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Topic: How's this? Proof (hopefully) that pi is irrational.
Replies: 5   Last Post: Sep 12, 2009 7:10 AM

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Re: How's this? Proof (hopefully) that pi is irrational.
Posted: Sep 12, 2009 7:10 AM

>
>
> In <tkidd.834615695@hubcap> tkidd@hubcap.clemson.edu
> (Travis Kidd) writes:
>

> >Yes. But nowhere is either the numerator *or* the
> denominator 0 until the
> >limit is reached. (I'll repeat what I just said in
> >I neglected to mention that k is positive.)
> Therefore (I hope...I agree this
> >is the weakness in the proof), since substituting k
> for x yields equivalent
> >functions, the limit of the quotient would be 1.
> >

>
> But this is definitely not true. You seem to want to
> think that
> if f and g are continuous functions,
> then
> lim f(x)/g(x) = f(k)/g(k)
> x->k
> but it isn't true unless f(x)/g(x) is itself
> continuous at k,
> i.e. unless g(k) not equal to 0.
>
> it's not clear what you mean when you say
> "substituing k for x yields equivalent functions" --
> once you substitute k for x, you no longer have
> functions, you have
> specific numbers.
>
> as someone else pointed out, choosing any k for which
> sin(k^2) = 0
> would work in your argument, whether or not k was an
> integer.
>
> Ted Alper
>
>
>
>

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