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Topic: Infinite Function?
Replies: 2   Last Post: Oct 12, 1998 1:15 PM

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Lou Talman

Posts: 876
Registered: 12/3/04
Re: Infinite Function?
Posted: Oct 12, 1998 12:20 PM
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Don Kahn wrote:

> Since pi over two is not rational or even algrebraic, the integers,
> when reduced mod pi over two are an infinite subset of the interval
> from 0 to pi over two. it follows that there are integers which when
> reduced modulo pi over two, are arbitrarily near pi over two. hence,
> there are integers for which tan is arbitrarly large. i hope this
> helps.


I'm afraid that argument doesn't work. It is certainly correct to argue
that the set of integers, reduced modulo Pi/2, yields an infinite subset
of the interval (0, Pi/2). But from this one can conclude only that the
resulting subset of (0, Pi/2) has an accumulation point *somewhere* in
[0, Pi/2]--and there is no a priori guarantee that this limit point must
be Pi/2.

--Lou Talman





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