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Random Number generator?

  1. Jun 11, 2004 #1
    Can somebody prove the following:

    A Random number which (truly) is uniformly distributed on [0 1] (or in fact any continuous random variable) is irrational with probability 1.
     
    Last edited: Jun 11, 2004
  2. jcsd
  3. Jun 11, 2004 #2

    HallsofIvy

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    In order for that problem to be "well-defined", you have to specify the measure. Assuming that the measure is the standard Lebesque measure, the set of all irrational numbers between 0 and 1 has measure 1 and the set of all rational numbers has measure 0.
     
  4. Jun 21, 2004 #3
    I don" know the prove! but I know an interesting way to get random numbers.
    just take a 4 digit number. get its square. keep two first digits away. then get the 4 next number az the next step iteration.
    some initial values dosent work. can you tell them???!!!

    for example:
    1-0.3265
    2-3265
    3-3265^2=10660225
    4-10_6602_25
    5-6602 ----0.6602
    6_ go to step 1.
     
  5. Jun 21, 2004 #4

    Gokul43201

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    The cardinality of the rationals is aleph_0 while that of the irrationals is aleph_1, I think !
     
  6. Jun 21, 2004 #5

    mathman

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    It is easy to prove that the measure of the rationals is 0, because of countability. Make a list of rational numbers. Cover the nth member of the list (symmetrically) by an interval of length x/2n. All the rational numbers are then covered by a set of measure less than x, since the union of these intervals has measure less than the sum of the individual measures. Since x can be made arbitrarily small, the measure of the rationals is 0.
     
  7. Jun 23, 2004 #6

    h2

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    Another way to get random numbers:
    Get ur telephone book, open it anywhere, choose a column, and pick the LAST digit in every phone number from the column…
     
  8. Jul 5, 2004 #7
    I have a question:
    What does random number exactly mean???
    I have this question since I hear the word!!!
    can you help me???
    Thanks in advanced. :smile:
     
  9. Jul 5, 2004 #8

    mathman

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    You need to first understand the concept of a random variable. It is a variable which has a value determined on the basis of a probability distribution. A random number is a random variable with a probability distribution uniform between 0 and 1.
     
  10. Jul 7, 2004 #9
    dear mathman;
    can you explain more or give me a reference to study???
    thanks in advanced.
    :smile:
     
  11. Jul 7, 2004 #10

    mathman

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    I am sorry to say that I haven't looked at any recent material on the subject. Feller's 2 volume "An Introduction to Probability ..." is a very good, but old, text. You can try probability theory with google.
     
  12. Jul 9, 2004 #11

    Gokul43201

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  13. Jul 9, 2004 #12

    mathman

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    The wolfram reference is a good description for those using random numbers. However, you need to look at a good basic probability textbook to understand the mathematical foundations behind the concept of random variable.
     
  14. Jul 11, 2004 #13
    Thanks alot for the informations
     
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