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From: ech@spuxll.UUCP (Ned Horvath)
Newsgroups: net.math
Subject: Re: Beyond Exponentiation
Message-ID: <616@spuxll.UUCP>
Date: Wed, 30-Jan-85 18:36:44 EST
Article-I.D.: spuxll.616
Posted: Wed Jan 30 18:36:44 1985
Date-Received: Thu, 31-Jan-85 07:24:39 EST
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I suggest you look at Ackermann's classic function, at least over the 
naturals.  The first few "rows" of that function correspond roughly to
"take the successor", "add", "multiply", "exponentiate", etc.  The recursion
is (for n,m >= 0)

	A(0, n) = n+1
	A(n+1, 0) = A (n, 1)
	A(n+1, m+1) = A (n, A (n+1,m))

How to generalize this to the reals is not obvious...

=Ned=