From Aristotle, "summation theory" is a political system wherein "it is possible that the many, no one of whom taken singly is a good man, may yet taken all together be better than the few, not individually but collectively, in the same way that a feast to which all contribute is better than one given at one man's expense" (Aristotle, Politics, tr. T.A. Sinclair, Penguin Books). Basically, the sum of the whole is greater than the sum of the few. Aristotle used this "theory" to explain how democratic governments work, but even he states that, in order to achieve the best results, there has to be a guiding hand within the system; otherwise, the out-of-control passions of the masses will bring about the destruction of the system leading to anarchy.
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It's not. It depends on the method you use for summation whether summation > integral or integral > summation.
Sum or summation
A summation is a recap of all the highlights of a presentation.
Summation is the process of adding things together or a sum total of things added together. The term summation has a special meaning related to extrapolation of context.
Gauss Summation: b(b+1)/2 adds all the integers from 1 & b.