In the middle of Hilbert 23 issues first asked that continual series base number issue. 希尔伯特二十三个问题当中的第一问,连续统基数问题。 The continual series issue, namely „between the denumerable aggregate base number and real number collection base numbers does not have other base number” the issue. 连续统问题,即“在可数集基数和实数集基数之间没有别的基数”的问题。 So-called „base number”, then refers to the set „estimates absolutely”. In a set has an element, then the cardinality of this set is one, two elements, the cardinality is two. Ex analogia. 所谓“基数”,便是指集合的“绝对测度”。一个集合里面有一个元素,那么这个集合的基数性就是一,有两个元素,基数性就是二。以此类推。 But „all integer all real numbers” this infinite denumerable aggregate, its cardinality, records to make „the Aleph null” divine land to call it „a Yuan fractional amount”, minimum infinite integer. 而“所有整数所有实数”这种无限可数集合,其基数性,就记做“阿列夫零”神州称之为“道元零数”,最小的无限整数。 The ancient in divine land once believes that the total of digit, infinite greatly is the digit of say/way. 神州的古人曾经认为,数字的总数、无限的大就是道的数字。 The Aleph null adds a Aleph null. The Aleph null Aliefu amortization is the Aleph null. The Aleph null is multiplied by Aliefu amortization is the Aleph null. 阿列夫零加一还是阿列夫零。阿列夫零加阿列夫零还是阿列夫零。阿列夫零乘以阿列夫零还是阿列夫零。 Just is infinitely great and infinite. The ordinary operating mode absolutely does not have the significance regarding this number. 无限大、正无穷。普通的操作方式对于这个数字完全没有意义。 Then, in the world also has ratio infinitely great digit bigger numerical code? 那么,世界上还有比这个无限大的数字更大的数码？ In fact has. 实际上是有的。 That is „power set” base number. 那就是“幂集”的基数。 If a set has „1” this element, then its power set does have two „1” also to have the null set?. 如果一个集合有“一”这一个元素,那么它的幂集就有两个“一”还有空集?。 If a set has „1,2” two elements, then it does have four power set null sets?, Set 1, set 2, set 1,2. 如果一个集合有“1,2”两个元素,那么它就有四个幂集空集?,集合一,集合二,集合1,2。 Ex analogia, when a set has three elements, then it has eight power sets. When the set element increased said four, the power set increased to 16. 以此类推,当一个集合有三个元素,那么它就有八个幂集。当集合元素增加道了四个的时候,幂集就增加到了十六个。 A power set of set, compares this set the element to be many forever. If a set has N elements, then it has 2 N power of exponent power set. 一个集合的幂集,永远比这个集合的元素要多。如果一个集合有n个元素,那么它就有二的n次方个幂集。 The power set of infinite denumerable aggregate, two Aleph null powers of exponent, are second infinitely great digital Aliefu of human discovery one. 无限可数集合的幂集,二的阿列夫零次方,就是人类发现的第二个无限大的数字阿列夫一。 But continual series issue, can summarize between „the Aleph null and Aliefu one, actually to have another base number?”. 而连续统问题,也可以概括为“阿列夫零和阿列夫一之间,究竟存不存在另一个基数？”。 Has a base number of set, explicit is bigger than infinitely great, is smaller than another infinitely great? 有没有一个集合的基数,明确的大于一个无限大,小于另一个无限大？ This is 23 asked during first asked. 这就是二十三问当中的第一问。 During 23 asked. Second asked that tenth asked that related to the arithmetic foundation, was considered as the extreme importance. Also because calculates Lord that „completeness, uniformity and decidability” thought that therefore these two asked that usually placed on a par. But from „quizzer” the mentality, first asked that with relations that second asked. Instead is closer. First asked that with second asked that the continual series and completeness, on the foundation are connected. 二十三问当中。第二问、第十问是关系到算学根基的,被认为是极端重要的。也正是因为算主那“完备性、一致性、可判定性”的思想,所以这两问素来被相提并论。但从“提问者”的思路来说,第一问和第二问的关系。反而更为紧密。第一问和第二问,连续统和完备性,根基上是相连的。 The question that first asked guided the question that second asked that the explanation that second asked inspired the explanation that tenth asked. 第一问的问题引导出了第二问的问题,第二问的解答启发了第十问的解答。 These issues, can be regarded as a system. 这几个问题,可以看做是一个体系。 Naturally. The Greek gate 23 asked during every asked that more or less in the middle of the issue with other 23 is connected, entire 23 asked, faintly is a whole. But the almost every aspect of arithmetic this whole, covers, an exercise key leaves, the arithmetic whole appears a huge progress on the convention. But the research that each calculates the family/home, more or less with 23 asked during one asked related. 当然。希门二十三问当中的每一问,都或多或少的与其他二十三当中的问题相关联,整个二十三问,隐隐是一个整体。而这一个整体,涵盖的算学的几乎每一个方面,一题解出,算学整体就会展现出一个巨大的进步。而每一个算家的研究,或多或少都与二十三问当中的某一问相关。 Has not calculated that the family/home can achieve this point, formerly did not have, later is also unlikely to have. Regarding the history of arithmetic. 23 asked that is one and grand leap. 从来就没有算家能够做到这一点,从前没有,以后也不大可能会有。对于算学的历史来说。二十三问是一个及其壮阔的飞跃。 But king Qiye settled on this point. He has solved second asked that tenth asked. Now ejects the solution that first asked that in fact was not the matter that shocked everybody specially. 而王崎也正是看中了这一点。他已经解决了第二问、第十问。现在抛出第一问的解,实际上也不是什么特别惊世骇俗的事情。 Moreover, the continual series supposition and complete certificate and decidability certificate are similar, is that type has the extreme importance position, but that type of itself relative independence. They look like first of one piece of dominoes, itself not, so long as will drop down will trigger the chain-reaction. 另外,连续统假设和完备性证明、可判定性证明差不多,都是那种拥有极端重要地位,但是本身相对独立的那一种。它们就像是一片多米诺骨牌的第一块,本身并不如何,但只要倒下就会引发连锁反应。 To solve these problems, has not needed how deep accumulation. These issue stresses „ingenious conception” very much. 想要解决这些问题,没并不需要多么深厚的积累。这些都问题都很偏重“巧思”。 In Earth, second asked the solutionists, tenth asked is quite young talent scholar. But solutionist who first asked that even strict did not understand that the mathematical logic p.j. Cohen's professional field analyzed. He was just attracted by this issue, that is all. 在地球,第二问、第十问的解答者都是相当年轻的天才学者。而第一问的解答者,甚至严格上来说并不懂得数学逻辑p.j.科恩的专业领域是分析。他只不过是被这一个问题所吸引了,仅此而已。 Solutionist p.j. Cohen who first asked cannot even understand application of proof law in logical domain oneself invented. 第一问的解答者p.j.科恩本人甚至不能理解自己发明的证明法在逻辑领域的应用。 In other words, this achievement, can advance „flashing before of talent inspiration” similarly middle. 也就是说,这一项成果,同样可以推到“天才灵感的闪现”当中去。 However. The biggest problem is...... 不过。最大的问题是…… „My ancestors have not gone to carry...... king Qi to feel some headaches this thing probably specially”. “我上辈子好像没有特别去将这个玩意背下来啊……”王崎又觉得有些头疼了。 The solution of dual first power regulation, the present is a middle-school student can. However, how many people know how should prove that solution? 二元一次方程的解法,现在是个中学生就会。但是,有多少人知道,应该如何证明那个解法呢？ „Knows that” and „proof” between distance, is equivalent to „cultivation not careful law” probably and „homemade not careful law”. Latter's difficulty, is former's innumerable times. “知道”和“证明”之间的距离,大概就相当于“修炼无上心法”和“自创无上心法”。后者的难度,是前者的无数倍。 Solution that let alone king Qi first asked „forcing method” it does not remember. Only remembers an approximate direction. 更何况王崎连第一问的解法“力迫法”本身都不记得了。只记得一个大致的方向。 „Present I, how long need, one side can come the proof process that first asked?” “现在的我,到底需要多久,才能够自己将第一问的证明过程来一边呢？” Can not help, king Qi starts to ponder this issue. 情不自禁的,王崎开始思考起这个问题。 Until really clarified that the child family background reminded: „Hey, boy.” 直到真阐子出身提醒:“喂,小子。” „Thinks the matter, should not be tired.” “想事情呢,别烦。” „I want to remind you, went to the place.” Really clarified that the child sighs deeply: „Does not descend, you flew.” “我是想提醒你,到地方了。”真阐子长叹:“再不降落,你就飞过去了。” „.” king Qiwang to body. That is the vast plain. The smooth ground has extended to Skyline that side, only then the west has the shadow of lofty mountain indistinctly. That is northern Kunlun Mountain. king Qi south, then there is a river current, even shop/spread of satin in the place, is nearly straight. That is the divine land's second largest rivers great river. Has the private residence to gather, is centered on the great river, spreads toward the north and south. But outside the town, is that kerchief general paddies. Now the wheat of new season just germinates, looks green from the upper air soft and thick. “哦哦。”王崎望向身下。那是一望无际的平原。平整的地面一直延伸到天际线那边,只有西面才隐约有崇山的阴影。那便是昆仑山的北段。王崎的南面,则有一条江流,缎子似的平铺于地,近乎笔直。那便是神州第二大河流大江。有民房聚集,以大江为中心,一路向着南北蔓延。而城镇之外,就是那一块块帕子一般的田地。如今新一季的小麦才刚刚发芽,从高空上望去绿茸茸的。 The green and brown, are the color in this ground. 绿色与褐色,就是这块地面的颜色。 „River north city .” king Qi sighed. “江北城,到了。”王崎感叹。 This scene, is not easy to see north Kunlun Mountains. dragon clan nailed tight the plate of West Sea, makes west the divine land the movement of land plate strange, west of Kunlun Mountains topography compared with Kunlun Mountains east of complex. 这种景象,在昆仑以北可不是那么容易见到的。龙族钉死了西海的板块,也使得神州西陆板块的运动诡异,昆仑以西的地势远比昆仑以东复杂。 king Qi comes by flies westward from Kunlun Mountains, has visited you scenery of that peak on top of peak. Now saw this lets the plain, suddenly feels completely relaxed, when thought deeply about the difficult problem an elegant sentiment that a moment ago brings also completely vanishes. 王崎一路从昆仑以西飞过来,早就看你了那层峦叠嶂的景色。如今看到了这让平原,顿觉心旷神怡,刚才思索难题时带来的一丝郁郁之情也完全消失。 Then, although he cultivated/repaired more than ten years of immortals, but actually could not find time to look at this world. That several years of most starting he in immortal institute wholly-absorbed studies, because later „exiles immortal” suspicion by „putting under house arrest” in god Capital. Besides went to one time with Chen wind deep and clear east, and Chen wind Chen went to a day spirit range by fine two people, has not basically gone out. After the thunder was positive, he has stayed in marine, almost does not have the side world that good attractive this life to have survived. 说起来,他虽然修了十多年的仙,但是却一直抽不出空来看看这个世界。最开始的那几年他在仙院专心学业,之后又因为“谪仙”的嫌疑而被“软禁”在神京。除了与辰风去过一次潇东、和辰风陈由嘉两人去过一次天灵岭之外,基本就没有出过门了。到了雷阳之后,他又一直呆在海上,几乎就没有好好看过今生所生存的这一方天地。 This universe is infinitely great, only then this moment star, to him but is quite special. 这个宇宙无限大,可是只有这一刻星球,对他而而言比较特殊啊。 Really clarified that the child also sighed: „Should the bloodlines of Luo,...... should here?” 真阐子也感叹道:“罗家的血脉,应该……应该就在这儿吧？” Lebanese shipyard Roche, really clarified that the child adoptive father family descendants the place that may have. 黎坞罗氏,真阐子义父家族后裔有可能存在的地方。 king Qiwen said that racket own ring: „Un un, I flew for a half month, to help you inquires into!” 王崎闻言,拍拍自己的戒指:“嗯嗯,我飞了半个多月,就是为了帮你寻根啊！” Really clarified the child illness brought on by the obstruction of flow of vital energy: „Does this listen to look like the deceased person to return home? Moreover why so dirty?” 真阐子气结:“这听着怎么这么像死人落叶归根呢？而且为什么这么龌龊？” „, Others do not inquire into look for the ancestor, your seeks ‚root’ looks for the later generation.” king Qi is innocent: „Isn't helping you look for the bloodlines root as for dirty...... me? In this also has other meaning?” “不不不,别人寻根是找祖宗,你这寻‘根’是找后人。”王崎一脸无辜:“至于龌龊……我不是在帮你找血脉根吗？难道这里面还有别的意思？” On that day, after saying goodbye to Chen wind, king Sakiya „journey that started him help ring old man to inquire into”. He first is looks for hair Zimiao, is pays new year's call. After having a plain meal, king Qi first is toward north, entered the category of crack summit island. 那一日,在告别了辰风之后,王崎也开始了他“帮助戒指老头寻根的旅途”。他首先是去找毛梓淼,算是拜个早年。在吃过一顿便饭之后,王崎首先是一路往北,进入了裂巅岛的范畴。 The crack summit island is very small, has not resulted in the Chinese hibiscus mainland compares. It situated in intersection point of West Sea and North Sea. Here has no huge biotic community, the quantity of monster clan compared with West Sea little. But after the sea-nymph must lose the most fearful quantity, nothing to be worried. On the other hand, there is also an unusual place. Now the law's first cultivates in the elementary force the person born on this island, grasps principles, cultivates regarding the general now law, the crack summit island even can call the first half sacred place. The mortal near crack summit island, can be called enjoys a good and prosperous life. 裂巅岛很小,和扶桑大陆没得比。它位于西海和北海的交界处。这里没有什么过于庞大的生物群落,妖族的数量比西海少很多。而海妖要失去了最可怕的数量之后,就不足为虑。另一方面,那里也是一个不同寻常的地方。今法第一修元力上人就在此岛上出世,悟道,对于一般的今法修来说,裂巅岛甚至可以称得上半个圣地了。裂巅岛附近的凡人,也称得上安居乐业。 king Qi arrives at the crack summit island time, is the beginning of the year one. In the crack summit island the heavy snow flutters about, clads in silvery white, a school of north scenery. king Qi when enjoying snowscape, visited the long Yuan that goes home to celebrate the new year. 王崎来到裂巅岛的时候,正是年初一。裂巅岛上大雪纷飞,银装素裹,一派北国风光。王崎在赏玩雪景之余,也去拜访了回家过年的艾长元。 When king Qi and Ai Changyuan when is young the friendship of together hitting. But king Qi has more operates cheating, practice to lead Ai Changyuan about 34 years. Before breaking through boundary, builds base period the long Yuan not to be victorious has tied pill king Qi. This makes the young master of Ai quite somewhat elegant. 王崎和艾长元时年轻时一起打出来的交情了。只不过王崎有弥开作弊器,修行上领先了艾长元三四年左右。在突破境界之前,筑基期的艾长元还打不过已经结丹的王崎。这让艾家的少爷颇有些郁郁。 After leaving crack summit island, king Qi is then going against Luo river, arrives in west Kunlun Mountains. Then, Kunlun Mountain, king Qi then abandoned flew to escape the law, protected oneself astral air/Qi does not use, purely depending on hands and feet time toward this first under heaven famous mountains. 在离开了裂巅岛之后,王崎便逆着罗江,一路到昆仑西麓。然后,昆仑山脚下,王崎便弃了飞遁之法,连护身罡气都不用,纯凭手脚功夫向着这天下第一名山。 This is not „informed and experienced” or „increases difficulty”. Even if king Qi does not need to fly to escape the law, does not need to protect oneself astral air/Qi, he is still member gold/metal pill, the physiological function by far any mediocre lifeform. Only with the hands and feet, he can also be able to glance through this mountain with ease. 这道不是什么“历练”或者“增加难度”。就算王崎不用飞遁之法,不用护身罡气,他也是金丹修士,生理机能远胜任何凡俗生物。只用手脚,他也能能够轻松翻阅这座高山。 Whatever just, the fresh breeze has blown the feeling of face, reaches at that moment the field of vision suddenly broad feeling, is really very interesting. 只不过,那任凭劲风吹过脸庞的感觉,还有登顶那一刻视野陡然宽阔的感觉,实在是很有意思。 In the Kunlun Mountains summit, king Qi then changed the direction, found the great river upstream toward the north, then downward. 在昆仑山顶,王崎便改变了方向,往北找到了大江上游,然后再一路往下。 He now is member gold/metal pill. Without enemy, more than ten hours can fly the world to be natural, West Sea that type is the environment of enemy other discusses everywhere again. All the way, he plays the time of spending to fly together escapes, but time. 他如今已经是金丹修士。在没有敌人的情况下,十多个小时就可以飞遍全球当然,西海那种到处都是敌人的环境另外再论。一路上,他游玩花的时间远多于飞遁但是时间。 „I have a look......, this north of the Changjiang River local characteristics eats......, the rice polishings meter/rice cake, a tea...... then the scenic spot...... no deep god, the most famous scenery or the spring and autumn have.” king Qifan travel notes on hand, seems to be calculating first plays. “我看看啊……嗯,这江北本地的特色名吃……嗯,糠米粑粑,还有面茶……然后名胜……没什么冥神,最有名的景色还是春天和秋天才有。”王崎泛着手上的一本游记,似乎在盘算先游玩一番。 But, really clarified that the child actually erupted the obstinance that was inconceivable: „First went to the city north Luo Village to have a look to the old man initially!”( To be continued.) The mobile phone user please visit http://m.piaotian.net 可是,真阐子却爆发出了难以想象的执拗:“给老夫先去城北当初罗家村看看！”(未完待续。)手机用户请访问http://m.piaotian.net