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The term

 “”

redirects here. For the printed grapheme, meet Quotation mark.

Unique string of length zero

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

Formal theory

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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 goose egg, and so there are no symbols in the string. In that location is only i empty string, because two strings are only different if they have different lengths or a dissimilar sequence of symbols. In formal treatments,^[1]
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 prepare of strings) that contains no strings, not fifty-fifty the empty cord.

The empty string has several properties:

• |ε| = 0. Its string length is zero.
• ε ⋅ s = s ⋅ ε = s. The empty cord is the identity element of the concatenation operation. The set of all strings forms a gratis monoid with respect to ⋅ and ε.
• ε^R
  = ε. Reversal of the empty string produces the empty string.
• The empty string precedes any other cord nether lexicographical order, because it is the shortest of all strings.^[two]

In context-gratis grammars, a product dominion that allows a symbol to produce the empty string is known as an ε-production, and the symbol is said to be “nullable”.

Utilise in programming languages

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In most programming languages, strings are a data type. Strings are typically stored at distinct memory addresses (locations). Thus, the same string (for example, the empty string) may be stored in 2 or more places in memory.

In this fashion, in that location could be multiple empty strings in retentivity, in contrast with the formal theory definition, for which at that place is just i possible empty string. However, a string comparison part would bespeak that all of these empty strings are equal to each other.

Even a string of length naught tin require memory to store information technology, depending on the format being used. In virtually programming languages, the empty cord is distinct from a zilch reference (or goose egg arrow) because a null reference points to no string at all, not even the empty cord. The empty cord is a legitimate cord, upon which most string operations should piece of work. Some languages treat some or all of the following in similar ways: empty strings, aught references, the integer 0, the floating signal number 0, the Boolean value false, the ASCII character NUL, or other such values.

The empty string is usually represented similarly to other strings. In implementations with cord terminating graphic symbol (nil-terminated strings or patently text lines), the empty string is indicated past the immediate use of this terminating graphic symbol.

Examples of empty strings

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This department needs expansion. You lot can help past adding to it. (March 2010)

The empty string is a syntactically valid representation of zero in positional note (in any base), which does not contain leading zeros. Since the empty string does not take a standard visual representation exterior of formal language theory, the number nix is traditionally represented by a single decimal digit
0
instead.

Zero-filled retentivity expanse, interpreted equally a null-terminated cord, is an empty cord.

Empty lines of text show the empty string. This can occur from 2 consecutive EOLs, as often occur in text files, and this is sometimes used in text processing to split paragraphs, e.k. in MediaWiki.

See also

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• Empty set
• Goose egg-terminated string
• Concatenation theory

References

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