23/07/22 16:13:37.42 uSulak9P.net
>>633
つづき
コイントスで{0,1}なのに、実数R全体から代表列をつくれば、そこから円周率πが出てくる。アホでしょ？ｗ
いまの場合、三角関数 "sin(e^{k+(m－1)100}π)"からなる超越数と分かっている。他の関数値はお呼びじゃない
だけど、実数R全体から代表列をつくれば、三角関数 sin以外の関数値が出てくる、アホでしょ？ｗ
(参考)
URLﾘﾝｸ(mathoverflow.net)
Probabilities in a riddle involving axiom of choice
asked Dec 9 '13 at 16:16 Denis
Alexander Pruss氏
Can you guess the first coin flip on the basis of all the others?
You might think: "Of course not! No matter what function from the values of flips X1,X2,... to {0,1} is chosen, the probability that the value of the function equals X0 is going to be 1/2."
That's a fine argument assuming the function is measurable.
But what if it's not?
Here is a strategy: Check if X1,X2,... fit with the relevant representative.
If so, then guess according to the representative.
If not, then guess π . (Yes, I realize that π not ∈{0,1}.)
Intuitively this seems a really dumb strategy.
(引用終り)
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