1 + 2 + 3 + 4 + · · · = - 1/12

1 + 2 + 3 + 4 + · · · = - 1/12

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送交者: suprathinker 于 2011-03-04, 14:44:53:

回答: crazy sum 1 + 2 + 3 + 4 + · · · = −1/12 由 suprathinker 于 2011-03-04, 14:43:55:

你要不是写错了-要不就是ILLUTIONALLY CRAZY，上面的和是无穷大。 (无内容) - meiyou (0 bytes) 2011-03-04, 15:21:23 (555902)
- no, it's deeply correct. (无内容) - suprathinker (0 bytes) 2011-03-04, 15:31:18 (555903)
  - show me, u genius (无内容) - meiyou (0 bytes) 2011-03-04, 15:44:19 (555907)
    - it's deeply tough to explain if u believe infinity is a bona fide number. - suprathinker (239 bytes) 2011-03-04, 16:11:16 (555918)
      - u r crazy. (无内容) - meiyou (0 bytes) 2011-03-04, 19:18:00 (555958)
        
        ur reaction is not a surprise. (无内容) - suprathinker (0 bytes) 2011-03-05, 02:51:05 (556025)
没看明白，？ (无内容) - 3747 (0 bytes) 2011-03-04, 14:45:36 (555885)
- 1-1+1-1+1-1+1-1+1-1+...............=1/2 is not crazy (无内容) - suprathinker (0 bytes) 2011-03-04, 14:47:06 (555887)
  - 要是能重排序不是可以得到任何和吗？好象在哪看过 (无内容) - lightman (0 bytes) 2011-03-04, 16:23:10 (555925)
    - define the properties of + and 重排序, result is definite n legitimate (无内容) - suprathinker (0 bytes) 2011-03-04, 16:39:32 (555931)
      - 算是一种重整化吧？如果是物理问题只要和实验对得上怎么做都对 (无内容) - lightman (0 bytes) 2011-03-04, 17:03:48 (555938)
        
        it's more exact, not the other way around. (无内容) - suprathinker (0 bytes) 2011-03-04, 17:05:14 (555939)
  - why? (无内容) - 3747 (0 bytes) 2011-03-04, 14:56:50 (555891)
    - the sum is 50% 0 and 50% 1. - suprathinker (39 bytes) 2011-03-04, 15:00:19 (555894)
      - why 50% 0 and 50% 1? (无内容) - 田野 (0 bytes) 2011-03-04, 16:45:33 (555933)
        
        the probabilities of getting the sum 0 and 1 are both 50% - suprathinker (171 bytes) 2011-03-04, 16:53:16 (555936)
        
        这是因为你把无穷序列作为有穷处理，把一个本来无穷推进的过程凝固的结果 (无内容) - 田野 (0 bytes) 2011-03-04, 17:24:51 (555941)
      - 正儿八经纠正一下，公比绝对值大于等于1的等比无穷数列之和不存在 - 羽矢 (60 bytes) 2011-03-04, 16:07:23 (555916)
        
        i'm serious. ur 不存在 is more real than 存在. we r living in a real world. (无内容) - suprathinker (0 bytes) 2011-03-04, 16:15:18 (555921)
      - or S - 1 = - S. (无内容) - suprathinker (0 bytes) 2011-03-04, 15:08:57 (555896)
        
        没想明白，，， (无内容) - 3747 (0 bytes) 2011-03-04, 15:14:43 (555898)
        
        you remove the first 1 from the sum and get a negative sum. (无内容) - suprathinker (0 bytes) 2011-03-04, 15:18:18 (555901)
        
        你喝高了吧？减去个1总和就在0和-1之中，也不一定是负的 (无内容) - Zzz (0 bytes) 2011-03-04, 16:13:39 (555919)
        
        1-1+1-1+，，，，=1/2---》-1+1-1+1+，，，，=-1/2 (无内容) - 3747 (0 bytes) 2011-03-04, 16:16:08 (555922)
        
        u already got it. he needs more time. (无内容) - suprathinker (0 bytes) 2011-03-04, 17:00:49 (555937)
        
        我不明白他贴的这些的实际意义，只是尽量按他的思路去理解 (无内容) - 3747 (0 bytes) 2011-03-04, 16:47:49 (555934)
        
        你用＂定理＂证明推论，进而连＂定理＂本身也接受了？ (无内容) - Zzz (0 bytes) 2011-03-04, 16:42:45 (555932)
        
        got it, thanks, (无内容) - 3747 (0 bytes) 2011-03-04, 15:37:54 (555904)
      - still can't. (无内容) - chouqilozi (0 bytes) 2011-03-04, 15:02:32 (555895)
    - the expectation value, that is. Not sure about the first one. (无内容) - chouqilozi (0 bytes) 2011-03-04, 14:58:05 (555892)
      - 能举个实际例子说明它的意义吗 (无内容) - 3747 (0 bytes) 2011-03-04, 15:00:02 (555893)