Definition:Polynomial Addition/Sequence

Definition
Let:
 * $f = \left \langle {a_k}\right \rangle = \left({a_0, a_1, a_2, \ldots}\right)$

and:
 * $g = \left \langle {b_k}\right \rangle = \left({b_0, b_1, b_2, \ldots}\right)$

be polynomials over a field $F$.

Then the operation of (polynomial) addition is defined as:
 * $f + g := \left({a_0 + b_0, a_1 + b_1, a_2 + b_2, \ldots}\right)$