b***k
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sunshinesea (我是阳光你是海) 于 (Mon Sep 24 23:55:37 2007) 提到:
X的无限个X次power（就是X的X次方的X次方......）最终等于2，问X是多少？
不知道发这个版可对？
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ashdown (chinook稀饭团团员) 于 (Tue Sep 25 00:42:38 2007) 提到:
hoho,
i cannot work out that one either
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robustzgy (浪迹天涯) 于 (Tue Sep 25 00:46:51 2007) 提到:
I guess it's sqrt(2)
let y=x^x^x^....
then y = x^y = 2, as x>0, x=sqrt(2)
I may be wrong...
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发帖数: 35 | 2 althea (...) 于 (Wed Sep 26 14:49:36 2007) 提到:
althea's explaination is good.
Let me try to analyze it from analysis point of view. Consider y_n=x^{x^{x^{
x^{x...}}}..} up to n. So, it is natural to figure out that the solution for
y_n \to k is just x=k^{1/k}. The key is in the process of finding that
solution, one assume the function f(y_n)=a^{y_n}, where a=k^{1/k}, always
has a fix point. So, to find out the condition of existence of solution, it
is equivalent to find out the existence conditio |
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