Why Do Plants Require Oxygen

Unique string of length zero

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

Formal theory [edit]

Formally, a cord 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 nil, so there are no symbols in the string. There is only one empty string, considering two strings are but different if they have different lengths or a unlike sequence of symbols. In formal treatments,^[one] the empty string is denoted with ε or sometimes Λ or λ.

The empty cord should not be dislocated with the empty language ∅, which is a formal language (i.e. a gear up of strings) that contains no strings, non fifty-fifty the empty string.

The empty string has several properties:

|ε| = 0. Its cord length is null.
ε ⋅ south = s ⋅ ε = south. The empty string is the identity element of the concatenation operation. 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 string.
The empty string precedes any other string under lexicographical order, because it is the shortest of all strings.^[ii]

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

Use in programming languages [edit]

In almost programming languages, strings are a data blazon. Strings are typically stored at distinct memory addresses (locations). Thus, the same string (for example, the empty string) may be stored in two or more places in retentivity.

In this way, there could be multiple empty strings in memory, in contrast with the formal theory definition, for which in that location is only 1 possible empty string. However, a string comparison function would indicate that all of these empty strings are equal to each other.

Fifty-fifty a cord of length zip tin crave memory to store information technology, depending on the format being used. In nearly programming languages, the empty cord is distinct from a nil reference (or nix pointer) because a zippo reference points to no string at all, not fifty-fifty the empty cord. The empty string is a legitimate string, upon which nigh string operations should work. Some languages treat some or all of the post-obit in similar means: empty strings, null references, the integer 0, the floating signal number 0, the Boolean value imitation, the ASCII grapheme NUL, or other such values.

The empty string is usually represented similarly to other strings. In implementations with string terminating character (cipher-terminated strings or plain text lines), the empty cord is indicated by the immediate use of this terminating character.

λ representation	Programming languages
`""`	C, C#, C++, Go, Haskell, Coffee, JavaScript, Julia, Lua, M, Objective-C (equally a C string), OCaml, Perl, PHP, Python, Cherry, Scala, Standard ML, Swift, Tcl, Visual Basic .NET
`''`	APL, Delphi, JavaScript, Lua, MATLAB, Pascal, Perl, PHP, Python, R, Ruby, Smalltalk, SQL
`graphic symbol(0)`	R^[iii]
`{'\0'}`	C, C++, Objective-C (as a C cord)
`std::string()`	C++
`""s`	C++ (since the 2014 standard)
`@""`	Objective-C (as a constant `NSString` object)
`[NSString cord]`	Objective-C (as a new `NSString` object)
`q(), qq()`	Perl
`str()`	Python
`%{}` `%()`	Cherry
`cord.Empty`	C#, Visual Basic .NET
`String.brand 0 '-'`	OCaml
`{}`	Tcl
`[[]]`	Lua

Examples of empty strings [edit]

This section needs expansion. You 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 cord does not have a standard visual representation outside of formal language theory, the number nothing is traditionally represented by a unmarried decimal digit 0 instead.

Aught-filled memory area, interpreted as a zilch-terminated cord, is an empty string.

Empty lines of text evidence the empty string. This can occur from two consecutive EOLs, equally often occur in text files, and this is sometimes used in text processing to carve up paragraphs, e.chiliad. in MediaWiki.

Run into too [edit]

Empty set up
Null-terminated cord
Concatenation theory

References [edit]

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