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From: lambert@boring.UUCP
Newsgroups: net.math
Subject: Re: Beyond Exponentiation
Message-ID: <6302@boring.UUCP>
Date: Thu, 31-Jan-85 10:08:52 EST
Article-I.D.: boring.6302
Posted: Thu Jan 31 10:08:52 1985
Date-Received: Thu, 7-Feb-85 03:38:28 EST
References: <186@ihnet.UUCP> <6298@boring.UUCP>
Reply-To: lambert@boring.UUCP (Lambert Meertens)
Organization: CWI, Amsterdam
Lines: 18
Summary: 
Apparently-To: rnews@mcvax.LOCAL

> [...]
> Now consider the function  y = 2~x,  assuming y(0) = 1.
> The function increases amazingly, taking on the values:
> 	1	2	4	16	65536	2^65536	huge	wow
> [...]
> If this function is f(x), then  f(x) = 2^f(x-1).
> [...]
> what is  2~2.5?

It is funny that this comes up now, since there is an
obvious relationship with the discussion on the square root
of exp.  For if g is the square root of exponentiation with
base two, we can obviously take f(x+1/2) = g(f(x)).
-- 

     Lambert Meertens
     ...!{seismo,philabs,decvax}!lambert@mcvax.UUCP
     CWI (Centre for Mathematics and Computer Science), Amsterdam