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math.NT2003
Representations of Omega in Number Theory: Finitude Versus Parity
Toby Ord, Tien D. Kieu
We present a new method for expressing Chaitin's random real, Omega, through Diophantine equations. Where Chaitin's method causes a particular quantity to express the bits of Omega…
math.NT2003
On the existence of a new family of Diophantine equations for
Toby Ord, Tien D. Kieu
We show how to determine the -th bit of Chaitin's algorithmically random real number by solving instances of the halting problem. From this we then reduce the problem of…