ε ⋅ s = s ⋅ ε = s. The empty string is the identity element of the concatenation operation. The set of all strings forms a free monoid with respect to ⋅ and ε. ε R = ε. Reversal of the empty string produces the empty string. The empty string precedes any other string under lexicographical order, because it is the shortest of all strings.
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