人。 tall Jiyang sinking sound said: „We could guess, second asked was solved. However, currently does not have the sign to indicate. First asked that was also solved by others. Therefore, this idea, should also be Junior Brother Su a person.” 高继扬沉声道:“我们或许可以猜测,第二问被人解决了。但是,目前还没有迹象表明。第一问也被其他人解决了。所以,这个想法,应该还属于苏师弟一个人的。” „If surrounding fellow apprentices also to the domain that in first asked did the research, moreover wanted the cheek. Should better not to listen, otherwise, if later had the dispute, on everyone cheek is unattractive.” “若是周围的师兄弟还向在第一问的领域里做研究,而且还要面皮的话。就最好不要听下去,不然的话,以后若是起了纠纷,大家面皮上都不好看。” After a while, the masters of 2-3 Yuan god periods drew back tall Jiyang the circle. The function of this spirit light halo is isolates inside and outside induces. So long as had/left this circle, regardless of Su Jun yu discussed that what they cannot hear and cannot see. 过了一会,2-3个元神期的宗师退了了高继扬的圈子。这个灵光圈的作用就是隔绝内外感应。只要出了这个圈子,苏君宇无论谈什么他们都听不到、看不到。 If they and Su Jun yu really had the similar inspiration. That is really does not talk clearly rational. Especially Su Jun yu seems like with two brother and sister of Bo relates well. But if therefore makes the bad impression in Bo this colossus eye, that is fortunately big. 如果他们和苏君宇真的有了相似的灵感。那才真是有理说不清。尤其是苏君宇看上去和薄家的两兄妹关系不错。若是因此而在薄家这个庞然大物眼中留下恶劣印象,那才是亏得大。 At this time, tall Jiyang said to Su Jun yu: „Junior Brother Su, you can continue. However, do not say too, the point till.” 这个时候,高继扬才对苏君宇说道:“苏师弟,你可以继续了。不过,不要说太多,点到为止。” Su Jun yu touched the back of the head with a smile: „In Junior Brother heart extremely, the rash, the Senior Brother taught for a while is.” 苏君宇笑着摸了摸后脑:“师弟心中太过,一时孟浪了,师兄教训得是。” „My domain with first asked luckily has nothing to do, otherwise I definitely could not bear want to listen.” tall Jiyang said with a smile: „Now you were say.” “幸好我的领域与第一问无关,不然我肯定也忍不住想去听一听。”高继扬笑道:“现在你就是说一说吧。” „Spoke!” People extremely angry say/way. “讲一下吧！”众人愤愤道。 „I spoke. First, what I must explain, this is only my present thought that a mentality, I do not have the concrete process, was not clear that this process prerequisite theory whether improves.” “那我就讲一下好了。首先,我要说明的是,这只是我现在的一个念头,一个思路,我没有具体的过程,也不清楚这个过程的前置理论是否完善。” „I think like this. First, we must first establish a frame, then the set theory axiom allows, all establish sets of existing to place in this frame. Then in this frame, we carry on such operation again......” “我是这样想的。首先,我们先要建立一个框架,然后集合论公理允许存在的、所有成立的集合都放在这个框架内。然后在这框架之内,我们再来进行这样的操作……” Su Jun yu surroundings gradually peaceful. 苏君宇的周围渐渐安静了下来。 „Now, I ponder the continual series again.” “现在,我还是重新来思考一下连续统。” In finishing after path Xiaoqian the letter exchange, king Qi sat oneself desk, started to ponder the continual series the proof issue. 在结束了与路小茜的信件交流之后,王崎又坐回了自己的书桌,开始思考连续统的证明问题。 „First, is Goodall's proof to this issue.” “首先,是哥德尔对这个问题的证明。” „Goodall's work, establishes a giant frame, in this frame, contained in all zf axiomatics all ‚to establish set’. Then, in this model, Goodall proved that in the zf axiomatics, the continual series hypothesis is unable to attest to falsity.” “哥德尔的工作,就是建立一个巨大的框架,这个框架之内,包含了所有zf公理体系中所有‘可建立集合’。然后,在这个模型当中,哥德尔证明了,zf公理体系之内,连续统假说无法证伪。” „However Goodall makes this certificate 23 years later, another mathematician Cohen made the proof. This proved that in the zf axiomatics, the continual series hypothesis is unable to confirm.” “而在哥德尔做出这个证明的二十三年后,另一位数学家科恩则做出了证明。这位证明了,在zf公理体系之内,连续统假说无法证实。” „In other words, the continual series hypothesis, is actually an undecidability problem. Its independence beyond set theory, the establishment is untenable, regardless of you are accept it or do not accept it, does not affect anything.” “换句话说,连续统假说,其实是一个不可判定问题。它独立于集合论之外,无论是成立还是不成立,无论你是接受它还是不接受它,都不影响什么。” „Set theory initiator asked according to the set theory the famous hypothesis , is actually the independence beyond the set theory, this is also people are just the victims of fate.” king Qi sighed one slightly. “集合论创始者根据集合论问出的著名假说,却是独立于集合论之外,这也算是造化弄人啊。”王崎微微感叹了一句。 „However the forcing method, was entirely different from Goodall's mentality.” “而力迫法,就和哥德尔的思路截然不同了。” „Forcing method” this name is quite violent, in fact, its mentality is also close to the violence decoding very much. It „may establish set” the range, the expansion said below minimum range that the zf axiomatics permits, then approaches that result gradually. “力迫法”这个叫法颇为暴力,事实上,它的思路也很接近暴力破解。它将“可建立集合”的范围,扩张道了zf公理体系所允许的最小范围以下,然后逐步逼近那个结果。 „Set that because this proof did not have related to creation”, therefore the proof process of Cohen forcing method, Goodall's process wants to be abstruse time. 由于这个论证涉及“创造原本不存在的集合”,所以科恩力迫法的证明过程,比哥德尔的过程要艰深许多倍。 But this is also the most essential part. „Forcing method” the significance, and not only lies in the continual series. Its appearance, causing the mathematician can discover that are many other independence in the proposition of zf axiomatics. 而这也是最关键的部分。“力迫法”的意义,并不仅仅在于连续统。它的出现,使得数学家可以发现去多其他独立于zf公理体系的命题。 If from the perspective of math, the shocking even Goodall incomplete theorem of forcing method is purely bigger. 如果单纯从数学的角度来讲,力迫法的冲击性甚至比哥德尔不完备定理更大。 In Earth historical, some mathematicians headed by Hilbert, to dying are disregarding Goodall. And no doubt has a large part of reasons is the struggle and belief struggle of idea, they are unable to accept Goodall's theory. 在地球的历史上,以希尔伯特为首的一部分数学家,一直到死都无视着哥德尔。其中固然有很大一部分原因是理念之争、信仰之争,他们根本无法接受哥德尔的理论。 But, this also with Goodall's elaboration „insufficient math” related. 可是,这也与哥德尔的论述“不够数学”有关。 It looks like in some mathematicians, Goodall incomplete theorem, what are more is only a literal elaboration, rather than the proof process of math. 在一部分数学家看来,哥德尔不完备定理,更多的只是一个文字性的论述,而非数学的证明过程。 „So long as I can complete the forcing method, the arithmetic of divine land can enter a new boundary.” “只要我能过完成力迫法,神州的算学就能够进入一个新的境界。” king Qi writes with vigor. At once, in the study room is only left over the sound that the pen tip and paper rub. 王崎奋笔疾书。一时之间,书房里就只剩下笔尖与纸张摩擦的声音。 „Seeks...... seeks may establish a set smaller set compared with the zf axiom under......” “寻找……寻找比zf公理下可建立集合更小的集合……” „Independent axiom......” “独立的公理……” „Independent......” “独立……” In king Zaki's ponder, the supernatural power of his within the body has the slight change again. 在王崎的思考当中,他体内的法力再次发生细微的改变。 This time, his body week has not presented any phenomenon, the supernatural power has not presented the sign of any rebellion or collapse. 只是这一次,他身周没有出现任何异象,法力也没有出现任何暴动或是崩溃的迹象。 All changes are probably silent. Probably was his supernatural power had the little tiny adjustment. 一切变化好像都是无声无息的。好像就是他的法力发生了一点点细小的调整。 king Qi do not know, actually this new adjustment has anything to affect.( To be continued.) 王崎自己都不知道,这新的调整究竟有什么作用。(未完待续。) ps: At the end of the month, asked the monthly ticket. 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