Re: Existence of function

In article
<aderamey.addw-E6A981.11202115112007@xxxxxxxxxxxxxxxxxxxxxx>,
The World Wide Wade <aderamey.addw@xxxxxxxxxxx> wrote:

In article <1195130134.355299@athprx04>,
"I.N. Galidakis" <morpheus@xxxxxxxxxxxx> wrote:

This probably belongs to mathematical/philosophical existentialism, but
here
goes:

1) Person A claims that a certain real analytic function f having certain
properties exists.
2) Person B claims that f does not exist.
3) Person A then displays a sequence of series f_n(x)=sum(a_k*x^k,k=0..n),
(with
a_n calculated numerically) which appear to approximate the function f to
any
degree desired, but A cannot prove convergence of the f_n.

Has A proved the "existence" of f?

4) To make the case more interesting, assume that the convergence of the
series
f_n cannot be proved by algebraic means.

Does f exist?

Many thanks for any ideas,

Well suppose further A can prove convergence of the f_n. Suppose the
claim is that there exists a real analytic f on (-1,1) such that
f(1/k) = e^(-k), k = 2, 3, ... and A produces f_n's as above that
converge uniformly on (-1,1) to a function f such that f(1/k) = e^(-k)
for all k. Should B be convinced?

Never mind, I read the problem carelessly, not realizing the form of
the f_n's.
.

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