unfortunately, JJ is winning this arguement, despite his garblings of a few concepts. Your equation for z is a non-linear transformation. Disregard y for now, simply look at the range [0,infinity).

By definition, within a given set, if all elements have an equal probability of being picked, then any “pick” will be random. z is such a function, shoosing fromt eh set of all numbers between 0 and 1.

Look at z=(1/x)-1 (ignoring y for now, it doesn’t change anything except for the sign). If 1>x>.1, then 9>z>0. in other words, 90% of the time, z is between 0 and 9. a number in the range (9,infinity) has only a 10% chance. Thus, all numbers do not have the same chance of being picked, and z is not a true random function.

I’ll post the complete derivation soon, using calculus, if you’re curious. suffice to say, you can only transform the random function linearly to preserve it’s randomness.

here is a linear transformation of x:

z=x*a, where a is any constant, will yield a range of random numbers from 0 to a.

lim (a–>infinity) of x*a = random number from the set [0,a] as a–> infinity.

In that sense JJ is right, the set must be bounded to choose a random number from it. the set can have an infinite number of elements within those boundaries. This is implicit in the random function x.

A better question would be, how can you make X in the first place?

simple…you can’t…not perfectly,anyway