### Chaitin's Assertions are not Well-Founded

At each point we have considered only a finite number of strings. Then it is always possible to add many times that many to tilt the probability back and forth. Note "halts for the first few inputs, loops on the next inputs for a lot more inputs".

What is the probability that the program that I describe will halt? There is none. "Probability of Halting" is as ill-defined as almost everything Chaitin says. His first version of omega was >1 (depending on how the Turing Machine is encoded!) which took him 20 years to realize and add a kludge rule about programs being inside of other programs. Now how does he know what THAT will produce?

His Invariance Theorem (that is said to be the foundation of his theory) is false. There is no bound between the lengths of the shortest program to perform a given function in two different programming languages (to justify using "length of the shortest program") because one language could require each character to be repeated 2 or more times due to its use over unreliable communications lines, and so the length can differ by any factor or absolute difference. "Length of the shortest program" is simple-minded nonsense - just like his "This is unprovable." use, the extent of his understanding of Godel - which is only the weaker Godel theorem based on Soundness and still weaker than Rosser's based on consistency - which is the maximum possible because in an inconsistent system every sentence is provable so there is no sentence that is undecidable.