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

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Subject: Re: Smullyan Shmullyan, give me a real example
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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


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