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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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Ted Alper

Posts: 51
Registered: 12/6/04
Re: How's this? Proof (hopefully) that pi is irrational.
Posted: Jun 13, 1996 4:07 PM
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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 reply to another post...
>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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