Mathematics – Number Theory
Scientific paper
2003-02-17
Mathematics
Number Theory
10 pages. To be presented at DMTCS'03
Scientific paper
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 by fluctuating between finite and infinite values, in our method this quantity is always finite and the bits of Omega are expressed in its fluctuations between odd and even values, allowing for some interesting developments. We then use exponential Diophantine equations to simplify this result and finally show how both methods can also be used to create polynomials which express the bits of Omega in the number of positive values they assume.
Kieu Tien D.
Ord Toby
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