zixinlxm 发表于 2018-7-31 17:34:02


I have recently done some research on thethird crisis in the history of mathematics and put forward bold assumptions. Allcolleagues who like math are welcome to criticize and correct.The third crisis in the history ofmathematics was the first paradox in Forti's revelation of set theory in 1897and after two years Cantor found a very similar paradox. It was finally causedby the hairdresser's paradox proposed by Russell in 1902. Russell suggestedthat there is such a hairdresser in a certain city. He wrote: "I have andonly shave all the people who don't shave their faces for the city." Butone day the barber saw it from the mirror. His own beard is long. Heinstinctively grabbed the razor. Can you see if he can shave himself? If hedoesn't shave himself, he belongs to "a person who doesn't shavehimself." He wants to shave himself, and if he shaves himself? He is alsoa "person who shaves himself," and he should not shave himself. That is,mathematically, A={x/x ∉ A}, defined as acollection that does not belong to its own collection. There are twoassumptions here.1. If x does not belong to set A, then thecondition x ∉ A is satisfied,then x belongs to set A;2. If x belongs to set A, then bar x ∉ A is not satisfied, then x does not belong to set A.From the above point of view, x should bean element that does not belong to set A and belongs to set A. The catassociated with Schrödinger, in a confined space, put a cat and a glass flaskcontaining hydrogen cyanide gas and radioactive material into a closed box.When the monitor inside the box detects decaying particles, it breaks the flaskand kills the cat. According to the Copenhagen Interpretation of QuantumMechanics, that is to say, there is a living and dead cat in this confinedspace that is not observed, and the cat is in a superimposed state of beingalive and dead. Or exist in two parallel spaces M, N, in the space M the cat isalive, and in the N space, the cat is indeed dead. Similarly, whether we can boldly assumethat there is such a parallel set M, N, x does not belong to set A in the Mset, and x belongs to set A for set N. Defining the parallel set M, N is: Undera defined set, there are two sets M, N, and the element x has no effect on theset N under the set M, and the same element x has no effect on the set M underthe set N. Thus we can obtain a new idea that x satisfies both the M set thatdoes not belong to set A and the N set that x belongs to set A. That is to say,the element x is in a superposition set belonging to the set A and notbelonging to the set A. Just like finding a set of numbers that are not on thenumber axis on the number axis, is there such a number axis or several numberaxes?
                                                                               -----A chemical cat who loves mathematics

最近对数学史上的第三次危机做了些研究,并提出了大胆性的假设,希望各位同僚,喜欢数学的同僚们批评加以指正。数学史上的第三次危机是由1897年在福尔蒂揭示集合论中的第一个悖论和于两年后康托尔发现了很相似的悖论。最终由罗素1902年提出的理发师悖论引起而出现的。罗素提出,在某个城市中有着这样一位理发师,他写到:“我且有且只为本城所有不给自己刮脸的人刮脸。”可是,某天这位理发师从镜子里看见自己的胡子长了,他本能地抓起了剃刀,你们看他能不能给他自己刮脸呢?如果他不给自己刮脸,他就属于“不给自己刮脸的人”,他就要给自己刮脸,而如果他给自己刮脸呢?他又属于“给自己刮脸的人”,他就不该给自己刮脸。也就是数学上的,A={x/x ∉ A}, 定义为所有不属于自身集合的集合。这里也就有两种假设,1.      若x不属于集合A,则满足条件x ∉ A,那么x就是属于集合A;2.      若x属于集合A,则不满足条x ∉ A,那么x就不属于集合A。从以上观点来看,x应该是一个不属于集合A又属于集合A的元素。那联想于薛定谔的猫,在一个密闭的空间里,把一只猫和一个装有氰化氢气体的玻璃烧瓶和放射性物质放进封闭的盒子里。当盒子内的监控器侦测到衰变粒子时,就会打破烧瓶,杀死这只猫。根据量子力学的哥本哈根诠释,那也就是说,在这个没有被观测的密闭空间里存在一只既活又死的猫,这只猫处于又活又死的叠加态。抑或存在于两个平行空间M,N,在空间M中这只猫处于活着的状态,而在N空间里,这只猫确实处于死的状态。同样,是否我们能大胆假设存在着这样一个平行集合M,N,在M集合中x不属于集合A,而对于集合N, x属于集合A。定义平行集合M,N为:在一个定义的集合下,存在两个集合M,N,且元素x在集合M下对集合N没有影响,同样元素x在集合N下对集合M没有影响。从而我们能获得一个新的设想,x既满足不属于集合A的M集合,又满足于x属于集合A的N集合。也就是说元素x处于一个属于集合A和不属于集合A的叠加集合之中。就如同在数轴上找到一个不属于数轴上数的数的集合,是否存在这样一根数轴或几根数轴呢?
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