Pick a Truly Random Number



15 thoughts on “Pick a Truly Random Number

  1. Hello Sir
    Nice Article,i see
    Will you please help me understand the last 2 bad drawings.I am not able to understand terms like ‘distribution’,’suitable distribution’ etc….
    Thanks you

    1. Sure!

      “Distribution” refers to all the possibilities in a situation, and how likely each of them is.

      For example, when you roll a die, there are six possibilities (1, 2, 3, 4, 5, or 6) and each is equally likely.

      Or, if you were to pick a random person from America and ask what state they live in, there’d be 50 possibilities (Alabama, Alaska, etc.), but not all equally likely (for example, California would be much more likely than Vermont).

      1. Even distribution is to distribute evenly.

        In a classroom, I give each child 1 pencil. Therefore, I distribute them evenly.

        If I distribute one phone book per house along a street, I distribute them evenly in one way, but not in another. Each household in the street gets 1 phone book. However, some households are two storeys high and maybe, they should get one phone book per floor. Or, some households have more people than others and bigger families have to share the phonebook amongst more people than their neighbours with a smaller family.

        Confused? Me too! I should have used the pizza analogy!

        Great article. Thank you.

  2. What I like is, if they play an infinite number of times, this transcendental will always happen if Mr. Right picks randomly. Poor Mr. Left.

    1. Well if they play a countably infinite number of times, which I assume because it will be an infinite integer, then the transcendental number will NEVER come up, because it’s uncountably infinite

    2. I think (though I am no mathematician) that whether or not it’s even possible to pick a random real number within a certain range but with no other restrictions depends on whether you accept the axiom of choice. You certainly can’t generate one by generating a random number of digits, at least not in finite time.

  3. Okay, I know this was posted quite a while ago, but just in case, the assumptions made here are less reasonable that one could expect : computable does not equal definable.

    Indeed, the existence of real numbers that cannot be communicated in finite time is *not* provable within ZFC! Since the property of being uniquely definable by a first-order formula cannot be internalized, the obvious cardinal argument is wrong. Consequently, there are models of ZFC where all numbers are definable : https://arxiv.org/pdf/1105.4597.pdf

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