Bruno Marchal wrote: >Proceeding that way you will run into trouble. But it is very easy to >find the k. >Let us be specific and let us imagine you have already written in >Fortran a generator of all programs of the one-variable partial >computable functions: F1 F2 F3 F4 F5 F6 F7 ... >The list of programs is P1 P2 P3 P4 P5 P6 ... Each Pi(n) computes Fi(n) > >Now program G in "Fortran". It is something like that: > >Begin G >Read X >Call the generator of program up to X, giving PX >Apply PX on X, and put the result in register 439 >Add 1 to the content of register 439 >Output the content of register 439 >End > >Now, look at your list of programs Pi until you find it, and look at >his number code (where n is the number code of Pn by definition). >Finding your program in your list of programs should be easy given that >the list P1 P2 P3 ... is ordered lexicographicaly (by length, and by >alphabetical order for those of same length). So you can find it >easily. Is number code is the number k. If you run G on k, your fortran >interpreter will run for ever (and your fortran compiler will generate >a code which run for ever). Speaking just a little bit loosely. > > > Let's be more specific. Begin G Read X Call generator of program which produces P1, P2, P3..in sequence. Select Program PX. Compute the value PX(X). Save the value into register 439 Add 1 to content of register 439. Call this value Y
Now look at the list of all programs P1(1), P2(2).... The scanning program could be: i = 1 (initiate counter i to 1) Start Loop If Pi(i) = Y then k=i; Exit Else i=i+1 End if End Loop My point is that the loop will never end and you will never find k. If you did find k then Pk(k) = P(k)+1 which is impossible. However, I don't see any problem in using P(x) for computing G(x) for any x --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
