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Polynomials

A polynomial over the reals is an infinite sequence of real numbers, the coefficients, of which only finitely many are different from 0:

p is polynomial : <=> p: N -> R /\  (exists k in N: forall i >= k: p_i = 0).

The degree of a polynomial is zero, if all coefficients are zero; otherwise, it is the index of the largest non-zero coeffient:

deg(p) :=

if forall i in N: pi = 0

then 0

else (such k in N: pk != 0 /\  (forall i > k: pi = 0)).