Re: Smullyan Shmullyan, give me a real example

2006-05-22 Thread George Levy
One can create faster and faster rising functions and larger and larger number until one is blue in the face. The point is that no matter how large a finite number n one defines, I can stand on the shoulder of giants and do better by citing n+1 using simple addition. Now if somehow one came u

Re: Smullyan Shmullyan, give me a real example

2006-05-22 Thread Russell Standish
On Thu, May 18, 2006 at 11:38:24AM +0200, Bruno Marchal wrote: > > > > Also the universal dovetailer idea is also one of those that is fairly > > obvious, and might have been discovered a number of times > > independently. > > > I'm not sure it is so easy, and in the present case I have never h

Re: Smullyan Shmullyan, give me a real example

2006-05-22 Thread Tom Caylor
Bruno Marchal wrote: > ... > I give, for all, one last exercise before introducing diagonalization: > define recursively in an explicit way the operation [i+1] from the > preceding operation [i]. If you know a "computer language" (Fortran, > Lisp, Prolog, c++, Java, whatever ...) write the program

Re: Smullyan Shmullyan, give me a real example

2006-05-22 Thread Bruno Marchal
Hi Tom, Apparently you have (re)discover Ackermann function which indeed provide formally a sequence of more and more growing functions, similar to the sequence I was pointing too. I will present it in a easier way for the benefit of the others, but also for using a presentation which will fa