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...'' is a formal system <math>\mathcal{L} = \mathcal{L}\ (\Alpha,\ \Omega,\ \Zeta,\ \Iota)</math>, whose formulas are constructed in the following manner: * The ''zeta set'' <math>\Zeta\!</math> is a finite set of ''transformation rules'' that are called ''infe

...e can index (count) them. A class is closed and unbounded if its indexing function is continuous and never stops. One can define addition, multiplication, an ...''α''. One proves by transfinite induction that there is one and only one function satisfying the recursion formula up to and including α.

...the defined operator <math>\operatorname{T}</math> has to be, in order to function properly in the standard context, in this case, <math>^{\backprime\backprim | '''AND''' we know that the function <math>f\!</math> is of the type <math>X \to Y</math>

...ts have been made to use the concepts of [[Turing machine]] or [[recursive function]] to fill this gap, leading to the claim that only questions regarding the ...mes. The first was Euclid's, the second was based on the [[Euler]] [[zeta function]], and the third was Chaitin's own, derived from [[algorithmic information

...ts have been made to use the concepts of [[Turing machine]] or [[recursive function]] to fill this gap, leading to the claim that only questions regarding the ...ts have been made to use the concepts of [[Turing machine]] or [[recursive function]] to fill this gap, leading to the claim that only questions regarding the