crazy sum 1 + 2 + 3 + 4 + · · · = −1/12
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送交者: suprathinker 于 2011-03-04, 14:43:55:
所有跟贴:
1 + 2 + 3 + 4 + · · · = - 1/12 (无内容)
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suprathinker
(0 bytes)
2011-03-04, 14:44:53
(555883)
你要不是写错了-要不就是ILLUTIONALLY CRAZY,上面的和是无穷大。 (无内容)
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meiyou
(0 bytes)
2011-03-04, 15:21:23
(555902)
no, it's deeply correct. (无内容)
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suprathinker
(0 bytes)
2011-03-04, 15:31:18
(555903)
show me, u genius (无内容)
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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.
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suprathinker
(239 bytes)
2011-03-04, 16:11:16
(555918)
u r crazy. (无内容)
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meiyou
(0 bytes)
2011-03-04, 19:18:00
(555958)
ur reaction is not a surprise. (无内容)
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suprathinker
(0 bytes)
2011-03-05, 02:51:05
(556025)
没看明白,? (无内容)
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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)
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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)
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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)
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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)
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lightman
(0 bytes)
2011-03-04, 17:03:48
(555938)
it's more exact, not the other way around. (无内容)
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suprathinker
(0 bytes)
2011-03-04, 17:05:14
(555939)
why? (无内容)
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3747
(0 bytes)
2011-03-04, 14:56:50
(555891)
the sum is 50% 0 and 50% 1.
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suprathinker
(39 bytes)
2011-03-04, 15:00:19
(555894)
why 50% 0 and 50% 1? (无内容)
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田野
(0 bytes)
2011-03-04, 16:45:33
(555933)
the probabilities of getting the sum 0 and 1 are both 50%
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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)
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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
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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)
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suprathinker
(0 bytes)
2011-03-04, 16:15:18
(555921)
or S - 1 = - S. (无内容)
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suprathinker
(0 bytes)
2011-03-04, 15:08:57
(555896)
没想明白,,, (无内容)
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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)
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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)
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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)
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3747
(0 bytes)
2011-03-04, 16:16:08
(555922)
u already got it. he needs more time. (无内容)
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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)
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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)
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Zzz
(0 bytes)
2011-03-04, 16:42:45
(555932)
got it, thanks, (无内容)
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3747
(0 bytes)
2011-03-04, 15:37:54
(555904)
still can't. (无内容)
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chouqilozi
(0 bytes)
2011-03-04, 15:02:32
(555895)
the expectation value, that is. Not sure about the first one. (无内容)
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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)
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3747
(0 bytes)
2011-03-04, 15:00:02
(555893)
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