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Unique string of length zero

In formal linguistic communication theory, the empty string, or empty give-and-take, is the unique string of length zero.

Formal theory [edit]

Formally, a string is a finite, ordered sequence of characters such every bit messages, digits or spaces. The empty string is the special case where the sequence has length null, so at that place are no symbols in the string. There is only 1 empty string, considering two strings are only different if they take different lengths or a unlike sequence of symbols. In formal treatments,^[i] the empty string is denoted with ε or sometimes Λ or λ.

The empty string should non be confused with the empty language ∅, which is a formal language (i.e. a ready of strings) that contains no strings, non even the empty string.

The empty cord has several properties:

|ε| = 0. Its cord length is zero.
ε ⋅ s = s ⋅ ε = s. The empty cord is the identity element of the chain functioning. The set of all strings forms a costless monoid with respect to ⋅ and ε.
ε^R = ε. Reversal of the empty cord produces the empty cord.
The empty string precedes any other string under lexicographical gild, because it is the shortest of all strings.^[2]

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".

Employ in programming languages [edit]

In near programming languages, strings are a data type. Strings are typically stored at distinct retentivity addresses (locations). Thus, the same cord (for case, the empty string) may exist stored in two or more than places in retention.

In this way, there could be multiple empty strings in memory, in contrast with the formal theory definition, for which there is only one possible empty cord. All the same, a cord comparing office would indicate that all of these empty strings are equal to each other.

Fifty-fifty a string of length zippo tin require retentiveness to store it, depending on the format being used. In nigh programming languages, the empty string is distinct from a null reference (or aught pointer) considering a naught reference points to no string at all, not even the empty cord. The empty cord is a legitimate string, upon which most string operations should work. Some languages treat some or all of the following in similar ways: empty strings, nix references, the integer 0, the floating point number 0, the Boolean value false, the ASCII character NUL, or other such values.

The empty string is commonly represented similarly to other strings. In implementations with cord terminating character (null-terminated strings or apparently text lines), the empty cord is indicated by the immediate employ of this terminating character.

λ representation	Programming languages
`""`	C, C#, C++, Go, Haskell, Java, JavaScript, Julia, Lua, M, Objective-C (as a C string), OCaml, Perl, PHP, Python, Reddish, Scala, Standard ML, Swift, Tcl, Visual Bones .NET
`''`	APL, Delphi, JavaScript, Lua, MATLAB, Pascal, Perl, PHP, Python, R, Carmine, Smalltalk, SQL
`character(0)`	R^[3]
`{'\0'}`	C, C++, Objective-C (every bit a C string)
`std::string()`	C++
`""southward`	C++ (since the 2014 standard)
`@""`	Objective-C (every bit a abiding `NSString` object)
`[NSString string]`	Objective-C (as a new `NSString` object)
`q(), qq()`	Perl
`str()`	Python
`%{}` `%()`	Ruby
`string.Empty`	C#, Visual Basic .Internet
`String.make 0 '-'`	OCaml
`{}`	Tcl
`[[]]`	Lua

Examples of empty strings [edit]

This section needs expansion. Y'all can help by adding to it. (March 2010)

The empty string is a syntactically valid representation of zero in positional notation (in any base), which does not contain leading zeros. Since the empty string does non have a standard visual representation outside of formal linguistic communication theory, the number zero is traditionally represented by a single decimal digit 0 instead.

Zero-filled retention area, interpreted as a naught-terminated string, is an empty string.

Empty lines of text show the empty cord. This can occur from two consecutive EOLs, as often occur in text files, and this is sometimes used in text processing to separate paragraphs, due east.thou. in MediaWiki.

See likewise [edit]

Empty gear up
Aught-terminated string
Concatenation theory

References [edit]

^ Corcoran, John; Frank, William; Maloney, Michael (1974). "Cord theory". Journal of Symbolic Logic. 39 (4): 625–637. doi:10.2307/2272846. JSTOR 2272846.
^ CSE1002 Lecture Notes – Lexicographic
^ There are two ways to create "empty strings" in R; the other is listed here as "". character(0) creates empty grapheme vectors, which volition output 0 when counted.