We were talking about somewhat different things, you meant doing it mathematically, sure, no problem, pick an infinite random sequence, I understood the question to mean how to do it in practice.
Actually I had something even stronger in mind, being able to pass the generated number around. For pi I can have a program that I can pass around and that will give everyone access to all the digits of pi, in base 16 we can even have random access to all the digits.
For generating a random Cauchy sequence things are not that easy. Locally I can just use a true random number generator - in case such a thing exists - and generate all the digits I am interested in on demand, storing them in case I have to look at a previously generated digit again. But I can not easily pass that number around, only the digits I have already generated. We would need a shared database where everyone can share all the generated digits.
Or I could try to replace the true random number generator with a pseudo random number generator, then I could just pass the seed around. Everyone would have to either agree how the sequence of random numbers is mapped to the sequence of digits or we would have to use a seekable random number generator. But this raises the question whether using a [specific] pseudo random number generator would still yield a normal number.
Actually I had something even stronger in mind, being able to pass the generated number around. For pi I can have a program that I can pass around and that will give everyone access to all the digits of pi, in base 16 we can even have random access to all the digits.
For generating a random Cauchy sequence things are not that easy. Locally I can just use a true random number generator - in case such a thing exists - and generate all the digits I am interested in on demand, storing them in case I have to look at a previously generated digit again. But I can not easily pass that number around, only the digits I have already generated. We would need a shared database where everyone can share all the generated digits.
Or I could try to replace the true random number generator with a pseudo random number generator, then I could just pass the seed around. Everyone would have to either agree how the sequence of random numbers is mapped to the sequence of digits or we would have to use a seekable random number generator. But this raises the question whether using a [specific] pseudo random number generator would still yield a normal number.