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.