3 ms·
N is not fixed, so we're always in case (i), position ≤ N. The equivalence class does indeed not specify the colour of the hat. The invocation of the Axiom of
by waqf 10y ago
N is not fixed, so we're always in case (i), position ≤ N.
The equivalence class does indeed not specify the colour of the hat. The invocation of the Axiom of Choice was used to tell the prisoner what to guess in that equivalence class, although there is no guarantee that it is correct in their specific case.
- leereeves 10y agoHow does a prisoner know where they are in the pre-chosen sequence? Seeing only an infinite number of hats ahead, which match some pre-chosen sequence after an unspecified finite number of hats, how do they know if they are in position, 1, .... i-1, i, i+1, etc? I mean, even if you know which equivalence class the sequence belongs to, you won't be able to guess at the color of your own hat without knowing your position.