Basic methods and concepts are introduced. They may be new to some students and are required in later sections.
Sums are conveniently written with the aid of the symbol S:
Naturally, the summation index i could be any other letter m, k, ···, so that you can also write
The rule for the product of two sums becomes now
Since the sequence of terms in a sum is arbitrary, you can interchange the sequence of the summations and also employ double summation:
This expression, rewritten in the form
becomes
and
At times, the summation index is not a number, but an element of some given set, for example, the set K of the names of your friends. If k is anyone of these friends - k e K, where e indicates that k is in the set K * - , then a(k) can be the number of persons in your friend k's family and the total number of persons related to your friends is
* In order to express that k is an element of the aggregate M, you write k e M.
The sum symbol is matched by the product symbol P, so that you write
