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January 6th, 2017, 12:41 PM   #1
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Quick question

In reference to 2.34 Theorem is $V_q$ supposed to be $V_p$?
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January 6th, 2017, 01:05 PM   #2
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This proof is almost identical but a bit clearer.

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January 6th, 2017, 01:22 PM   #3
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Quote:
Originally Posted by ProofOfALifetime View Post

In reference to 2.34 Theorem is $V_q$ supposed to be $V_p$?
No.

There is no such thing as $V_p$.

The sets $V_q,W_q$ are defined for points $q \in K$.

The proof in your book is valid.

Last edited by quasi; January 6th, 2017 at 01:30 PM.
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January 6th, 2017, 01:26 PM   #4
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I've just never seen him refer to a neighborhood of $p$ using $V_q$

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January 6th, 2017, 01:28 PM   #5
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I realize that there is no such thing as $V_p$ but thanks for pointing that out anyways.

I was not questioning the validity of the proof, just the notation.

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January 6th, 2017, 01:37 PM   #6
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Quote:
Originally Posted by ProofOfALifetime View Post

I've just never seen him refer to a neighborhood of $p$ using $V_q$

Thanks .
But the author defines $V_q,W_q$ to be neigbhorhoods of $p,q$, respectively.

But they're not just any old neigborhoods. The radii are defined so as to force them to be disjoint.

For the proof in question, the point $p$ is fixed; the points $q$ vary (over the points of $K$).

The neighborhoods $V_q,W_q$ are defined based on the variable point $q \in K$.

Last edited by quasi; January 6th, 2017 at 01:49 PM.
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January 6th, 2017, 01:54 PM   #7
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Okay I get it. Thanks quasi. I get the whole radii thing. I get the proof I guess the notation confused me a little at first.
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