現代数学の系譜工学物理雑談古典ガロア理論も読む45

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む45 (835ﾚｽ)
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471: 現代数学の系譜 工学物理雑談 古典ガロア理論も読む [sage] 2017/11/06(月) 00:04:32.15 ID:1Au30FRy

>>470 つづき

で、むしろ時枝記事に近いのは、君が>>295（>>304）で紹介した下記の方が、時枝に近いだろう
ここでは、任意の関数f(x)の任意の貴方の選ぶ１点（”You pick an x ∈ Ｒ”）を、” whatever f Bob picked, you will win the game with probability 1!”、”it’s arbitrary: it doesn’t have to be continuous or anything”の条件で当てられるとあるよ

Ｎ⊂Ｒだから、”You pick an n ∈ Ｎ”とすれば、時枝記事の場合を含むことになろう
で、時枝記事のように、どこの箱が当たるか分らず、また確率99/100に対して、これは自分で選んだｘであり、”with probability 1!”だから、こちらの解法がよほど優れている

おっちゃん（>>461）、どうだ？（＾＾

https://xorshammer.com/2008/08/23/set-theory-and-weather-prediction/
SET THEORY AND WEATHER PREDICTION XOR’S HAMMER Some things in mathematical logic that I find interesting WRITTEN BY MKOCONNOR Blog at WordPress.com. AUGUST 23, 2008
(抜粋)
Here’s a puzzle:
You and Bob are going to play a game which has the following steps.

1)Bob thinks of some function f： Ｒ → Ｒ (it’s arbitrary: it doesn’t have to be continuous or anything).
2)You pick an x ∈ Ｒ.
3)Bob reveals to you the table of values {(x0, f(x0))｜ x0 ≠  x } of his function on every input except the one you specified
4)You guess the value f(x) of Bob’s secret function on the number x that you picked in step 2.

You win if you guess right, you lose if you guess wrong. What’s the best strategy you have?

This initially seems completely hopeless: the values of f on inputs x0 ≠  x have nothing to do with the value of f on input x, so how could you do any better then just making a wild guess?

In fact, it turns out that if you, say, choose x in Step 2 with uniform probability from [ 0,1 ], the axiom of choice implies that you have a strategy such that, whatever f Bob picked, you will win the game with probability 1!

つづく

http://rio2016.5ch.net/test/read.cgi/math/1508931882/471

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