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罗素悖论的解决
李均宇(李林星) 2001.12.26. email:myvbvc@tom.com QQ:165442523
到现在为止,我并不知道罗素悖论是否被别人解决了.如果不包含下列的理论,我认为<<集合论>>是不完整的.
让我们首先讨论N度空间开始.
定义1:自然数,整数,有理数,叫做0度空间.
定义2:线,平面,立体空间,叫做1度空间.
定义3:N度空间的点的集合数叫做N度空间的曲线数.
根据相对论,同一时间不同的点可以转化为不同时间相同的点."不同的点"是"曲线"的另一种表达方式.所以我们三维空间看来是曲线在四维空间看来是一个点.一个实数可以看成是一系列的有理数集合.于是我提出如下的物理学假设:N度空间的一条曲线在(N+1)度空间将是一个点.显然,0度空间的所有点数可以用希伯来字母表示为X0,1度空间的所有点数可以表示为X1.根据数学归纳法,N度空间的曲线数是X(n+1),N度空间的点数就是Xn.
让我们再进一步讨论这个物理学假设.建立一个直角坐标系,X轴正方向表示一个实数的小数位数,X轴负方向表示一个实数的整数位数.Y轴表示0到9个数字.于是一个实数能用一条曲线表示.一个循环小数能用一个周期曲线来表示.于是N度空间一个周期曲线能表示成(N+1)度空间的一个有理数,N度空间的一条无限不周期曲线能表示成(N+1)度空间的一个实数.直线X=0截取这条曲线,左边部分为整数部分,右边部分为小数部分,于是能排序.
罗素悖论的问题在于"所有集合的集合".因为所有集合的集合是最上级的集合.表示无限大的数字Χ的下标也趋于无限大了,也就是limΧn(n→∞),我将这个叫做"L".
集合论的创立者G.CANTOR证明了Χn=2^Χ(n-1),还证明了Χ1=2^Χ0,Χ0，Χ1,Χ2的意义.现在我假设"所有集合的集合"的基数是固定的下标值."所有集合的集合"中任何一个元素都可以"取"或"舍",于是产生一个新集合,明显地这个新集合符合2^Χn=Χ(n+1),"所有集合的集合"已经是至高无上的集合了,所以它应包含这个新集合,所以它的基数应是Χ(n+1),这与原先假设"所有集合的集合"的基数是Χn相矛盾.所以"所有集合的集合"的基数是is L=limΧn(n→∞).
一个无限集的基数是L=limΧn(n→∞)是很少见的,所以罗素悖论没有动摆现有科学的基础.
Solving of Russell Logic Paradox
So far,Ido
not known whether Russell logic paradox have been solved by anyone else
. I think that the <<theory of set>>is not complete if itdo
es not include the following theory.
Let's talk about the concept of n-degree space first.
Definition 1:natural number,integer,rational number are call 0-degree space.
Definition 2:line,plane,interspace call 1-degree space.
Definition 3: the sets of poits of n-degree space is call the curves of n-degree space .
According as theory of relativity,the different poits at same time will change to the same poit in different time.The "different poits" is the another name of the "curve".then
what we look as a curve will be a poit at the four dimension space.A real number can be convergent by a set of rational number.So put forward the following physics hypothesis:A CURVE AT N-DEGREE SPACE WILL BE A POIT AT (N+1)-DEGREE SPACE.By all appearances,the numbers of poits of 0-degree space is rabbinical X0,the numbers of poits of 1-degree space is rabbinical X1.BY mathematics epagoge, the numbers of curves of n-degree space is rabbinical X(n+1),the numbers of poits of n-degree space is rabbinical Xn.
Let's discuss the physics hypothesis advanced.Set up a right-angled reference frame.The X horizontal right axis means the decimal digits of a real number,the X horizontal negative axis means the integer digits of a real number,the Y vertical axis means the numbers from 0 to 9.then
a real number can be used a folding line to denote.A circulating decimal can be a periodic curve.then
a periodic curve of n-degree space will change to a rational number of (n+1)-degree space,a limitless non-periodic curve of n-degree space will change to a real number of (n+1)-degree space.The intercept of Y axis of curves of n-degree space which is the value when x equal zero will change to integer digits of a real number of (n+1)-degree space,the curve oneself will change to decimal digits of a real number of (n+1)-degree space,it can be ordered just as normal.
The problem of Russell logic paradox rest with "A SET OF ALL SET".BECAUSE A SET OF ALL SET IS A VERY BLUE RIBBON SET ,the cardinal number of infinity set is rabbinical Χ which subscript go to infinity ,that is limΧn(n→∞),I name it "L".
G.CANTOR,the founder of set theory had demonstrate Χn=2^Χ(n-1)，and demonstrate the meaning of Χ1=2^Χ0 , Χ0，Χ1 and Χ2.Now I suppose that the cardinal number of "A SET OF ALL SET" is discretional fixed value Χn。Anyone of discretional element of "A SET OF ALL SET " will be "taken " and "abandon",thus generate a new power set,obviously the cardinal number of the new power set is 2^Χn=Χ(n+1)."A set of all set " is already a set of immanence,so should include this new power set ,thus the cardinal number of it change to Χ(n+1), contrary to the supposing of Χn.So the cardinal number of "a set of all set "is L=limΧn(n→∞).
A infinity SET which cardinal number is L=limΧn(n→∞) is infrequent,so the Russell logic paradoxdo
not waver the base of science.
李均宇(李林星) 2001.12.26. email:myvbvc@tom.com QQ:165442523
到现在为止,我并不知道罗素悖论是否被别人解决了.如果不包含下列的理论,我认为<<集合论>>是不完整的.
让我们首先讨论N度空间开始.
定义1:自然数,整数,有理数,叫做0度空间.
定义2:线,平面,立体空间,叫做1度空间.
定义3:N度空间的点的集合数叫做N度空间的曲线数.
根据相对论,同一时间不同的点可以转化为不同时间相同的点."不同的点"是"曲线"的另一种表达方式.所以我们三维空间看来是曲线在四维空间看来是一个点.一个实数可以看成是一系列的有理数集合.于是我提出如下的物理学假设:N度空间的一条曲线在(N+1)度空间将是一个点.显然,0度空间的所有点数可以用希伯来字母表示为X0,1度空间的所有点数可以表示为X1.根据数学归纳法,N度空间的曲线数是X(n+1),N度空间的点数就是Xn.
让我们再进一步讨论这个物理学假设.建立一个直角坐标系,X轴正方向表示一个实数的小数位数,X轴负方向表示一个实数的整数位数.Y轴表示0到9个数字.于是一个实数能用一条曲线表示.一个循环小数能用一个周期曲线来表示.于是N度空间一个周期曲线能表示成(N+1)度空间的一个有理数,N度空间的一条无限不周期曲线能表示成(N+1)度空间的一个实数.直线X=0截取这条曲线,左边部分为整数部分,右边部分为小数部分,于是能排序.
罗素悖论的问题在于"所有集合的集合".因为所有集合的集合是最上级的集合.表示无限大的数字Χ的下标也趋于无限大了,也就是limΧn(n→∞),我将这个叫做"L".
集合论的创立者G.CANTOR证明了Χn=2^Χ(n-1),还证明了Χ1=2^Χ0,Χ0，Χ1,Χ2的意义.现在我假设"所有集合的集合"的基数是固定的下标值."所有集合的集合"中任何一个元素都可以"取"或"舍",于是产生一个新集合,明显地这个新集合符合2^Χn=Χ(n+1),"所有集合的集合"已经是至高无上的集合了,所以它应包含这个新集合,所以它的基数应是Χ(n+1),这与原先假设"所有集合的集合"的基数是Χn相矛盾.所以"所有集合的集合"的基数是is L=limΧn(n→∞).
一个无限集的基数是L=limΧn(n→∞)是很少见的,所以罗素悖论没有动摆现有科学的基础.
Solving of Russell Logic Paradox
So far,Ido
not known whether Russell logic paradox have been solved by anyone else
. I think that the <<theory of set>>is not complete if itdo
es not include the following theory.
Let's talk about the concept of n-degree space first.
Definition 1:natural number,integer,rational number are call 0-degree space.
Definition 2:line,plane,interspace call 1-degree space.
Definition 3: the sets of poits of n-degree space is call the curves of n-degree space .
According as theory of relativity,the different poits at same time will change to the same poit in different time.The "different poits" is the another name of the "curve".then
what we look as a curve will be a poit at the four dimension space.A real number can be convergent by a set of rational number.So put forward the following physics hypothesis:A CURVE AT N-DEGREE SPACE WILL BE A POIT AT (N+1)-DEGREE SPACE.By all appearances,the numbers of poits of 0-degree space is rabbinical X0,the numbers of poits of 1-degree space is rabbinical X1.BY mathematics epagoge, the numbers of curves of n-degree space is rabbinical X(n+1),the numbers of poits of n-degree space is rabbinical Xn.
Let's discuss the physics hypothesis advanced.Set up a right-angled reference frame.The X horizontal right axis means the decimal digits of a real number,the X horizontal negative axis means the integer digits of a real number,the Y vertical axis means the numbers from 0 to 9.then
a real number can be used a folding line to denote.A circulating decimal can be a periodic curve.then
a periodic curve of n-degree space will change to a rational number of (n+1)-degree space,a limitless non-periodic curve of n-degree space will change to a real number of (n+1)-degree space.The intercept of Y axis of curves of n-degree space which is the value when x equal zero will change to integer digits of a real number of (n+1)-degree space,the curve oneself will change to decimal digits of a real number of (n+1)-degree space,it can be ordered just as normal.
The problem of Russell logic paradox rest with "A SET OF ALL SET".BECAUSE A SET OF ALL SET IS A VERY BLUE RIBBON SET ,the cardinal number of infinity set is rabbinical Χ which subscript go to infinity ,that is limΧn(n→∞),I name it "L".
G.CANTOR,the founder of set theory had demonstrate Χn=2^Χ(n-1)，and demonstrate the meaning of Χ1=2^Χ0 , Χ0，Χ1 and Χ2.Now I suppose that the cardinal number of "A SET OF ALL SET" is discretional fixed value Χn。Anyone of discretional element of "A SET OF ALL SET " will be "taken " and "abandon",thus generate a new power set,obviously the cardinal number of the new power set is 2^Χn=Χ(n+1)."A set of all set " is already a set of immanence,so should include this new power set ,thus the cardinal number of it change to Χ(n+1), contrary to the supposing of Χn.So the cardinal number of "a set of all set "is L=limΧn(n→∞).
A infinity SET which cardinal number is L=limΧn(n→∞) is infrequent,so the Russell logic paradoxdo
not waver the base of science.
]