Suppose $Σ=\{0,1\}$; then $Σ^*$ is the set of all strings over $Σ$.
Is $Σ^*$ over $Σ$ finte?
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Sign up to join this communitySuppose $Σ=\{0,1\}$; then $Σ^*$ is the set of all strings over $Σ$.
Is $Σ^*$ over $Σ$ finte?
The star operator is a unary operator known as Kleene star (or Kleene closure) and the result of its application on $\Sigma$ (an arbitrary set of strings) is another set that contains all possible finite strings constructed using only strings from $\Sigma$.
Assuming that the set contains at least one non-empty string, the cardinality of the set produced by the Kleene star operator is infinite since we can always generate a new unique string by appending one of the non-empty strings.