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Empty string

In formal language theory, the empty string, or empty word, is the unique string of length zero.

The term  ""  redirects here. For the printed character, see Quotation mark.

|ε| = 0. Its is zero.

string length

ε ⋅ s = s ⋅ ε = s. The empty string is the of the concatenation operation. The set of all strings forms a free monoid with respect to ⋅ and ε.

identity element

εR = ε. Reversal of the empty string produces the empty string, so the empty string is a .

palindrome

. Statements that are about all characters in a string are .

vacuously true

The empty string precedes any other string under , because it is the shortest of all strings.[2]

lexicographical order

Formally, a string is a finite, ordered sequence of characters such as letters, digits or spaces. The empty string is the special case where the sequence has length zero, so there are no symbols in the string. There is only one empty string, because two strings are only different if they have different lengths or a different sequence of symbols. In formal treatments,[1] the empty string is denoted with ε or sometimes Λ or λ.


The empty string should not be confused with the empty language ∅, which is a formal language (i.e. a set of strings) that contains no strings, not even the empty string.


The empty string has several properties:


In context-free grammars, a production rule that allows a symbol to produce the empty string is known as an ε-production, and the symbol is said to be "nullable".

Empty set

Null-terminated string

Concatenation theory

String literal