infinite domain uniform random number

Hello,

I am wondering if I can generate a set of random numbers which are distributed uniformly in an (-\infty, \infty) domain.

Thank you :)

Answer 1

[Andrew Newell]

Not in practice. If you could, then with probability 1 they would be too large to represent.

Answer 2

[Walter Roberson]

No, a uniform distribution over an infinite domain would require that each point have a probability of 0. And you would not be able to represent any results outside of +/- 1.7E308 as that is about the largest number that can be represented in double precision.

Uniform distribution over [-realmax, realmax] is not possible either, as double precision floating point numbers are not able to represent all numbers in that range

The number of distinct double precision floating numbers is less than 10^20, and those are not evenly spaced.