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→{{anchor|nullable symbol}}Formal theory: Added vacuous truth (see also talk page) |
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* 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<sup>R</sup> = ε. Reversal of the empty string produces the empty string.
* <math>\forall c \in s: P(c)</math>. Statements that are about all characters in a string are [[vacuous truth|vacuously true]].
* The empty string precedes any other string under [[lexicographical order]], because it is the shortest of all strings.<ref>[http://cs.fit.edu/~ryan/cse1002/lectures/lexicographic.pdf CSE1002 Lecture Notes – Lexicographic]</ref>
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