I was thinking about the Halting Problem and I started thinking that if a "undefined" state is necessary for binary mathematics then doesn't that suggest that logic should be trinary? I am not saying that we should not use binary mathematics but it does seem to suggest that the trinary system should be theoretically foundational. Then I started thinking about the Gödel Theorem and then I started thinking about Cantor's Diagonal Argument. I'm a crazy man - I am moved by the Cantor tragedy - but I just do not accept the diagonal argument as sound (no mean pun intended.) So then I started feeling that I should redefine the rational number so that it naturally (pun intended) includes rational and non-rational numbers. I felt that I should give it a special name - like rational process number - to avoid confusion. OK, how do I go about this? The definition of the Rational Process Number has to include rational numbers and non-rational numbers as subsets. The definition has to have some utility. But, it also has to fit my argument that the non-rational numbers do correspond to a rational process of some sort that can lead to a direct computational method. So the rational process definition can't be rocking and rolling without being grounded. But the real question is: Would this have anything to do with AI and AGI? I think it must. I mean, if it can be defined then it probably will have some effect on AI and AGI. But I don't know for sure. Jim Bromer
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