From: rclark9189@aol.com (RClark9189)
Newsgroups: sci.math
Subject: Re: highest increasing function?
Date: 14 Jan 1998 16:48:51 GMT

Ackermann Function.

Consider the following function:

F: N x N ---> N   (N = Natural Numbers 1,2,3,...)

Defined recusively as follows:

F(1,b) = 2b;
F(a+1,1)=2;
F(a+1,b+1)=F(a,F(a+1,b));

The Ackermann Function G(x) = F(x,x);

R
==============================================================================

From: brennan4481@my-dejanews.com
Newsgroups: sci.math
Subject: Help with Ackermann function
Date: Sat, 26 Sep 1998 21:33:24 GMT

 I have a function defined as:

 A(n,x,y) = {
                      x+1     if n=0
                        x       if n=1 and y=0
                        0       if n=2 and y=0
                        1       if n=3 and y=0
                        2       if n>=4 and y=0
                     A(n-1, A(n,x,y-1), x)  if n and y do not equal 0
                   }

This is supposed to be Ackermann's function, but it varies somewhat from other
references I've seen.

It's clear that:

   if n=0, we get x+1
   if n=1, we get x+y
   if n=2, we get x*y
   if n=3, we get x^y
   if n=4, we get 2^(x^y)

  Beyond that, I'm not sure.  And of course, the numbers are too large to
calculate and examine.  Now, I can see that x+y is
the same as adding 1 to x "y" times, and x*y could be adding x "y" times or
adding y "x" times, but I can quite chain the logic
together throughout.  Of course, I'm supposed to be finding the non-recursive
general solution.

 Any help would be greatly appreciated.
 brennan@lcc.net


-----== Posted via Deja News, The Leader in Internet Discussion ==-----
http://www.dejanews.com/rg_mkgrp.xp   Create Your Own Free Member Forum