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
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" <Daddycaylor.domain.name.hidden>
To: "Everything List" <everything-list.domain.name.hidden>
Subject: Re: Smullyan Shmullyan, give me a real example
Date: Sun, 21 May 2006 19:49:11 -0700
Message-ID: <1148266151.070713.279490.domain.name.hidden>
In-Reply-To: <1148195305.041978.291700.domain.name.hidden>
References: <14762723.1143066850497.JavaMail.root.domain.name.hidden>
<200603241938.14450.quentin.anciaux.domain.name.hidden>
<1143229104.805923.181410.domain.name.hidden>
<200603242045.08484.quentin.anciaux.domain.name.hidden>
<1143229759.310865.304480.domain.name.hidden>
<44245849.3060503.domain.name.hidden>
<442485EE.6010907.domain.name.hidden>
<44f38451d0bd50dafb206875eb78cd17.domain.name.hidden>
<1147793509.349430.290120.domain.name.hidden>
<020c0db89efdf147a862b8c8e2bee821.domain.name.hidden>
<1148195305.041978.291700.domain.name.hidden>
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.domain.name.hidden
To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden
For more options, visit this group at
http://groups.google.com/group/everything-list
-~----------~----~----~----~------~----~------~--~---
Received on Sun May 21 2006 - 22:50:12 PDT