DavidW
Posts:
274
Registered:
5/29/09
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Re: Rotwang's proof that the infinite sum for e converges
Posted:
May 8, 2012 6:54 PM
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Rotwang wrote:
> On 08/05/2012 05:45, DavidW wrote:
>> The entire proof, which was posted by Rotwang in the "Warning to
>> visitors to sci.math" thread at UTC 16 Mar 2012 02:38:08, is below.
>>
>> I have some questions about the proof. First, I want to make sure I
>> understand the Usenet notation that Rotwang is using. The first
>> lemma includes: "Let P be the maximum of |a_0|, |a_1|, ...> a_{n +
>> 1}|" This looks like it means that the maximum of the absolute values of
>> the terms 0 to n of a Cauchy sequence is greater than the absolute
>> value of term n+1. Is this true? Also, there's only one '|'
>> character on a_{n + 1}, on the right. Should there be a matching
>> one?
>
> I think what may have happened is that your newsreader saw a line that
> started with '|', assumed it was supposed to indicate a quote, and
> replaced it with '>'.
Yes, that's what's happened. I never would have guessed it, since it replaced
one mathematical symbol with another and produced an almost syntactically
correct result. No wonder I couldn't make any sense of it.
In the lemma you are using an arbitrary epsilon of 1. I'm wondering why that is
when the reasoning should work for any value, so it could just be left as
epsilon as it is in other sequence-related proofs. I notice that Spivak also
uses 1 on p. 379 of "Calculus".
> What I actually wrote can be seen here:
>
> http://mathforum.org/kb/plaintext.jspa?messageID=7745502
>
> I intended that P should be the maximum of {|a_i| | 0 <= i <= n + 1}.
>
>
>> And, is it important that the first term is
>> denoted as a_0? It seems to be the convention that enumerations of
>> sequence terms start at 1.
>
> It's not important, no - some authors start enumerations of sequences
> with 0, others with 1. It makes no difference to anything that follows
> which convention one uses.
Okay, and I read the other post.
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