Apatriarca defined a function P that maps some subsets of the natural numbers to real numbers between 0 and 1. This function is not a probability, as it does not satisfy the third axiom described here. If you relax the axiom to require only finite sums to work, then it would be fine.

Alternatively, we could forget about natural numbers and work with infinite sequences of bits. Or, almost equivalently, we could imagine there is a "0." before the sequence of bits, and what we are doing is picking a random real number between 0 and 1 uniformly (technically we are assigning probabilities to subsets of [0,1] using the Lebesgue measure, for the sigma-algebra of measurable sets). Now "the first bit is set" means "x >= 0.5" and the "first two bits are set" means "x>=0.75". Computing those kinds of probabilities is easy, since the probability of an interval is its length.

Now, what was the question again?

The OP is quite unable to express him meaningly, But this tricks me too, I will elaborate further.

Someone picks any positive whole number (N={0,1,2.....}).

- what is the probability I pick the same one? (it cannot be 0 since it is possible to happen, but extremly unlikely to happen )

- if someone says the number is odd, how bigger is probability I will gess what number is picked?

We are speaking of a number from N set. (I do not know how those numbers are called in english exactly,I am talking of the set N={0,1,2,...})

Interisting question becouse of wheather disputing meaning of them, the question just makes sence.

The probability being a real number : f e R; f e (0,0,1.0) ; f>0.0 ;f<1.0;