Comment Re:prove that the program works (Score 1) 189
Both are also general case statements. There are many, many programs which can be proven to halt or to loop indefinitely quite easily. The trick is that you can't create a program which, when given ANY program as input determines whether it will halt. Your program may well work for billions of programs, but there is at least one program for which it must fail. (Actually, there are infinitely many programs for which it must fail, but they're sparse in the space of all possible programs...)