我们知道,
共产主义就是没有私有财产了,
一切都属于社会了。
如果一个社会里每个人的钱都可以想要多少就有多少,
那就等于是共产主义社会了。
我今天刚刚证明了任何两个数都相等,
所以任何人的钱都等于任何他或她想要的那个数目,
所以共产主义今天被我实现了。
这里是任何两个数相等的证明:
首先,
1=1+0+0+0+0+..........
=1+(1-1)+(1-1)+(1-1)+(1-1)+..........
=(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..........
=2+0+0+0+0+..........
=2
有了1=2,
马上可以证明任何两个正整数都相等,
比如3=2+1=1+1=2=1。
证明了所有正整数相等之后,
0和负整数也都和这些正整数相等了,
比如0=1-1=2-1=1,
-1=1-2=3-2=1.
证明了所有整数相等之后,
所有有理数也相等,
因为p/q=p/p=1.
证明了所有有理数相等之后,
马上可以证明所有实数相等,
因为实数是有理数序列的极限,
既然有理数都相等,
任何一个有理数序列都是一个常数序列,
所以极限就等于这个常数。
证明了所有实数相等之后,
马上就可以证明所有复数也相等,
因为虚数i是方程x^2=-1的解,
这个方程和方程x^2=1是一样的,
而x^2=1的解是1或者-1,
于是i=1或者i=-1,
但-1=1,
所以i=1.
于是我们看到所有的数都相等,
这个定理的实际应用就是上面所说的:
世界上没有穷人和富人,
大家的钱都一样多,
哈哈,
共产主义居然已经实现了。
- Re: 共产主义已经被我实现了,哈哈posted on 02/13/2009
哈哈,great job!
1=1+0+0+0+0+..........
我也学慧元MM认真一回哈,这个的premise是 inf*0 = 0,这个故事告诉我们,如果 inf*0 is defined,共产主义就可以实现了 :) - posted on 02/13/2009
浮生 wrote:
哈哈,great job!
1=1+0+0+0+0+..........我也学慧元MM认真一回哈,这个的premise是 inf*0 = 0,这个故事告诉我们,如果 inf*0 is defined,共产主义就可以实现了 :)
错!
按照严格的级数理论,
1+0+0+0+0+.........=1,
这是因为无穷级数的和的定义是有限和序列的极限,
这个级数的有限和序列是{1,1,1,1,1,1,1........},
所以极限是1,
也就是说,
1+0+0+0+0+.........=1。
哈哈哈,
共产主义依然被我实现了。 - Re: 共产主义已经被我实现了,哈哈posted on 02/13/2009
inf*0=0, I'm not convinced (yet).
ok, let's look at the next step then:
=1+(1-1)+(1-1)+(1-1)+(1-1)+..........
=(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..........
The premise here is inf = inf - 1, if inf can be used as a constant this way, then anything can be proven.
But don't get me wrong, I'm quite willing to go with the idea that 共产主义已经实现了 :) - posted on 02/13/2009
浮生 wrote:
inf*0=0, I'm not convinced (yet).
ok, let's look at the next step then:
=1+(1-1)+(1-1)+(1-1)+(1-1)+..........The premise here is inf = inf - 1, if inf can be used as a constant this way, then anything can be proven.
=(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..........
But don't get me wrong, I'm quite willing to go with the idea that 共产主义已经实现了 :)
你比令胡冲好,
至少找到了出问题的这一步,
但你的解释并不对,
这里没有无限。
所以共产主义暂时还是被实现了,
不过已经危机重重了,
哈哈 - Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
唉。Inf 当然等于 inf-1。没有听说过Hilbert Paradox of Grand Hotel? :)
- posted on 02/14/2009
令胡冲 wrote:
唉。Inf 当然等于 inf-1。没有听说过Hilbert Paradox of Grand Hotel? :)
You've read Gamow's One, Two, three ... Infinity? ;-) There was a Chinese translation (从一到无穷大)in the late 70's.
Anyway by now 裹尸 is busy trying to figure out where his "proof" went terribly wrong. ;-)
Actually what's interesting is that in the smallest set of inifinity aleph-null, there is one very ingenious proof that all natural numbers belong to the set and have the equal cardinality.
It's very counter-intuitive to think about it, since there are infinite rational numbers between any two whole numbers, shouldn't there be more rational numbers than the whole numbers?
The proof is that any pair of rational numbers can be expressed as the ratio of two whole numbers (0.6=3/5 and 1.6666..=5/3, etc.), therefore, having a direct one to one relationship. Hence there are exactly the same number of whole numbers as all rational numbers. Neat, no? ;-)
- Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
There is an inf here, which is the pairs of (1-1).
inf = inf -1 but inf is bigger than any given number, which means
a=a -1 does not apply on any 'a' other than inf
And, 0+0+..0 if the # of 0 is N (whatever it is), they sum to 0
but if N = inf, they don't sum to 0
症结就这么简单:有限个0相加还是0,但无限个0相加就不是0 - Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
加法有交换率或者分配率吗? - Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
有啊,这不就是: - posted on 02/14/2009
mahuiyuan wrote:
There is an inf here, which is the pairs of (1-1).
inf = inf -1 but inf is bigger than any given number, which means
a=a -1 does not apply on any 'a' other than inf
And, 0+0+..0 if the # of 0 is N (whatever it is), they sum to 0
but if N = inf, they don't sum to 0
这个问题从头到尾都没有无穷大,
一切都是有限的。
0+0+0+0+0+..........当然等于零,
因为这是一个{0,0,0,0,.....}这个序列的极限。
可能你没学过级数,
但如果你学过,
呵呵,
级数这部分不及格。 - Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
0+0+0+0+0+.........嘿嘿,这是有限还是无限啊?级数不是这么表达的吧。
如果你的。。。表达的是有限的话,规范化的第一步就该写成
1=1+0+0+0+0+..........
=1+(1-1)+(1-1)+(1-1)+(1-1)+..........+(1-1)
这样下面一步就马上看出毛病了。
如果...表达的是无限的话,
1=1+0+0+0+0+.......... 本身就不成立。
因为如果任意多个0(包括有限和无限)相加都是0,那么不会有微积分了,因为每个点的面积都是0,那么所有区域的面积都是0 - posted on 02/14/2009
mahuiyuan wrote:
0+0+0+0+0+.........嘿嘿,这是有限还是无限啊?级数不是这么表达的吧。
如果任意多个0(包括有限和无限)相加都是0,那么不会有微积分了,因为每个点的面积都是0,那么所有区域的面积都是0
你还是要回去补习一下微积分。
给定一个级数a_1+a_2+a_3+......
我们可以做有限和s_n=a_1+.......+a_n,
有限和序列{s_n}的极限lim_{n to infty}s_n如果存在,
就说这个级数收敛,
并且定义级数的和为这个极限,
也就是说,
a_1+a_2+a_3+......=lim_{n to infty}s_n.
积分的定义不是每个点或线的面积的和,
如果那样定义面积的话,
积分也总是0,
面积的定义是先把区间分为有限多个小区间,
区间长度乘上任意一点的函数值,
得到这个小区间上面积的逼近值,
然后加起来,
得到整个区间上的面积逼近值,
然后再令小区间长度趋于0,
如果这时上面得到的逼近面积值有极限,
那个极限就是面积或积分。
这和把无穷多个等于0的面积加起来是两回事。
科普有时能帮助人们理解一些抽象的东西,
但碰到严格的技术性问题如果用科普的东西来做常常出错。 - posted on 02/14/2009
首先,“给定一个级数a_1+a_2+a_3+......”本身就不是科学的表达,“..."后面到底是什么?
再有,无穷多个0和有穷多个0有什么区别?为什么要有“无穷”这个概念?为什么不用一个有穷但很大的概念代替?你认为Inf * 0 = 0?
看好戏 wrote:
mahuiyuan wrote:你还是要回去补习一下微积分。
0+0+0+0+0+.........嘿嘿,这是有限还是无限啊?级数不是这么表达的吧。
如果任意多个0(包括有限和无限)相加都是0,那么不会有微积分了,因为每个点的面积都是0,那么所有区域的面积都是0
给定一个级数a_1+a_2+a_3+......
我们可以做有限和s_n=a_1+.......+a_n,
有限和序列{s_n}的极限lim_{n to infty}s_n如果存在,
就说这个级数收敛,
并且定义级数的和为这个极限,
也就是说,
a_1+a_2+a_3+......=lim_{n to infty}s_n.
积分的定义不是每个点或线的面积的和,
如果那样定义面积的话,
积分也总是0,
面积的定义是先把区间分为有限多个小区间,
区间长度乘上任意一点的函数值,
得到这个小区间上面积的逼近值,
然后加起来,
得到整个区间上的面积逼近值,
然后再令小区间长度趋于0,
如果这时上面得到的逼近面积值有极限,
那个极限就是面积或积分。
这和把无穷多个等于0的面积加起来是两回事。
科普有时能帮助人们理解一些抽象的东西,
但碰到严格的技术性问题如果用科普的东西来做常常出错。 - posted on 02/14/2009
mahuiyuan wrote:
首先,“给定一个级数a_1+a_2+a_3+......”本身就不是科学的表达,“..."后面到底是什么?
再有,无穷多个0和有穷多个0有什么区别?为什么要有“无穷”这个概念?为什么不用一个有穷但很大的概念代替?你认为Inf * 0 = 0?
看来你还真没学过级数,
难怪。
这里不能打数学符号,
所以才写a_1+a_2+a_3+......,
严格的写法是Sigma_{n=1}^{infty}a_n.
当然是严格得不能再严格的表达。
无穷和有穷有本质的区别,
所以无限求和要给出确切定义,
我给出的是几百年来无数数学家研究后给出的精确定义。
无穷这个概念不能乱用,
乱用要出错的。
inf*0是一个符号,
意思是有两个序列或函数,
一个的极限是无穷,
另一个的极限是0,
如果要求两个序列或函数的乘积的极限,
通常把这一类极限记成是inf*0类的,
这一类极限有各种可能,
自然不一定等于0,
但我们这里讲的和这无关,
因为我们不是求这样一个极限。
- Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
嘿嘿,我不愿去判断“你(没)学过什么”,因为那又要落到所有论坛争论的本质了。:)
上一个回复已经说完了要说的--最初的表达就是ambiguous的
如果你的。。。表达的是有限的话,规范化的第一步就该写成
1=1+0+0+0+0+........+0
=1+(1-1)+(1-1)+(1-1)+(1-1)+..........+(1-1)
- posted on 02/14/2009
tar wrote:
You've read Gamow's One, Two, three ... Infinity? ;-) There was a Chinese translation (从一到无穷大)in the late 70's.
No I read it from the popular book "Fermat's Last Theorem", by Simon Singh. It rephrased the Hilbert paradox in such an simple way that I simply scanned, understaood, and remembered it.
I regret when I was little, I wasn't so lucky to read good books like that.
Anyway by now 裹尸 is busy trying to figure out where his "proof" went terribly wrong. ;-)
He screwed himself up, didnot he? Ha ha... He has to call himself "被看好戏"。
Apparently he got himself into an awkward situation that he doesn't understand this question is not as simple as he thought he could understand. :)
- posted on 02/14/2009
Is this finding of the 看好戏 as revolutionary as the "universal revulsion" theory?
At least this 看好戏 gave a "proof" that tricked some into thinking in artificial "calculus" ways.
(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+.......... is actually
(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..........(-1+1) -1
=(1+1)+ lim[n*(-1+1)] -1
=(1+1) +lim(n*0) -1
=(1+1) +lim(0) -1
=(1+1) +0 -1
=1
SOmeone here said that "infinity" times 0 is not equal to 0. But what is "infinity"? That is a question in philosophy, not a pure mathematical one. "Infinity" is still a thorn in the eyes of pure mathematicians. But that is not relevant to that "proof".
Now I just lifted myself to the level of titans like you.
看好戏 wrote:
我们知道,
共产主义就是没有私有财产了,
一切都属于社会了。
如果一个社会里每个人的钱都可以想要多少就有多少,
那就等于是共产主义社会了。
我今天刚刚证明了任何两个数都相等,
所以任何人的钱都等于任何他或她想要的那个数目,
所以共产主义今天被我实现了。
这里是任何两个数相等的证明:
首先,
1=1+0+0+0+0+..........
=1+(1-1)+(1-1)+(1-1)+(1-1)+..........
=(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..........
=2+0+0+0+0+..........
=2
- posted on 02/14/2009
st e-dou #65 wrote:
(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+.......... is actually
(1+1)+(-1+1)+(-1+1)+(-1+1)+(-1+1)+..........(-1+1) -1
=(1+1)+ lim[n*(-1+1)] -1
=(1+1) +lim(n*0) -1
=(1+1) +lim(0) -1
=(1+1) +0 -1
=1
You screw yourself up as simply & bluntly as 看好戏。 :)
It's the most rubbish math I ever saw. I am so depressed you don't even undertand a 12 year old should understand - there is a simple concept called limit and infinite.:)
You know what? It's a miracle that I didn' become touche and funny and just call you low life!! :)
其实看好戏的原题是个歪打正着很不错的题。只是他自己不知道该如何解决,结果给搞成了手足无措。CND那里网友多,很多人在芝加哥、斯坦福之类的大学当数学教授,他们可能会给你一个意想不到的回答,让我们重温过去的时光。:)
- Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
唉,咖啡客为什么不先对楼主的机智和幽默表示一下欣赏,反而纷纷板着脸来显示自己的高明呢?难道楼主自己不知道这是个paradox, 不知道症结在哪里? - posted on 02/14/2009
一元 wrote:
唉,咖啡客为什么不先对楼主的机智和幽默表示一下欣赏,反而纷纷板着脸来显示自己的高明呢?难道楼主自己不知道这是个paradox, 不知道症结在哪里?
澳,原来是楼主在当众显示机智幽默和高明啊?一元听着比其他“咖啡客”都高明嘛。:)
这不是一个paradox。这里面唯一的所谓幽默或paradox就是楼主以为自己知道症结在哪里,却找不出来也说不出来。Maybe Rumsfeld is right, - sometimes we know what we know, sometimes we know what we don't know but don't know what we know; and, there are times we don‘t know what we don't know. :) - Re: 共产主义已经被我实现了,哈哈posted on 02/14/2009
Look at the vileness demonstrated by some's posts here. Those vile ones never understand that they can never hurt anyone who is not attched to or dependent on anything that they themselves think valuable to them.
Please don't change any of yours posts. Please expose yourselves more. This whole thing is a group therapy anyway. I'm a spectator.
HeeHeeHee! - posted on 02/14/2009
岂敢,俺只有五体投地的份。好奇楼主怎么想出这样的歪门邪道来:)
令胡冲 wrote:
一元 wrote:澳,原来是楼主在当众显示机智幽默和高明啊?一元听着比其他“咖啡客”都高明嘛。:)
唉,咖啡客为什么不先对楼主的机智和幽默表示一下欣赏,反而纷纷板着脸来显示自己的高明呢?难道楼主自己不知道这是个paradox, 不知道症结在哪里?
这不是一个paradox。这里面唯一的所谓幽默或paradox就是楼主以为自己知道症结在哪里,却找不出来也说不出来。Maybe Rumsfeld is right, - sometimes we know what we know, sometimes we know what we don't know but don't know what we know; and, there are times we don‘t know what we don't know. :)
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