17/11/30 22:27:46.93 IqNIthYM.net
>>50 つづき
45 スレリンク(math板:471番)
471 現代数学の系譜 工学物理雑談 古典ガロア理論も読む 20171106
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
URLリンク(xorshammer.com)
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