A question regarding infinite chains and probability.

Hey there! I'm currently studying Phyrronic Skepticism and have come up with a question that will seriously affect the conclusions I reach.

P(n) depends on P(n+1) in such a way that if P(n+1) is true, P(n) has a 99.9% chance of being true. You can extend this indefinitely (so that P(1939532) has a 99.9% chance of being true if P(1939533) is true, and so on)

Is the probability of P(n) being true ultimately 0?

Probability
Itai Riftin Itai Riftin
2
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  • Savionf Savionf
    +2

    Questions at this level should come with a bounty.

    • Itai Riftin Itai Riftin
      +1

      Hey! Im aware, which is why I don't really expect an answer and I don't blame anyone who skips over it. Unfortunately I do not currently have the financial capability to provide a bounty. I figured this was worth a shot.

1 Answer

Not necessarily. P(n) could be false for all n > 10, for example.

Mathe Mathe
3.3K
  • Savionf Savionf
    +1

    This does not contradict what Itai is trying to prove. He wants to prove that the probability of P(n) being true converges to zero as n goes to infinity, which is also the case in your example.

    • Mathe Mathe
      +1

      None of the cases P(n) have to be true (or with probability 1). In fact, if one case is true for a number N*, they can't be true for any n > N*. The chains would be finite necessarily.

  • Itai Riftin Itai Riftin
    0

    Thanks a ton for the answer! And I do apologize for not being clearer- assuming I understood you correctly, it's important for me to add that if P(n+1) is false then P(n) is also false

    • Mathe Mathe
      0

      I think I'm having trouble understanding what you mean by true/false and your probability statements. Are you familiar with basic measure theory?

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