[time 970] Re: [time 968] Re: [time 964] LaTex version of my paper

Hitoshi Kitada (hitoshi@kitada.com)
Wed, 3 Nov 1999 22:46:33 +0900

Dear Bill,

I saw your new version a few days ago. On the section 2 A priori notions of
change that you changed in this version, I have a small question: I am not sure
about the meaning of f_n. In the first equation, f_n seems to be a constant. In
fact you differentiate exp(tf_n) and get

(d/dt)(exp(tf_n)) = f_n exp(tf_n). (1)

But if we understood f_n as in the second formula in the section, f_{n+1} seems
to mean

f_{n+1} = f_n exp(tf_n),

which depends on the variable t so that we can no more differentiate
exp(tf_{n+1}) as in (1): In this case we have to write

(d/dt)(exp(tf_{n+1})) = (df_{n+1}/dt) exp(tf_{n+1}).

Then inductive definition of f_n seems to break down.

Or in other words, my question is what the subscript n in f_n means and what
role it does play in your argument.

Best wishes,

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