Basic notes on algebra
Given a finite set and a function , represents the sum of all the elements of applied to . Basically, if , then .
Summing up over intervals of integers is so common that there is an special notation for it. Something like can be re-expressed as . The general form is , assuming that .
The product quantifier has the same syntax as the summation quantifier, but of course we calculate the product of every function application. The product of all numbers in a set by the power of two is: .