how to make a bijection map of a set of sequences

i dont know to approach this problem , how can i make bijection map for such a setConsider the set S of all sequences of natural numbers, such that each sequencein S has values 0 from some point onwardsS = {(n0, n1, n2, . . . nk, . . .) | ∀i∈N ni ∈ N, ∃k0∈N ∀i≥k0 ni = 0}

Is S infinite and uncountable? Prove your answer.