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The empty string has several properties: |ε| = 0. Its string length is zero. 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, so the empty string is a palindrome.
A string is a prefix [1] of a string if there exists a string such that =. A proper prefix of a string is not equal to the string itself; [2] some sources [3] in addition restrict a proper prefix to be non-empty. A prefix can be seen as a special case of a substring.
This module is intended to provide access to basic string functions. Most of the functions provided here can be invoked with named parameters, unnamed parameters, or a mixture. If named parameters are used, Mediawiki will automatically remove any leading or trailing whitespace from the
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But {{{1|}}} will evaluate to the empty string (a false value) because the vertical bar or pipe character, "|", immediately following the parameter name specifies a default value (here an empty string because there is nothing between the pipe and the first closing curly brace) as a "fallback" value to be used if the parameter is undefined.
In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element.
[note 2] [4] String homomorphisms are monoid morphisms on the free monoid, preserving the empty string and the binary operation of string concatenation. Given a language , the set () is called the homomorphic image of . The inverse homomorphic image of a string is defined as
The empty string is alphanumeric, because a string being alphanumeric is defined as all characters in the string being letters or numbers. However, it is false to say that it's not alphanumeric, because then we're no longer saying "all" so "there does not exist", we're saying "not all" so " does exist", which is always false for the empty string.