Hello everybody, i recently fell across the highly interesting matters of goedels incompletness theorem. Since i dont really have any algebraic or mathematical background, i need to ask for help: how can i put goedels theorem into a short formula? The purpose may sound confusing, but i need it for a t-shirt motive i want to create. I found this example by Rucker suitable for my level of undersanding to follow matters: << The proof of Goedel's Incompleteness Theorem is so simple, and so sneaky, that it is almost embarassing to relate. His basic procedure is as follows: 1. Someone introduces Goedel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all. 2. Goedel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine. 3. Smiling a little, Goedel writes out the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Goedel. Note that G is equivalent to: "UTM will never say G is true." 4. Now Goedel laughs his high laugh and asks UTM whether G is true or not. 5. If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements. 6. We have established that UTM will never say G is true. So "UTM will never say G is true" is in fact a true statement. So G is true (since G = "UTM will never say G is true"). 7. "I know a truth that UTM can never utter," Goedel says. "I know that G is true. UTM is not truly universal." >> How can i put this into a short, striking formula? Does it sum up to something like (s for statment): s: s is false. Assuming this is summing it up, is there a way, for sole purposes of mystification, to replace ":" and "is false" with aequivalent mathemathical symbols? I know how to replace "is" with "=", but what aequivalent mathemathical symbold do i need to apply for ":" and "false"? Regards, FEOV ------------------------- Sorry for bad english -- "If you think that big government interferes in your life too much NOW, just wait till the government starts regulating the genetic constitution of your children" Theodore Kaczynski', "Industrial Society And Its Future"