FOM: Re: Midwest Model Theory Meeting
Charles Silver
silver_1 at mindspring.com
Mon Nov 8 18:14:51 EST 1999
C. Silver:
>>Why not just use that old technique supposedly intuited by Little Gauss
>>(when he was eight?), which can be used to solve all problems of this
>>general type? In particular:
>>
>> 1 + 2 + 3 + ... +(n-2) +(n-1) +n
>> + n +(n-1) + (n-2) + ... + 3 + 2 +1
>>-----------------------------------------------------------------
>> (n+1)+ (n+1)+(n+1)+...+(n+1)+(n+1)+(n+1)
>>
>> Since the sum above, n(n+1), represents twice the number we're looking
>>for, the result is half that, or n(n+1)/2.
Vaughan Pratt:
>The inventor of Boolean logic also invented the finite difference calculus
>("A Treatise on the Calculus of Finite Differences", first edition 1860,
>second edition substantially reworked by John Moulton 1872), whose toolkit
>provides induction-free methods for a much larger class of such problems,
>including summing n^i for fixed integer i and much more.
Can these methods be formalized?
Charlie Silver
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