on 6/25/01 9:10 AM, george murphy at gmurphy@raex.com wrote:
> Tim Ikeda wrote:
>
>> ...............................................
>>
>> I purposefully skipped the series proofs because I have an irrational fear
>> that prevents me from even considering infinite series (Well, that and a
>> problem I have getting the signs of the odd and even terms correct).
>
> ................................................
> This is unfortunate because it probably keeps you from accepting a
> brilliant proof of the doctrine of _creatio ex nihilo_:
>
> 1 - 1 + 1 - 1 + ....
> = (1-1) + (1-1) + ....
> = 0 + 0 + 0 ....
> = 0
> 1 - 1 + 1 - 1 + ....
> = 1 - (1-1) - (1-1) - ....
> = 1 - 0 - 0 ....
> = 1
> Therefore 0 = 1.
>
> Shalom, George
This "proof" does not appear so brilliant to me.
In the above proof one has to assume that inserting ( ) and adjusting signs
does not alter the equivalence of the initial infinite series and that an
equivalence between infinite series is the same as equal for finite numbers.
Inserting the ( ) maintains a one to one correspondence needed for
equivalence. However, you are interpreting 0 = 1 as equals. Isn't this
misleading? It should not be interpreted as an equality.
Something out of nothing with finite numbers is often shown from 1 - 1 = 0
Here we "create" two somethings out of nothing.
To me _creatio ex nihilo_ is only a convenient assumption for a story.
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