Random double

[Andrea Fontana]

On Wednesday, 24 April 2013 at 10:33:49 UTC, Ivan Kazmenko wrote:
> On Wednesday, 24 April 2013 at 10:26:19 UTC, Andrea Fontana 
> wrote:
>>> I'd like to mention that there's no such mathematical object 
>>> as "uniform distribution on [0..+infinity)".
>>
>> ... you neither can choose a random real number in any 
>> interval ...
>
> ... but that is at least valid mathematically, albeit 
> achievable only approximately on a computer.  On the other 
> hand, an infinite case, even if it would be possible, won't be 
> practical anyway since with probability 1, the result would 
> require more bits to store than available on any modern 
> hardware.

I mean that a random real number is not valid mathematically too. 
In any given real interval there are infinite numbers, how you 
can choose a number in an infinite (and non-numerable!) interval? 
I think you always need some sampling.

What's the probability to guess a precise number in [0..1]? I 
think is 0 as long as you have infinite numbers.

What's the probability to guess a interval in [0..1]? I think 
it's the interval size.

Am I wrong?