  This text provides very easy and short proofs of some basic properties of
complex power series (addition, subtraction, multiplication, division,
rearrangement, composition, differentiation, uniqueness, Taylor's series,
Principle of Identity, Principle of Isolated Zeros, and Binomial Series). This
is done by simplifying the usual presentation of unordered sums of a
(countable) family of complex numbers. All the proofs avoid formal power
series, double series, iterated series, partial series, asymptotic arguments,
complex integration theory, and uniform continuity. The use of function
continuity as well as epsilons and deltas is kept to a minimum.
