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====Free monoid==== {{Main|Free monoid}} If ''A'' is a set, the [[free monoid]] over ''A'' (denoted ''A''<sup>*</sup>, also called [[Kleene star]] of ''A'') is a [[monoid]] containing all the finite sequences (or strings) of zero or more elements of ''A'', with the binary operation of concatenation. The [[free semigroup]] ''A''<sup>+</sup> is the subsemigroup of ''A''<sup>*</sup> containing all elements except the empty sequence.
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