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Probablity & infinity

  1. Oct 22, 2013 #1
    If there is an actual infinity of throws of two dice, would all combinations have the same probability (that is each combination would happen an infinite amount of times)?
     
  2. jcsd
  3. Oct 22, 2013 #2

    mfb

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    They have the same probability for every throw (assuming they are fair).

    That would even happen with loaded dice.
    You can make a stronger statement: if you consider the fraction of [result X] in the first N throws, this fraction goes to the same value (1/36 for regular dice) as N->infinity.
     
  4. Oct 22, 2013 #3
    Does N-> Infinity imply a potential infinity instead of actual infinity?
     
  5. Oct 22, 2013 #4
    When we discuss heat, we never start with "Oh, fire is caused by phlogiston. But more recent thinkers consider it a chemical process." No. We discard ancient, obsolete ideas, and adopt the new ones.

    It's nice that Aristotle talked about actual and potential infinity. If you're discussing the history of philosophical ideas about infinity, it's good information to know.

    But since the work of Cantor in the 1880's and the set theorists of the 20th century, we now have much more precise concepts of mathematical infinity.

    Let us dispense with the meaningless concepts of "potential" and "actual" infinity. Those terms have no meaning in modern mathematics.

    An infinite set of dice rolls would be a function f:N -> {1,2,3,4,5,6} where N is the set of natural numbers. That's how to think about it and talk about it.
     
  6. Oct 25, 2013 #5

    Stephen Tashi

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    And for fair dice, each such set of rolls has probability zero.

    As to whether a given infinite set of dice rolls happens an infinite number of times, you'd have to say how many infinite sets of rolls you intend to toss for that question to have any meaning.
     
  7. Nov 26, 2013 #6
     
  8. Nov 26, 2013 #7

    Office_Shredder

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  9. Nov 27, 2013 #8

    mfb

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  10. Dec 12, 2013 #9
    No.

    You are applying concepts from probability on a finite set to an infinite set. This gives no useful result.
     
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