\begin{definition}[Definition:Addition of Polynomials/Sequence]
Let:
:$f = \sequence {a_k} = \tuple {a_0, a_1, a_2, \ldots}$
and:
:$g = \sequence {b_k} = \tuple {b_0, b_1, b_2, \ldots}$
be polynomials over a field $F$.
Then the operation of '''(polynomial) addition''' is defined as:
:$f + g := \tuple {a_0 + b_0, a_1 + b_1, a_2 + b_2, \ldots}$
\end{definition}