Tilde

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Short description: Diacritical mark (~)
For signing your comments on Wikipedia, see WP:Signatures.
~ ◌̃
Tilde (symbol), Combining tilde (diacritic)
See alsoDouble tilde: Approximation [≈] or Double negation [ ~(~ ]

The tilde (/ˈtɪldeɪ, -di, -də, ˈtɪld/)[1] ˜ or ~, is a grapheme with a number of uses. The name of the character came into English from Spanish, which in turn came from the Latin titulus, meaning "title" or "superscription".[2][lower-alpha 1] Its primary use is as a diacritic (accent) in combination with a base letter; but, for historical reasons, it is also used in standalone form within a variety of contexts.

History

Use by medieval scribes

The tilde was originally written over an omitted letter or several letters as a scribal abbreviation, or "mark of suspension" and "mark of contraction",[3] shown as a straight line when used with capitals. Thus, the commonly used words Anno Domini were frequently abbreviated to Ao Dñi, with an elevated terminal with a suspension mark placed over the "n". Such a mark could denote the omission of one letter or several letters. This saved on the expense of the scribe's labor and the cost of vellum and ink. Medieval European charters written in Latin are largely made up of such abbreviated words with suspension marks and other abbreviations; only uncommon words were given in full.

The text of the Domesday Book of 1086, relating for example, to the manor of Molland in Devon (see adjacent picture), is highly abbreviated as indicated by numerous tildes.

Text of Exeter Domesday Book of 1086

The text with abbreviations expanded is as follows:

Mollande tempore regis Edwardi geldabat pro quattuor hidis et uno ferling. Terra est quadraginta carucae. In dominio sunt tres carucae et decem servi et triginta villani et viginti bordarii cum sedecim carucis. Ibi duodecim acrae prati et quindecim acrae silvae. Pastura tres leugae in longitudine et latitudine. Reddit quattuor et viginti libras ad pensam. Huic manerio est adjuncta Blachepole. Elwardus tenebat tempore regis Edwardi pro manerio et geldabat pro dimidia hida. Terra est duae carucae. Ibi sunt quinque villani cum uno servo. Valet viginti solidos ad pensam et arsuram. Eidem manerio est injuste adjuncta Nimete et valet quindecim solidos. Ipsi manerio pertinet tercius denarius de Hundredis Nortmoltone et Badentone et Brantone et tercium animal pasturae morarum.

Role of mechanical typewriters

Further information: Dead key and Diacritic
An Olivetti Lettera 32 typewriter (Portuguese Model) with tilde (and circumflex) dead-key beside
Spanish typewriter (QWERTY keyboard) with dead keys for acute, circumflex, diaeresis and grave accents. Ñ/ñ is present as a precomposed character only.

On typewriters designed for languages that routinely use diacritics (accent marks), there are two possible solutions. Keys can be dedicated to precomposed characters or alternatively a dead key mechanism can be provided. With the latter, a mark is made when a dead key is typed, but unlike normal keys, the paper carriage does not move on and thus the next letter to be typed is printed under that accent. Typewriters for Spanish typically have a dedicated key for Ñ/ñ but, as Portuguese uses Ã/ã and Õ/õ, a single dead-key (rather than take two keys to dedicate) is the most practical solution.

The tilde symbol did not exist independently as a movable type or hot-lead printing character since the type cases for Spanish or Portuguese would include sorts for the accented forms.

The centralized ASCII tilde

Serif: —~—
Sans-serif: —~—
Monospace: —~—
A free-standing tilde between two em dashes
in three font families

The first ASCII standard (X3.64-1963) did not have a tilde.[4]:246 Like Portuguese and Spanish, the French, German and Scandinavian languages also needed symbols in excess of the basic 26 needed for English. The ASA worked with and through the CCITT to internationalize the code-set, to meet the basic needs of at least the Western European languages.

It appears to have been at their May 13–15, 1963 meeting that the CCITT decided that the proposed ISO 7-bit code standard would be suitable for their needs if a lower case alphabet and five diacritical marks [...] were added to it.[5] At the October 29–31 meeting, then, the ISO subcommittee altered the ISO draft to meet the CCITT requirements, replacing the up-arrow and left-arrow with diacriticals, adding diacritical meanings to the apostrophe and quotation mark, and making the number sign a dual[lower-alpha 2] for the tilde.[6]

Thus ISO 646 was born (and the ASCII standard updated to X3.64-1967), providing the tilde and other symbols as optional characters.[4]:247[lower-alpha 3]

ISO 646 and ASCII incorporated many of the overprinting lower-case diacritics from typewriters, including tilde. Overprinting was intended to work by putting a backspace code between the codes for letter and diacritic.[7] However even at that time, mechanisms that could do this or any other overprinting were not widely available, did not work for capital letters, and were impossible on video displays, with the result that this concept failed to gain significant acceptance. Consequently, many of these free-standing diacritics (and the underscore) were quickly reused by software as additional syntax, basically becoming new types of syntactic symbols that a programming language could use. As this usage became predominant, type design gradually evolved so these diacritic characters became larger and more vertically centered, making them useless as overprinted diacritics but much easier to read as free-standing characters that had come to be used for entirely different and novel purposes. Most modern fonts align the plain ASCII "spacing" (free-standing) tilde at the same level as dashes, or only slightly higher.

The free-standing tilde is at code 126 in ASCII, where it was inherited into Unicode as U+007E.

A similar shaped mark (⁓) is known in typography and lexicography as a swung dash: these are used in dictionaries to indicate the omission of the entry word.[8]

Connection to Spanish

Main page: Ñ
Logo of the Instituto Cervantes
Logo of CNN en Español

As indicated by the etymological origin of the word "tilde" in English, this symbol has been closely associated with the Spanish language. The connection stems from the use of the tilde above the letter ⟨n⟩ to form the (different) letter ⟨ñ⟩ in Spanish, a feature shared by only a few other languages, most of which are historically connected to Spanish. This peculiarity can help non-native speakers quickly identify a text as being written in Spanish with little chance of error. Particularly during the 1990s, Spanish-speaking intellectuals and news outlets demonstrated support for the language and the culture by defending this letter against globalisation and computerisation trends that threatened to remove it from keyboards and other standardised products and codes.[9][10] The Instituto Cervantes, founded by Spain's government to promote the Spanish language internationally, chose as its logo a highly stylised Ñ with a large tilde. The 24-hour news channel CNN in the US later adopted a similar strategy on its existing logo for the launch of its Spanish-language version, therefore being written as CN͠N. And similarly to the National Basketball Association (NBA), the Spain men's national basketball team is nicknamed "ÑBA".

In Spanish itself the word tilde is used more generally for diacritics, including the stress-marking acute accent.[11] The diacritic ~ is more commonly called virgulilla or la tilde de la eñe, and is not considered an accent mark in Spanish, but rather simply a part of the letter ñ (much like the dot over ı makes an i character that is familiar to readers of English).

Usage

Letters with tilde

This is a table of precomposed letters with tilde:

Template:Letters with diacritic/header

Template:Letters with diacritic/footer

A tilde diacritic can be added to almost any character by using a combining tilde. Greek and Cyrillic letters with tilde (Α͂ ᾶ, Η͂ ῆ, Ι͂ ῖ, ῗ, Υ͂ ῦ, ῧ and А̃ а̃, Ә̃ ә̃, Е̃ е̃, И̃ и̃, О̃ о̃, У̃ у̃) are formed using this method.

Common use in English

The English language does not use the tilde as a diacritic, though it is used in some loanwords. The standalone form of the symbol is used more widely. Informally,[12] it means "approximately", "about", or "around", such as "~30 minutes before", meaning "approximately 30 minutes before".[13][14] It may also mean "similar to",[15] including "of the same order of magnitude as",[12] such as "x ~ y" meaning that x and y are of the same order of magnitude. Another approximation symbol is the double tilde ≈, meaning "approximately/almost equal to".[13][15][16] The tilde is also used to indicate congruence of shapes by placing it over an = symbol, thus ≅.

In more recent digital usage, tildes on either side of a word or phrase have sometimes come to convey a particular tone that "let[s] the enclosed words perform both sincerity and irony", which can pre-emptively defuse a negative reaction.[17] For example, BuzzFeed journalist Joseph Bernstein interprets the tildes in the following tweet:

"in the ~ spirit of the season ~ will now link to some of the (imho) #Bestof2014 sports reads. if you hate nice things, mute that hashtag."

as a way of making it clear that both the author and reader are aware that the enclosed phrase – "spirit of the season" – "is cliche and we know this quality is beneath our author, and we don't want you to think our author is a cliche person generally".[17][lower-alpha 4]

Among other uses, the symbol has been used on social media to indicate sarcasm.[18] It may also be used online, especially in informal writing such as fanfiction, to convey a cutesy, playful, or flirtatious tone.[19]

Diacritical use

In some languages, the tilde is a diacritic mark placed over a letter to indicate a change in its pronunciation:

Pitch

The tilde was firstly used in the polytonic orthography of Ancient Greek, as a variant of the circumflex, representing a rise in pitch followed by a return to standard pitch.

Abbreviation

Carta marina showing Finnish economy, with the captions Hic fabricantur naves and Hic fabricantur bombarde abbreviated

Later, it was used to make abbreviations in medieval Latin documents. When an ⟨n⟩ or ⟨m⟩ followed a vowel, it was often omitted, and a tilde (physically, a small ⟨N⟩) was placed over the preceding vowel to indicate the missing letter; this is the origin of the use of tilde to indicate nasalization (compare the development of the umlaut as an abbreviation of ⟨e⟩.) The practice of using the tilde over a vowel to indicate omission of an ⟨n⟩ or ⟨m⟩ continued in printed books in French as a means of reducing text length until the 17th century. It was also used in Portuguese and Spanish.

The tilde was also used occasionally to make other abbreviations, such as over the letter ⟨q⟩, making q̃, to signify the word que ("that").

Nasalization

It is also as a small ⟨n⟩ that the tilde originated when written above other letters, marking a Latin ⟨n⟩ which had been elided in old Galician-Portuguese. In modern Portuguese it indicates nasalization of the base vowel: mão "hand", from Lat. manu-; razões "reasons", from Lat. rationes. This usage has been adopted in the orthographies of several native languages of South America, such as Guarani and Nheengatu, as well as in the International Phonetic Alphabet (IPA) and many other phonetic alphabets. For example, [ljɔ̃] is the IPA transcription of the pronunciation of the French place-name Lyon.

In Breton, the symbol ⟨ñ⟩ after a vowel means that the letter ⟨n⟩ serves only to give the vowel a nasalised pronunciation, without being itself pronounced, as it normally is. For example, ⟨an⟩ gives the pronunciation [ãn] whereas ⟨añ⟩ gives [ã].

In the DMG romanization of Tunisian Arabic, the tilde is used for nasal vowels õ and ṏ.

Palatal n

Main page: Ñ

The tilded ⟨n⟩ (⟨ñ⟩, ⟨Ñ⟩) developed from the digraph ⟨nn⟩ in Spanish. In this language, ⟨ñ⟩ is considered a separate letter called eñe (IPA: [ˈeɲe]), rather than a letter-diacritic combination; it is placed in Spanish dictionaries between the letters ⟨n⟩ and ⟨o⟩. In Spanish, the word tilde actually refers to diacritics in general, e.g. the acute accent in José,[20] while the diacritic in ⟨ñ⟩ is called "virgulilla" (IPA: [birɣuˈliʝa]) (yeísta) or (IPA: [birɣuˈliʎa]) (non-yeísta). [21] Current languages in which the tilded ⟨n⟩ (⟨ñ⟩) is used for the palatal nasal consonant /ɲ/ include


Tone

In Vietnamese, a tilde over a vowel represents a creaky rising tone (ngã). Letters with the tilde are not considered separate letters of the Vietnamese alphabet.

International Phonetic Alphabet

In phonetics, a tilde is used as a diacritic that is placed above a letter, below it or superimposed onto the middle of it:

  • A tilde above a letter indicates nasalization, e.g. [ã], [ṽ].
  • A tilde superimposed onto the middle of a letter indicates velarization or pharyngealization, e.g. [ɫ], [z̴]. If no precomposed Unicode character exists, the Unicode character U+0334 ◌̴ COMBINING TILDE OVERLAY can be used to generate one.
  • A tilde below a letter indicates laryngealisation, e.g. [d̰]. If no precomposed Unicode character exists, the Unicode character U+0330 ◌̰ COMBINING TILDE BELOW can be used to generate one.

Letter extension

In Estonian, the symbol ⟨õ⟩ stands for the close-mid back unrounded vowel, and it is considered an independent letter.

Other uses

Some languages and alphabets use the tilde for other purposes, such as:

  • Arabic script: A symbol resembling the tilde (U+0653 ـٓ ARABIC MADDAH ABOVE) is used over the letter ⟨ا⟩ (/a/) to become ⟨آ⟩, denoting a long /ʔaː/ sound.
  • Guaraní: The tilded ⟨G̃⟩ (note that ⟨G/g⟩ with tilde is not available as a precomposed glyph in Unicode) stands for the velar nasal consonant. Also, the tilded ⟨y⟩ (⟨Ỹ⟩) stands for the nasalized upper central rounded vowel [ɨ̃]. Munduruku, Parintintín, and two older spellings of Filipino words also use ⟨g̃⟩.
  • Syriac script: A tilde (~) under the letter Kaph represents a [t͡ʃ] sound, transliterated as ch or č.[22]
  • Estonian and Võro use the tilde above the letter o (õ) to indicate the vowel [ɤ], a rare sound among languages.
  • Unicode has a combining vertical tilde character: U+033E ◌̾ COMBINING VERTICAL TILDE. It is used to indicate middle tone in linguistic transcription of certain dialects of the Lithuanian language.[23]

Punctuation

The tilde is used in various ways in punctuation, such as:

Range

In some languages (though not generally in English), a tilde or a tilde-like wave dash (Unicode: U+301C 〜 WAVE DASH) may be used as a punctuation mark (instead of an unspaced hyphen, en dash or em dash) between two numbers, to indicate a range. Doing so avoids the risk of confusion with subtraction or a hyphenated number (such as a part number or model number). For example, "12~15" means "12 to 15", "~3" means "up to three", and "100~" means "100 and greater".[citation needed] East Asian languages almost always use this convention, but it is sometimes done for clarity in some other languages as well. Chinese uses the wave dash and full-width em dash interchangeably for this purpose. In English, the tilde is often used to express ranges and model numbers in electronics, but rarely in formal grammar or in type-set documents, as a wavy dash preceding a number sometimes represents an approximation (see below).

Approximation

Before a number the tilde can mean 'approximately'; '~42' means 'approximately 42'.[24] When used with currency symbols that precede the number (national conventions differ), the tilde precedes the symbol, thus for example '~$10' means 'about ten dollars'.[25]

The symbols ≈ (almost equal to) and ≅ (approximately equal to) are among the other symbols used to express approximation.

Japanese

The wave dash (波ダッシュ, nami dasshu) is used for various purposes in Japanese, including to denote ranges of numbers (e.g., 5〜10 means between 5 and 10) in place of dashes or brackets, and to indicate origin. The wave dash is also used to separate a title and a subtitle in the same line, as a colon is used in English.

When used in conversations via email or instant messenger it may be used as a sarcasm mark[citation needed].

The sign is used as a replacement for the chōon, katakana character, in Japanese, extending the final syllable.

Unicode and Shift JIS encoding of wave dash
Correct JIS wave dash
Correct JIS wave dash, current in Unicode
Previous Unicode wave dash (incorrect)
Previous Unicode wave dash (incorrect)

In practice the full-width tilde (全角チルダ, zenkaku chiruda) (Unicode U+FF5E ～ FULLWIDTH TILDE), is often used instead of the wave dash (波ダッシュ, nami dasshu) (Unicode U+301C 〜 WAVE DASH), because the Shift JIS code for the wave dash, 0x8160, which should be mapped to U+301C,[26][27] is instead mapped to U+FF5E[28] in Windows code page 932 (Microsoft's code page for Japanese), a widely used extension of Shift JIS.

This decision avoided a shape definition error in the original (6.2) Unicode code charts:[29] the wave dash reference glyph in JIS / Shift JIS[30][31] matches the Unicode reference glyph for U+FF5E FULLWIDTH TILDE,[32] while the original reference glyph for U+301C[29] was reflected, incorrectly,[33] when Unicode imported the JIS wave dash. In other platforms such as the classic Mac OS and macOS, 0x8160 is correctly mapped to U+301C. It is generally difficult, if not impossible, for users of Japanese Windows to type U+301C, especially in legacy, non-Unicode applications.

A similar situation exists regarding the Korean KS X 1001 character set, in which Microsoft maps the EUC-KR or UHC code for the wave dash (0xA1AD) to U+223C ∼ TILDE OPERATOR,[34][35] while IBM and Apple map it to U+301C.[36][37][38] Microsoft also uses U+FF5E to map the KS X 1001 raised tilde (0xA2A6),[35] while Apple uses U+02DC ˜ SMALL TILDE.[38]

The current Unicode reference glyph for U+301C has been corrected[33] to match the JIS standard[39] in response to a 2014 proposal, which noted that while the existing Unicode reference glyph had been matched by fonts from the discontinued Windows XP, all other major platforms including later versions of Microsoft Windows shipped with fonts matching the JIS reference glyph for U+301C.[40]

The JIS / Shift JIS wave dash is still formally mapped to U+301C as of JIS X 0213,[41] whereas the WHATWG Encoding Standard used by HTML5 follows Microsoft in mapping 0x8160 to U+FF5E.[42] These two code points have a similar or identical glyph in several fonts, reducing the confusion and incompatibility.

Mathematics

As a unary operator

A tilde in front of a single quantity can mean "approximately", "about"[13] or "of the same order of magnitude as."

In written mathematical logic, the tilde represents negation: "~p" means "not p", where "p" is a proposition. Modern use often replaces the tilde with the negation symbol (¬) for this purpose, to avoid confusion with equivalence relations.

As a relational operator

In mathematics, the tilde operator (which can be represented by a tilde or the dedicated character U+223C ∼ TILDE OPERATOR), sometimes called "twiddle", is often used to denote an equivalence relation between two objects. Thus "x ~ y" means "x is equivalent to y". It is a weaker statement than stating that x equals y. The expression "x ~ y" is sometimes read aloud as "x twiddles y", perhaps as an analogue to the verbal expression of "x = y".[43]

The tilde can indicate approximate equality in a variety of ways. It can be used to denote the asymptotic equality of two functions. For example, f (x) ~ g(x) means that [math]\displaystyle{ \lim_{x \to \infty} \frac{f(x)}{g(x)} = 1 }[/math].[12]

A tilde is also used to indicate "approximately equal to" (e.g. 1.902 ~= 2). This usage probably developed as a typed alternative to the libra symbol used for the same purpose in written mathematics, which is an equal sign with the upper bar replaced by a bar with an upward hump, bump, or loop in the middle (︍︍♎︎) or, sometimes, a tilde (≃). The symbol "≈" is also used for this purpose.

In physics and astronomy, a tilde can be used between two expressions (e.g. h ~ 10−34 J s) to state that the two are of the same order of magnitude.[12]

In statistics and probability theory, the tilde means "is distributed as";[12] see random variable(e.g. X ~ B(n,p) for a binomial distribution).

A tilde can also be used to represent geometric similarity (e.g. ∆ABC ~ ∆DEF, meaning triangle ABC is similar to DEF). A triple tilde (≋) is often used to show congruence, an equivalence relation in geometry.

In graph theory, the tilde can be used to represent adjacency between vertices. The edge [math]\displaystyle{ (x,y) }[/math] connects vertices [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] which can be said to be adjacent, and this adjacency can be denoted [math]\displaystyle{ x \sim y }[/math].

As a diacritic

The symbol "[math]\displaystyle{ \tilde{f} }[/math]" is pronounced as "eff tilde" or, informally, as "eff twiddle".[44][45] This can be used to denote the Fourier transform of f, or a lift of f, and can have a variety of other meanings depending on the context.

A tilde placed below a letter in mathematics can represent a vector quantity (e.g. [math]\displaystyle{ (x_1, x_2, x_3, \ldots, x_n) = \underset{^\sim}{\mathbf x} }[/math]).

In statistics and probability theory, a tilde placed on top of a variable is sometimes used to represent the median of that variable; thus [math]\displaystyle{ \tilde{\mathbf y} }[/math] would indicate the median of the variable [math]\displaystyle{ \mathbf y }[/math]. A tilde over the letter n ([math]\displaystyle{ \tilde{n} }[/math]) is sometimes used to indicate the harmonic mean.

In machine learning, a tilde may represent a candidate value for a cell state in GRUs or LSTM units. (e.g. c̃)

Physics

Often in physics, one can consider an equilibrium solution to an equation, and then a perturbation to that equilibrium. For the variables in the original equation (for instance [math]\displaystyle{ X }[/math]) a substitution [math]\displaystyle{ X\to x+\tilde{x} }[/math] can be made, where [math]\displaystyle{ x }[/math] is the equilibrium part and [math]\displaystyle{ \tilde{x} }[/math] is the perturbed part.

A tilde is also used in particle physics to denote the hypothetical supersymmetric partner. For example, an electron is referred to by the letter e, and its superpartner the selectron is written ẽ.

In multibody mechanics, the tilde operator maps three-dimensional vectors [math]\displaystyle{ \boldsymbol{\omega}\in\mathbb{R}^3 }[/math] to skew-symmetrical matrices [math]\displaystyle{ \tilde{\boldsymbol{\omega}}=\begin{bmatrix}0&-\omega_3& \omega_2\\ \omega_3& 0& -\omega_1\\ -\omega_2&\omega_1&0\end{bmatrix} }[/math] (see [46] or [47]).

Economics

For relations involving preference, economists sometimes use the tilde to represent indifference between two or more bundles of goods. For example, to say that a consumer is indifferent between bundles x and y, an economist would write x ~ y.

Electronics

It can approximate the sine wave symbol (∿, U+223F), which is used in electronics to indicate alternating current, in place of +, −, or ⎓ for direct current.

Linguistics

The tilde may indicate alternating allomorphs or morphological alternation, as in //ˈniː~ɛl+t// for kneel~knelt (the plus sign '+' indicates a morpheme boundary).[48][49]

The tilde may represent some sort of phonetic or phonemic variation between two sounds, which might be allophones or in free variation. For example, [χ ~ x] can represent "either [χ] or [x]".

In formal semantics, it is also used as a notation for the squiggle operator which plays a key role in many theories of focus.[50]

Computing

Computer programmers use the tilde in various ways and sometimes call the symbol (as opposed to the diacritic) a squiggle, squiggly, swiggle, or twiddle. According to the Jargon File, other synonyms sometimes used in programming include not, approx, wiggle, enyay (after eñe) and (humorously) sqiggle /ˈskɪɡəl/.

Directories and URLs

On Unix-like operating systems (including AIX, BSD, Linux and macOS), tilde normally indicates the current user's home directory. For example, if the current user's home directory is /home/user, then the command cd ~ is equivalent to cd /home/user, cd $HOME, or cd. This convention derives from the Lear-Siegler ADM-3A terminal in common use during the 1970s, which happened to have the tilde symbol and the word "Home" (for moving the cursor to the upper left) on the same key.[citation needed] When prepended to a particular username, the tilde indicates that user's home directory (e.g., ~janedoe for the home directory of user janedoe, such as /home/janedoe).[51]

Used in URLs on the World Wide Web, it often denotes a personal website on a Unix-based server. For example, http://www.example.com/~johndoe/ might be the personal website of John Doe. This mimics the Unix shell usage of the tilde. However, when accessed from the web, file access is usually directed to a subdirectory in the user's home directory, such as /home/username/public_html or /home/username/www.[52]

In URLs, the characters %7E (or %7e) may substitute for a tilde if an input device lacks a tilde key.[53] Thus, http://www.example.com/~johndoe/ and http://www.example.com/%7Ejohndoe/ will behave in the same manner.

Computer languages

The tilde is used in the AWK programming language as part of the pattern match operators for regular expressions:

  • variable ~ /regex/ returns true if the variable is matched.
  • variable !~ /regex/ returns false if the variable is matched.

A variant of this, with the plain tilde replaced with =~, was adopted in Perl, and this semi-standardization has led to the use of these operators in other programming languages, such as Ruby or the SQL variant of the database PostgreSQL.

In APL and MATLAB, tilde represents the monadic logical function NOT, and in APL it additionally represents the dyadic multiset function without (set difference).

In C the tilde character is used as bitwise NOT unary operator, following the notation in logic (an ! causes a logical NOT, instead). This is also used by most languages based on or influenced by C, such as C++, D and C#. The MySQL database also use tilde as bitwise invert[54] as does Microsoft's SQL Server Transact-SQL (T-SQL) language. JavaScript also uses tilde as bitwise NOT, and because JavaScript internally uses floats and the bitwise complement only works on integers, numbers are stripped of their decimal part before applying the operation. This has also given rise to using two tildes ~~x as a short syntax for a cast to integer (numbers are stripped of their decimal part and changed into their complement, and then back).

In C++ and C#, the tilde is also used as the first character in a class's method name (where the rest of the name must be the same name as the class) to indicate a destructor – a special method which is called at the end of the object's life.

In ASP.NET application tilde ('~') is used as a shortcut to the root of the application's virtual directory.

In the CSS stylesheet language, the tilde is used for the indirect adjacent combinator as part of a selector.

In the D programming language, the tilde is used as an array concatenation operator, as well as to indicate an object destructor and bitwise not operator. Tilde operator can be overloaded for user types, and binary tilde operator is mostly used to merging two objects, or adding some objects to set of objects. It was introduced because plus operator can have different meaning in many situations. For example, what to do with "120" + "14" ? Is this a string "134" (addition of two numbers), or "12014" (concatenation of strings) or something else? D disallows + operator for arrays (and strings), and provides separate operator for concatenation (similarly PHP programming language solved this problem by using dot operator for concatenation, and + for number addition, which will also work on strings containing numbers).

In Eiffel, the tilde is used for object comparison. If a and b denote objects, the boolean expression a ~ b has value true if and only if these objects are equal, as defined by the applicable version of the library routine is_equal, which by default denotes field-by-field object equality but can be redefined in any class to support a specific notion of equality. If a and b are references, the object equality expression a ~ b is to be contrasted with a = b which denotes reference equality. Unlike the call a.is_equal (b), the expression a ~ b is type-safe even in the presence of covariance.

In the Apache Groovy programming language the tilde character is used as an operator mapped to the bitwiseNegate() method.[55] Given a String the method will produce a java.util.regex.Pattern. Given an integer it will negate the integer bitwise like in C. =~ and ==~ can in Groovy be used to match a regular expression.[56][57]

In Haskell, the tilde is used in type constraints to indicate type equality.[58] Also, in pattern-matching, the tilde is used to indicate a lazy pattern match.[59]

In the Inform programming language, the tilde is used to indicate a quotation mark inside a quoted string.

In "text mode" of the LaTeX typesetting language a tilde diacritic can be obtained using, e.g., \~{n}, yielding "ñ". A stand-alone tilde can be obtained by using \textasciitilde or \string~. In "math mode" a tilde diacritic can be written as, e.g., \tilde{x}. For a wider tilde \widetilde can be used. The \sim command produce a tilde-like binary relation symbol that is often used in mathematical expressions, and the double-tilde ≈ is obtained with \approx. The url package also supports entering tildes directly, e.g., \url{http://server/~name}. In both text and math mode, a tilde on its own (~) renders a white space with no line breaking.

In MediaWiki syntax, four tildes are used as a shortcut for a user's signature.

In Common Lisp, the tilde is used as the prefix for format specifiers in format strings.[60]

In Max/MSP, a tilde is used to denote objects that process at the computer's sampling rate, i.e. mainly those that deal with sound.

In Standard ML, the tilde is used as the prefix for negative numbers and as the unary negation operator.

In OCaml, the tilde is used to specify the label for a labeled parameter.

In R, the tilde operator is used to separate the left- and right-hand sides in a model formula.[61]

In Object REXX, the twiddle is used as a "message send" symbol. For example, Employee.name~lower() would cause the lower() method to act on the object Employee's name attribute, returning the result of the operation. ~~ returns the object that received the method rather than the result produced. Thus it can be used when the result need not be returned or when cascading methods are to be used. team~~insert("Jane")~~insert("Joe")~~insert("Steve") would send multiple concurrent insert messages, thus invoking the insert method three consecutive times on the team object.

In Raku, ~~ is used instead of =~ for a regular expression. Because the dot operator is used for member access instead of ->, concatenation is done with a single tilde. 

my $concatResult = "Hello " ~ "world!";
$concatResult ~~ /<|w><[A..Z]><[a..z]>*<|w>/;

say $/; # outputs "Hello"
# the $/ variable holds the last regex match result

Keyboards

The presence (or absence) of a tilde engraved on the keyboard depends on the territory where it was sold. In either case, computer's system settings determine the keyboard mapping and the default setting will match the engravings on the keys. Even so, it certainly possible to configure a keyboard for a different locale than that supplied by the retailer. On American and British keyboards, the tilde is a standard keytop and pressing it produces a free-standing "ASCII Tilde". To generate a letter with a tilde diacritic requires the US international or UK extended keyboard setting.

  • With US-international, the `/~ key is a dead key: pressing the key and then a letter produces the tilde-accented form of that letter. (For example,   produces ã.) With this setting active, an ASCII tilde can be inserted with the dead key followed by the space bar, or alternatively by striking the dead key twice in a row.
  • With UK-extended, the key works normally but becomes a 'dead key' when combined with AltGr. Thus followed by a letter produces the accented form of that letter.
  • With a Mac either of the Alt/Option keys function similarly.
  • With Linux, the compose key facility is used.

Instructions for other national languages and keyboards are beyond the scope of this article.

In the US and European Windows systems, the Alt code for a single tilde is 126.

Backup filenames

The dominant Unix convention for naming backup copies of files is appending a tilde to the original file name. It originated with the Emacs text editor[62] and was adopted by many other editors and some command-line tools.

Emacs also introduced an elaborate numbered backup scheme, with files named filename.~1~, filename.~2~ and so on. It didn't catch on, as the rise of version control software eliminates the need for this usage.

Microsoft filenames

The tilde was part of Microsoft's filename mangling scheme when it extended the FAT file system standard to support long filenames for Microsoft Windows. Programs written prior to this development could only access filenames in the so-called 8.3 format—the filenames consisted of a maximum of eight characters from a restricted character set (e.g. no spaces), followed by a period, followed by three more characters. In order to permit these legacy programs to access files in the FAT file system, each file had to be given two names—one long, more descriptive one, and one that conformed to the 8.3 format. This was accomplished with a name-mangling scheme in which the first six characters of the filename are followed by a tilde and a digit. For example, "Program Files" might become "PROGRA~1".

The tilde symbol is also often used to prefix hidden temporary files that are created when a document is opened in Windows. For example, when a document "Document1.doc" is opened in Word, a file called "~$cument1.doc" is created in the same directory. This file contains information about which user has the file open, to prevent multiple users from attempting to change a document at the same time.

Juggling notation

In the juggling notation system Beatmap, tilde can be added to either "hand" in a pair of fields to say "cross the arms with this hand on top". Mills Mess is thus represented as (~2x,1)(1,2x)(2x,~1)*.[63]

Unicode

Variants and similars

Unicode has code-points for many forms of non-combined tilde, for symbols incorporating tildes, and for characters visually similar to a tilde.

Character Code point Name Comments
~ U+007E TILDE The keyboard tilde. Center-height alignment.
˜ U+02DC SMALL TILDE A spacing version of the combining tilde diacritic.
˷ U+02F7 MODIFIER LETTER LOW TILDE A spacing version of the combining tilde diacritic.
◌̃ U+0303 COMBINING TILDE Used in IPA to indicate a nasal vowel.
◌̰ U+0330 COMBINING TILDE BELOW Used in IPA to indicate creaky voice.
◌̴ U+0334 COMBINING TILDE OVERLAY Overstrikes the preceding letter. Used in IPA to indicate velarization or pharyngealization.
◌̾ U+033E COMBINING VERTICAL TILDE
◌͂ U+0342 COMBINING GREEK PERISPOMENI Used as an Ancient Greek accent under the name "circumflex"; it can also be written as an inverted breve.
◌͊ U+034A COMBINING NOT TILDE ABOVE Used in extIPA to indicate a denasalization.
◌͋ U+034B COMBINING HOMOTHETIC ABOVE Used in extIPA to indicate a nareal fricative.
◌͠◌ U+0360 COMBINING DOUBLE TILDE A diacritic that applies to a pair of letters.
◌֘ U+0598 HEBREW ACCENT ZARQA Hebrew cantillation mark.
◌֮ U+05AE HEBREW ACCENT ZINOR Hebrew cantillation mark.
◌᷉ U+1DC9 COMBINING ACUTE-GRAVE-ACUTE Used in IPA as a tone mark.
⁓ U+2053 SWUNG DASH A punctuation mark.
∼ U+223C TILDE OPERATOR Used in mathematics. In-line. Ends not curved as much.
∽ U+223D REVERSED TILDE In some fonts it is the tilde's simple mirror image; others extend the tips to resemble a ᔕ, or an open ∞.
∿ U+223F SINE WAVE Used in electronics to indicate alternating current, in place of +, −, or ⎓ for direct current.
≁ U+2241 NOT TILDE
≂ U+2242 MINUS TILDE
≃ U+2243 ASYMPTOTICALLY EQUAL TO
≄ U+2244 NOT ASYMPTOTICALLY EQUAL TO
≅ U+2245 APPROXIMATELY EQUAL TO
≆ U+2246 APPROXIMATELY BUT NOT ACTUALLY EQUAL TO
≇ U+2247 NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO
≈ U+2248 ALMOST EQUAL TO
≉ U+2249 NOT ALMOST EQUAL TO
≊ U+224A ALMOST EQUAL OR EQUAL TO
≋ U+224B TRIPLE TILDE
≌ U+224C ALL EQUAL TO
⋍ U+22CD REVERSED TILDE EQUALS
⍨ U+2368 APL FUNCTIONAL SYMBOL TILDE DIAERESIS
⍫ U+236B APL FUNCTIONAL SYMBOL DEL TILDE
⍭ U+236D APL FUNCTIONAL SYMBOL STILE TILDE
⍱ U+2371 APL FUNCTIONAL SYMBOL DOWN CARET TILDE
⍲ U+2372 APL FUNCTIONAL SYMBOL UP CARET TILDE
⥲ U+2972 TILDE OPERATOR ABOVE RIGHTWARDS ARROW
⥳ U+2973 LEFTWARDS ARROW ABOVE TILDE OPERATOR
⥴ U+2974 RIGHTWARDS ARROW ABOVE TILDE OPERATOR
⧤ U+29E4 EQUALS SIGN AND SLANTED PARALLEL WITH TILDE ABOVE
⨤ U+2A24 PLUS SIGN WITH TILDE ABOVE
⨦ U+2A26 PLUS SIGN WITH TILDE BELOW
⩪ U+2A6A TILDE OPERATOR WITH DOT ABOVE
⩫ U+2A6B TILDE OPERATOR WITH RISING DOTS
⩳ U+2A73 EQUALS SIGN ABOVE TILDE OPERATOR
⫇ U+2AC7 SUBSET OF ABOVE TILDE OPERATOR
⫈ U+2AC8 SUPERSET OF ABOVE TILDE OPERATOR
⫳ U+2AF3 PARALLEL WITH TILDE OPERATOR
⭁ U+2B41 REVERSE TILDE OPERATOR ABOVE LEFTWARDS ARROW
⭇ U+2B47 REVERSE TILDE OPERATOR ABOVE RIGHTWARDS ARROW
⭉ U+2B49 TILDE OPERATOR ABOVE LEFTWARDS ARROW
⭋ U+2B4B LEFTWARDS ARROW ABOVE REVERSE TILDE OPERATOR
⭌ U+2B4C RIGHTWARDS ARROW ABOVE REVERSE TILDE OPERATOR
⸛ U+2E1B TILDE WITH RING ABOVE
⸞ U+2E1E TILDE WITH DOT ABOVE
⸟ U+2E1F TILDE WITH DOT BELOW
ⸯ U+2E2F VERTICAL TILDE
〜 U+301C WAVE DASH Used in Japanese punctuation.
〰 U+3030 WAVY DASH
◌︢ U+FE22 COMBINING DOUBLE TILDE LEFT HALF
◌︣ U+FE23 COMBINING DOUBLE TILDE RIGHT HALF
◌︩ U+FE29 COMBINING TILDE LEFT HALF BELOW
◌︪ U+FE2A COMBINING TILDE RIGHT HALF BELOW
﹋ U+FE4B WAVY OVERLINE
﹏ U+FE4F WAVY LOW LINE
～ U+FF5E FULLWIDTH TILDE Em wide. In-line. Ends not curved much.
  ~   U+E007E TAG TILDE Formatting tag control character.

Precomposed characters

A number of characters in Unicode, have tilde precomposed.

Unicode precomposaed characters with tilde diacritic
Letter Code point Name
Ẵ U+1EB4 LATIN CAPITAL LETTER A WITH BREVE AND TILDE
ẵ U+1EB5 LATIN SMALL LETTER A WITH BREVE AND TILDE
Ẫ U+1EAA LATIN CAPITAL LETTER A WITH CIRCUMFLEX AND TILDE
ẫ U+1EAB LATIN SMALL LETTER A WITH CIRCUMFLEX AND TILDE
à U+00C3 LATIN CAPITAL LETTER A WITH TILDE
ã U+00E3 LATIN SMALL LETTER A WITH TILDE
ᵬ U+1D6C LATIN SMALL LETTER B WITH MIDDLE TILDE
ᵭ U+1D6D LATIN SMALL LETTER D WITH MIDDLE TILDE
Ễ U+1EC4 LATIN CAPITAL LETTER E WITH CIRCUMFLEX AND TILDE
ễ U+1EC5 LATIN SMALL LETTER E WITH CIRCUMFLEX AND TILDE
Ḛ U+1E1A LATIN CAPITAL LETTER E WITH TILDE BELOW
ḛ U+1E1B LATIN SMALL LETTER E WITH TILDE BELOW
Ẽ U+1EBC LATIN CAPITAL LETTER E WITH TILDE
ẽ U+1EBD LATIN SMALL LETTER E WITH TILDE
ᵮ U+1D6E LATIN SMALL LETTER F WITH MIDDLE TILDE
Ḭ U+1E2C LATIN CAPITAL LETTER I WITH TILDE BELOW
ḭ U+1E2D LATIN SMALL LETTER I WITH TILDE BELOW
Ĩ U+0128 LATIN CAPITAL LETTER I WITH TILDE
ĩ U+0129 LATIN SMALL LETTER I WITH TILDE
Ɫ U+2C62 LATIN CAPITAL LETTER L WITH MIDDLE TILDE
ɫ U+026B LATIN SMALL LETTER L WITH MIDDLE TILDE
ꭞ U+AB5E MODIFIER LETTER SMALL L WITH MIDDLE TILDE
ꬸ U+AB38 LATIN SMALL LETTER L WITH DOUBLE MIDDLE TILDE
ᷬ U+1DEC COMBINING LATIN SMALL LETTER L WITH DOUBLE MIDDLE TILDE
ᵯ U+1D6F LATIN SMALL LETTER M WITH MIDDLE TILDE
ᵰ U+1D70 LATIN SMALL LETTER N WITH MIDDLE TILDE
Ñ U+00D1 LATIN CAPITAL LETTER N WITH TILDE
ñ U+00F1 LATIN SMALL LETTER N WITH TILDE
Ỗ U+1ED6 LATIN CAPITAL LETTER O WITH CIRCUMFLEX AND TILDE
ỗ U+1ED7 LATIN SMALL LETTER O WITH CIRCUMFLEX AND TILDE
Ỡ U+1EE0 LATIN CAPITAL LETTER O WITH HORN AND TILDE
ỡ U+1EE1 LATIN SMALL LETTER O WITH HORN AND TILDE
Ṍ U+1E4C LATIN CAPITAL LETTER O WITH TILDE AND ACUTE
ṍ U+1E4D LATIN SMALL LETTER O WITH TILDE AND ACUTE
Ṏ U+1E4E LATIN CAPITAL LETTER O WITH TILDE AND DIAERESIS
ṏ U+1E4F LATIN SMALL LETTER O WITH TILDE AND DIAERESIS
Ȭ U+022C LATIN CAPITAL LETTER O WITH TILDE AND MACRON
ȭ U+022D LATIN SMALL LETTER O WITH TILDE AND MACRON
Õ U+00D5 LATIN CAPITAL LETTER O WITH TILDE
õ U+00F5 LATIN SMALL LETTER O WITH TILDE
ᵱ U+1D71 LATIN SMALL LETTER P WITH MIDDLE TILDE
ᵳ U+1D73 LATIN SMALL LETTER R WITH FISHHOOK AND MIDDLE TILDE
ᵲ U+1D72 LATIN SMALL LETTER R WITH MIDDLE TILDE
ꭨ U+AB68 LATIN SMALL LETTER TURNED R WITH MIDDLE TILDE
ᵴ U+1D74 LATIN SMALL LETTER S WITH MIDDLE TILDE
ᵵ U+1D75 LATIN SMALL LETTER T WITH MIDDLE TILDE
Ữ U+1EEE LATIN CAPITAL LETTER U WITH HORN AND TILDE
ữ U+1EEF LATIN SMALL LETTER U WITH HORN AND TILDE
Ṹ U+1E78 LATIN CAPITAL LETTER U WITH TILDE AND ACUTE
ṹ U+1E79 LATIN SMALL LETTER U WITH TILDE AND ACUTE
Ṵ U+1E74 LATIN CAPITAL LETTER U WITH TILDE BELOW
ṵ U+1E75 LATIN SMALL LETTER U WITH TILDE BELOW
Ũ U+0168 LATIN CAPITAL LETTER U WITH TILDE
ũ U+0169 LATIN SMALL LETTER U WITH TILDE
Ṽ U+1E7C LATIN CAPITAL LETTER V WITH TILDE
ṽ U+1E7D LATIN SMALL LETTER V WITH TILDE
Ỹ U+1EF8 LATIN CAPITAL LETTER Y WITH TILDE
ỹ U+1EF9 LATIN SMALL LETTER Y WITH TILDE
ᵶ U+1D76 LATIN SMALL LETTER Z WITH MIDDLE TILDE

See also

  • Circumflex
    • Caret (computing)
  • Tittle
  • Double tilde (disambiguation)
  • Backtick

Notes

  1. ↑ Several more or less common informal names are used for the tilde that usually describe the shape, including squiggly, squiggle(s), and flourish.
  2. ↑ alternative association for the same code point
  3. ↑ ISO 646 (and ASCII, which it includes) is a standard for 7-bit encoding, providing just 96 printable characters (and 32 control characters). This was insufficient to meet the needs of Western European languages and so the standard specifies certain code points that are available for national variation. With the arrival of 8-bit "extended ASCII", this issue was largely mitigated, though not fully resolved until Unicode was established.
  4. ↑ See also Air quotes.

References

  1. ↑ "tilde". The Chambers Dictionary (9th ed.). Chambers. 2003. ISBN 0-550-10105-5. 
  2. ↑ "tilde". Boston: Houghton Mifflin Harcourt. 2014. https://www.ahdictionary.com/word/search.html?q=tilde. 
  3. ↑ Martin, Charles Trice (1910). The record interpreter : a collection of abbreviations, Latin words and names used in English historical manuscripts and records (2nd ed.). London, preface, p.5 [1]
  4. ↑ 4.0 4.1 Coded Character Sets, History and Development. The Systems Programming Series (1 ed.). Addison-Wesley Publishing Company, Inc.. 1980. ISBN 978-0-201-14460-4. https://textfiles.meulie.net/bitsaved/Books/Mackenzie_CodedCharSets.pdf. Retrieved 2019-08-25. 
  5. ↑ "Meeting of CCITT Working Party on the New Telegraph Alphabet". CCITT. May 15, 1963. https://www.cl.cam.ac.uk/~mgk25/ucs/ascii-history/ccit.html.  See Paragraph 3.
  6. ↑ "Memorandum to Members, Alternates, and Consultants of A.S.A. X3.2 and task groups". US Department of the Navy. 29 November 1963. p. 8. https://www.cl.cam.ac.uk/~mgk25/ucs/ascii-history/iso.html. 
  7. ↑ "Second ISO draft proposal | 6 and 6 bit character codes for information processing interchange". ISO. December 1963. https://www.cl.cam.ac.uk/~mgk25/ucs/ascii-history/draft.html.  See paragraph 2
  8. ↑ "Swung dash", WordNet (3.0 ed.), http://wordnetweb.princeton.edu/perl/webwn?s=swung+dash&sub=Search+WordNet&o2=&o0=1&o8=1&o1=1&o7=&o5=&o9=&o6=&o3=&o4=&h=000000000000 
  9. ↑ "26 argumentos para seguir defendiendo la Ñ". 11 January 2011. http://www.larazon.es/historico/651-26-argumentos-para-seguir-defendiendo-la-n-SLLA_RAZON_352314#.Ttt1ZN8CWth9pio. 
  10. ↑ AFP (18 November 2004). "Batalla de la Ñ: Una aventura quijotesca para defender el alma de la lengua". http://www.abc.com.py/edicion-impresa/internacionales/batalla-de-la-n-una-aventura-quijotesca-para-defender-el-alma-de-la-lengua-797718.html. 
  11. ↑ Diccionario de la lengua española, Real Academia Española
  12. ↑ 12.0 12.1 12.2 12.3 12.4 "Tilde". Wolfram/MathWorld. 3 November 2011. http://mathworld.wolfram.com/Tilde.html. 
  13. ↑ 13.0 13.1 13.2 "All Elementary Mathematics – Mathematical symbols dictionary". Bymath. http://www.bymath.com/symbols/symbols.html. Retrieved 2014-09-25. 
  14. ↑ "Character design standards - Maths". https://www.microsoft.com/typography/developers/fdsspec/maths.aspx. 
  15. ↑ 15.0 15.1 Quinn, Liam. "HTML 4.0 Entities for Symbols and Greek Letters". HTML help. http://htmlhelp.com/reference/html40/entities/symbols.html. 
  16. ↑ "Math Symbols... Those Most Valuable and Important: Approximately Equal Symbol". Solving Math problems. 20 September 2010. http://www.solving-math-problems.com/math-symbols-approximately-equal.html. 
  17. ↑ 17.0 17.1 Bernstein, Joseph (5 January 2015). "The Hidden Language of The ~Tilde~" (in en). https://www.buzzfeednews.com/article/josephbernstein/the-hidden-language-of-the-tilde. 
  18. ↑ Jess Kimball Leslie (June 5, 2017). "The Internet Tilde Perfectly Conveys Something We Don't Have the Words to Explain". https://www.thecut.com/article/why-the-internet-tilde-is-our-most-perfect-tool-for-snark.html. 
  19. ↑ "What Are Tildes ( ~ ) And How Do You Use Them?". April 12, 2022. https://www.thesaurus.com/e/grammar/tildes/. 
  20. ↑ Ortografía de la lengua española. Madrid: Real Academia Española. 2010. p. 279. ISBN 978-84-670-3426-4. 
  21. ↑ "Lema en la RAE". Real Academia Española. http://lema.rae.es/drae/?val=virgulilla. 
  22. ↑ Nestle, Eberhard (1888). Syrische Grammatik mit Litteratur, Chrestomathie und Glossar. Berlin: H. Reuther's Verlagsbuchhandlung. [translated to English as Syriac grammar with bibliography, chrestomathy and glossary, by R. S. Kennedy. London: Williams & Norgate 1889. p. 5].
  23. ↑ Lithuanian Standards Board (LST), proposal for a zigzag diacritic
  24. ↑ "Tilde Definition". The Linux Information Project. 24 June 2005. http://www.linfo.org/tilde.html. 
  25. ↑ "Using a tilde with currency". https://english.stackexchange.com/questions/116048/using-a-tilde-with-currency. 
  26. ↑ "Appendix 1: Shift_JIS-2004 vs Unicode mapping table", JIS X 0213:2004, X 0213, http://x0213.org/codetable/sjis-0213-2004-std.txt .
  27. ↑ Shift-JIS to Unicode, Unicode, https://www.unicode.org/Public/MAPPINGS/OBSOLETE/EASTASIA/JIS/SHIFTJIS.TXT .
  28. ↑ "Windows 932_81". Microsoft. http://www.microsoft.com/globaldev/reference/dbcs/932/932_81.htm. 
  29. ↑ 29.0 29.1 CJK Symbols and Punctuation (Unicode 6.2), Unicode, http://www.unicode.org/charts/PDF/U3000.pdf .
  30. ↑ Japanese National Committee on ISO/TC97/SC2, ISO-IR-87: Japanese Graphic Character Set for Information Interchange, ITSCJ/IPSJ, https://www.itscj.ipsj.or.jp/iso-ir/087.pdf 
  31. ↑ Japanese Industrial Standards Committee, ISO-IR-233: Japanese Graphic Character Set for Information Interchange, Plane 1 (Update of ISO-IR 228), ITSCJ/IPSJ, https://www.itscj.ipsj.or.jp/iso-ir/233.pdf 
  32. ↑ Halfwidth and Fullwidth Forms, Unicode, https://www.unicode.org/charts/PDF/UFF00.pdf .
  33. ↑ 33.0 33.1 Errata Fixed in Unicode 8.0.0, Unicode, https://www.unicode.org/versions/Unicode8.0.0/erratafixed.html 
  34. ↑ "windows-949-2000 (lead byte A1)". ICU Demonstration - Converter Explorer. International Components for Unicode. https://icu4c-demos.unicode.org/icu-bin/convexp?conv=windows-949-2000&b=A1&s=ALL#layout. 
  35. ↑ 35.0 35.1 "Lead Byte A1-A2 (Code page 949)". MSDN. Microsoft. 6 February 2008. https://msdn.microsoft.com/en-us/library/cc194958.aspx. 
  36. ↑ "ibm-1363_P110-1997 (lead byte A1)". ICU Demonstration - Converter Explorer. International Components for Unicode. https://icu4c-demos.unicode.org/icu-bin/convexp?conv=ibm-1363_P110-1997&b=A1&s=ALL#layout. 
  37. ↑ "euc-kr (lead byte A1)". ICU Demonstration - Converter Explorer. International Components for Unicode. https://icu4c-demos.unicode.org/icu-bin/convexp?conv=euc-kr&b=A1&s=ALL#layout. 
  38. ↑ 38.0 38.1 "Map (external version) from Mac OS Korean encoding to Unicode 3.2 and later.". Apple. https://unicode.org/Public/MAPPINGS/VENDORS/APPLE/KOREAN.TXT. 
  39. ↑ CJK Symbols and Punctuation, Unicode, https://www.unicode.org/charts/PDF/U3000.pdf 
  40. ↑ Komatsu, Hiroyuki, L2/14-198: Proposal for the modification of the sample character layout of WAVE_DASH (U+301C), https://www.unicode.org/L2/L2014/14198-wave-dash.pdf 
  41. ↑ Shift_JIS-2004 (JIS X 0213:2004 Appendix 1) vs Unicode mapping table, x0213.org, http://x0213.org/codetable/sjis-0213-2004-std.txt 
  42. ↑ "Shift_JIS visualization", Encoding Standard (WHATWG), https://encoding.spec.whatwg.org/shift_jis.html 
  43. ↑ Derbyshire, J (2004), Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, New York: Penguin, http://mathworld.wolfram.com/Tilde.html .
  44. ↑ "Tilde". Wolfram Research. http://mathworld.wolfram.com/Tilde.html. 
  45. ↑ Choy, Stephen TL; Jesudason, Judith Packer; Lee, Peng Yee (1988). Proceedings of the Analysis Conference, Singapore 1986. Elsevier. ISBN 9780080872612. https://books.google.com/books?id=SY5fZIK63NMC&q=schlange+twiddle&pg=PA53. 
  46. ↑ Wallrapp (1994). "Standardization of flexible body modeling in multibody system codes, Part I: Definition of Standard Input Data". Mechanics of Structures and Machines 22 (3): 283–304. doi:10.1080/08905459408905214. 
  47. ↑ Valembois, R. E.; Fisette, P.; Samin, J. C. (1997). "Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics". Nonlinear Dynamics 12 (4): 367–397. doi:10.1023/A:1008204330035. 
  48. ↑ Collinge (2002) An Encyclopedia of Language, §4.2.
  49. ↑ Hayes, Bruce (2011). Introductory Phonology. John Wiley & Sons. pp. 87–88. ISBN 9781444360134. 
  50. ↑ Buring, Daniel (2016). Intonation and Meaning. Oxford University Press. pp. 36–41. doi:10.1093/acprof:oso/9780199226269.003.0003. ISBN 978-0-19-922627-6. 
  51. ↑ "Tilde expansion", C Library Manual, The GNU project, https://www.gnu.org/s/libc/manual/html_node/Tilde-Expansion.html, retrieved 4 July 2010 .
  52. ↑ "Module mod_userdir", HTTP Server Documentation (version 2.0 ed.), The Apache foundation, http://httpd.apache.org/docs/2.0/mod/mod_userdir.html, retrieved 4 July 2010 .
  53. ↑ Berners-Lee, T.; Fielding, R.; Masinter, L. (2005), RFC 3986, IETF, doi:10.17487/RFC3986, http://tools.ietf.org/html/rfc3986#page-12 .
  54. ↑ "MySQL :: Reference Manual :: Bit Functions and Operators". https://dev.mysql.com/doc/refman/8.0/en/bit-functions.html#operator_bitwise-invert. 
  55. ↑ "The Groovy programming language - Operators". http://groovy.codehaus.org/Operator%20Overloading. [yes|permanent dead link|dead link}}]
  56. ↑ Groovy Regular Expression User Guide, Code haus, http://groovy.codehaus.org/Regular+Expressions, retrieved 11 November 2010 .
  57. ↑ Groovy RegExp FAQ, Code haus, http://groovy.codehaus.org/FAQ+-+RegExp, retrieved 11 November 2010 .
  58. ↑ "Type Families", Haskell Wiki, http://www.haskell.org/haskellwiki/GHC/Type_families#Equality_constraints .
  59. ↑ "Lazy pattern match - HaskellWiki". http://www.haskell.org/haskellwiki/Lazy_pattern_match. 
  60. ↑ "CLHS: Section 22.3". Lispworks.com. 2005-04-11. http://www.lispworks.com/documentation/HyperSpec/Body/22_c.htm. 
  61. ↑ The R Reference Index
  62. ↑ Emacs Manual
  63. ↑ "The Internet Juggling Database". http://www.jugglingdb.com/help/?id=125. 



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