Definition:Polynomial Addition/Sequence

Definition
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:
 * $f + g := \tuple {a_0 + b_0, a_1 + b_1, a_2 + b_2, \ldots}$