##S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i ##(adsbygoogle = window.adsbygoogle || []).push({});

methinks yes because:

##S = \bigcup _{i=1}^{∞}\left\{{0,1}\right\}^i \equiv \left\{{0,1}\right\}^\mathbb{N}##

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# Is this set uncountable

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