To be slightly more clear d(m,n) = f(1,m,f(2,m,f(3,m,f(4,m,...f(n,m,n)...)

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Note that the it's only the innermost function that has degree n. To simplify things, I suppose we could just consider f(n,m,n) by itself. This has the same property that as n approaches infinity, the degree of operation approaches infinity. This gives a larger growth (as n approaches infinity) than fixing the degree at any finite number. And then, instead of substituting n into the degree, we could substitute things like f(n,m,n) into the degree to get f(f(n,m,n),m,n). Tom X-Google-Language: ENGLISH,ASCII-7-bit Received: by 10.11.88.14 with SMTP id l14mr36988cwb; Sun, 21 May 2006 19:49:11 -0700 (PDT) X-Google-Token: xMTf1AwAAADf4R2x5ktCHDVWo87JexXS Received: from 207.200.116.67 by u72g2000cwu.googlegroups.com with HTTP; Mon, 22 May 2006 02:49:11 +0000 (UTC) From: "Tom Caylor" <[EMAIL PROTECTED]> To: "Everything List" <everything-list@googlegroups.com> Subject: Re: Smullyan Shmullyan, give me a real example Date: Sun, 21 May 2006 19:49:11 -0700 Message-ID: <[EMAIL PROTECTED]> In-Reply-To: <[EMAIL PROTECTED]> References: <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> User-Agent: G2/0.2 X-HTTP-UserAgent: Mozilla/4.0 (compatible; MSIE 6.0; AOL 9.0; Windows NT 5.1; Q312461; SV1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) X-HTTP-Via: HTTP/1.1 (Velocity/1.3.32 [uScMs f p eN:t cCMp s ]), HTTP/1.1 Turboweb [ntc-td054 8.4.0], HTTP/1.0 cache-ntc-ab03.proxy.aol.com[CFC87443] (Traffic-Server/6.1.0 [uScM]) Mime-Version: 1.0 Content-Type: text/plain To be slightly more clear d(m,n) = f(1,m,f(2,m,f(3,m,f(4,m,...f(n,m,n)...) Note that the it's only the innermost function that has degree n. To simplify things, I suppose we could just consider f(n,m,n) by itself. This has the same property that as n approaches infinity, the degree of operation approaches infinity. This gives a larger growth (as n approaches infinity) than fixing the degree at any finite number. And then, instead of substituting n into the degree, we could substitute things like f(n,m,n) into the degree to get f(f(n,m,n),m,n). Tom --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---