An infinite binary word a is a string (a1 a2 a3 ....), where each an ∈ {0, 1}. Fix a word s = (s1 s2 s3 ....), where sn = 0 if and only if n is even and s_n = 1 if and only if n is odd.

Let S = {a = (a1 a2 a3 ....) | ∃m ∈ \(\mathbb{N}\)N" id="MathJax-Element-2137-Frame" role="presentation" style="display: inline; position: relative;" tabindex="0">N�" id="MathJax-Element-84-Frame" role="presentation" style="position: relative;" tabindex="0">��" id="MathJax-Element-37-Frame" role="presentation" style="position: relative;" tabindex="0">��" id="MathJax-Element-705-Frame" role="presentation" style="position: relative;" tabindex="0">�$\mathbb{�}$ $\mathbb{�}$ $\mathbb{�}$ $\mathbb{�}$  such that an = sn, ∀n ≥ 1000}.

What is the cardinality of S? (Choose the most appropriate option.)