# 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

```