Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!mnetor!uunet!husc6!think!ames!amdcad!decwrl!reid
From: reid@decwrl.dec.com (Brian Reid)
Newsgroups: comp.misc
Subject: Re: The Ackermann function
Message-ID: <171@bacchus.DEC.COM>
Date: Sat, 5-Dec-87 16:56:46 EST
Article-I.D.: bacchus.171
Posted: Sat Dec  5 16:56:46 1987
Date-Received: Thu, 10-Dec-87 20:40:35 EST
References: <2093@umd5.umd.edu> <123BRENT@MAINE>
Reply-To: reid@decwrl.UUCP (Brian Reid)
Organization: DEC Western Research
Lines: 27

The easiest way to *understand* Ackermann's function (rather than defining it
or characterizing it) is as follows.

0: If you take the number "N" and add 1 to it "K" times,
   you do an operation called "addition" of N plus K.

1: If you take the number "N" and add it to itself "K" times,
   you do an operation called "multiplication" of N times K.

2: If you take the number "N" and multiply it by itself "K" times,
   you do an operation called "exponentiation" of N to the power K.

3: If you take the number "N" and raise it to its own power "K" times,
   you get some operation whose name I can't remember. Let's call
   it "hyperexponentiation" of N to the power K.

4: and so forth.

If you define "operator number" to be 0 for addition, 1 for multiplication, 2
for exponentiation, 3 for ?hyperexponentiation, and so forth, then you
can imagine that the higher-order operators are pretty fierce. 

Ackermann's function A(N, J) means to perform operation number J on the
number N, N times. 

Other respondents have explained admirably why Ackermann's function is
interesting. It is not at all useful.