Decimals to fraction strings

[Cameron Laird]

In article <slrn8i882a.39n.jraven at corvus.local>,
Jeff Raven <jraven at psu.edu> wrote:
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>Dirichlet proved that given any number alpha and integer N, there
>is always a 'good' approximation p/q such that q < N. This fraction
>can be calculated directly using a rather clever argument, but
>the method of continued fractions ought to give you the same thing.
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Let me be sure I understand your quantifiers.  "Dirichlet
proved that ... there is always at least one 'good' ...",
correct?

Here's where I'm ignorant:  how is Dirichlet's construction
more of a "direct calculation" than a standard continued-
fraction computation?
-- 

Cameron Laird <claird at NeoSoft.com>
Business:  http://www.Phaseit.net
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