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I can't seem to solve this question, I found similar questions, but I wouldn't consider them exactly the same. Struggle to understand what the asterix means in this situation?

Hanul Jeon
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Soda Party
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    To be clear, the set of finite length bit-strings is indeed countable. If you allow infinite-length bit strings then the set is no longer countable. "Struggle to understand what the asterisk means in this situation" That is the Kleene Star, and means we are looking at the set of finite length strings creatable using elements of the set in question. So, ${0,1}^* = {\varepsilon,0,1,00,01,10,11,000,001,010,011,100,101,110,111,0000,\dots}$ – JMoravitz Mar 05 '21 at 14:16
  • As for proving it is countable, my starting to write out the set fully above should be a very clear hint as to how to proceed. – JMoravitz Mar 05 '21 at 14:16

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