Tilde

~
Tilde
˜ ∼ ◌̃ Small tilde Tilde operator Combining tilde

The tilde (/ˈtɪldə/;^[1] ˜ or ~)^[2] is a grapheme with several uses. The name of the character came into English from Spanish, which in turn came from the Latin titulus, meaning "title" or "superscription."^[1]

The reason for the name was that it was originally written over a letter as a scribal abbreviation, as a "mark of suspension", shown as a straight line when used with capitals. Thus the commonly used words Anno Domini were frequently abbreviated to A^o Dñi, 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 labour 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 tilde has since been applied to a number of other uses as a diacritic mark or a character in its own right. These are encoded in Unicode at U+0303 ◌̃ COMBINING TILDE and U+007E ~ TILDE (as a spacing character), and there are additional similar characters for different roles. In lexicography, the latter kind of tilde and the swung dash (⁓) are used in dictionaries to indicate the omission of the entry word.^[3]

Common use

This symbol (in English) informally^[4] means "approximately", "about", or "around", such as "~30 minutes before", meaning "approximately 30 minutes before".^[5][6] It can mean "similar to",^[7] including "of the same order of magnitude as",^[4] 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 equal to",^[5][7][8] the critical difference being the subjective level of accuracy: ≈ indicates a value which can be considered functionally equivalent for a calculation within an acceptable degree of error, whereas ~ is usually used to indicate a larger, possibly significant, degree of error. The tilde is also used to indicate "equal to" or "approximately equal to" by placing it over the "=" symbol, like so: ≅.

History

Use by medieval scribes

The text of the Domesday Book of 1086, relating for example, to the manor of Molland in Devon (see image left), is highly abbreviated as indicated by numerous tildes. The text with abbreviations expanded is as follows:

"Mollande tempore regis Edwardi geldabat pro iiii hidis et uno ferling. Terra est xl carucis. In dominio sunt iii carucae et x servi et xxx villani et xx bordarii cum xvi carucis. Ibi xii acrae prati et xv acrae silvae. Pastura iii leugae in longitudine et latitudine. Libras ad pensam. Huic manerio est adjuncta Blachepole. Elwardus tenebat tempore regis Edwardi pro manerio et geldabat pro dimidia hida. Terra est ii carucis. Ibi sunt v villani cum i servo. Valet xx solidos ad pensam et arsuram. Eidem manerio est injuste adjuncta Nimete et valet xv solidos. Ipsi manerio pertinet tercius denarius de Hundredis Nortmoltone et Badentone et Brantone et tercium animal pasturae morarum."

Role of mechanical typewriters

The incorporation of the tilde (~) into ASCII is a direct result of its appearance as a distinct character on mechanical typewriters in the late nineteenth century. When all character sets were pieces of metal permanently installed, and number of characters much more limited than in typography, the question of which languages and markets required which characters was an important one. Any good typewriter store had a catalog of alternative keyboards that could be specified for machines ordered from the factory.

At that time, the tilde was used only in Spanish and Portuguese typewriters (keyboards). In Modern Spanish, the tilde is used only with n and N. Both were conveniently assigned to a single mechanical typebar, which sacrificed a key that was felt to be less important, usually the  ¹⁄₂— ¹⁄₄ key.

Portuguese, however, uses not ñ but nh. It uses the tilde on the vowels a and o. So as not to sacrifice two of the tightly limited keys to ã Ã õ Õ, the decision was made to make the ~ a separate "dead" character in which the carriage holding the paper did not move. Dead keys, which had a notch cut out to avoid hitting a mechanical linkage that triggered carriage movement, were used for characters that were intended to be combined (overstruck).

On mechanical typewriters, Spanish keyboards (the first, or one of the first, non-English keyboards) had a dead key, which contained the acute accent (´), used over any vowel, and the dieresis (¨), used only over u. It was a simple matter to create a dead key for a Portuguese keyboard (created later than the Spanish one) to be overstruck with a and o and so the ~ was born as a typographical character, which did not exist previously as a type or hot-lead printing character. That was probably a product of the first and leading manufacturer of (mechanical) typewriters, Remington.

Connection to Spanish

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 "ñ" in Spanish, a feature shared by only a few other languages, all 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. In addition, most native speakers, although not all, use the word "español" to refer to their language. 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. A 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.

Diacritical use

In some languages, the tilde is used as a diacritical mark ( ˜ ) placed over a letter to indicate a change in pronunciation, such as nasalization.

Pitch

It was first 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

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 (i.e., 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⟩ ("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].

Palatal n

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⟩. As the word tilde can also refer to the most common diacritic in this language, e.g., the acute accent in José is also called a tilde in Spanish,^[11] the diacritic in ⟨ñ⟩ is called "virgulilla".^[12] Current languages in which the tilded ⟨n⟩ (⟨ñ⟩) is used for the palatal nasal consonant /ɲ/ include:

• Asturian
• Basque
• Chamorro language
• Filipino
• Galician
• Guaraní
• Iñupiaq
• Mapudungun
• Papiamento
• Quechua
• Spanish
• Tetum

Tone

In Vietnamese, a tilde over a vowel represents a creaky rising tone (ngã).

International Phonetic Alphabet

In phonetics, a tilde is used as a diacritic either placed above a letter, below it or superimposed onto the middle of it (see International Phonetic Alphabet → Diacritics):

• 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:

• 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 /aː/ sound ([ʔæː]).
• 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]. A small number of other alphabets also use ⟨g̃⟩.
• Syriac script: A tilde (~) under the letter Kaph represents a [t͡ʃ] sound, transliterated as ch or č.^[13]
• 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.^[14]

Precomposed Unicode characters

The following letters using the tilde as a diacritic exist as precomposed or combining Unicode characters:

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
Ã	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
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

Similar characters

There are many Unicode characters for tildes, symbols incorporating tildes, and characters visually similar to a tilde:

Character	Code point	Name	Comments
~	U+007E	TILDE	Same as keyboard tilde. In-line.
˜	U+02DC	SMALL TILDE	Raised but quite small.
˷	U+02F7	MODIFIER LETTER LOW TILDE
◌̃	U+0303	COMBINING TILDE
◌̰	U+0330	COMBINING TILDE BELOW	Used in IPA to indicate creaky voice
◌̴	U+0334	COMBINING TILDE OVERLAY	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	Raised, small, with slash through.
◌͠◌	U+0360	COMBINING DOUBLE TILDE
◌֘	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
∼	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 ∞.
∿	U+223F	SINE WAVE
≁	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	50% wider. In-line. Ends not curved much.
~	U+E007E	TAG TILDE	Formatting tag control character.

ASCII tilde (U+007E)

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

Most modern proportional fonts align plain spacing tilde at the same level as dashes, or only slightly upper. This distinguishes it from a small tilde ( ˜ ), which is always raised. But in some monospace fonts, especially used in text user interfaces, ASCII tilde character is raised too. This apparently is a legacy of typewriters, where pairs of similar spacing and combining characters relied on one glyph. Even in line printers' age character repertoires were often not large enough to distinguish between plain tilde, small tilde and combining tilde. Overprinting of a letter by the tilde was a working method of combining a letter.

Punctuation

The swung dash (~) is used in various ways in punctuation:

Authorial intention

The sports blog Card Chronicle uses the tilde as a form of irony punctuation after the period at the end of a sentence: it indicates that readers should take the preceding text as intended sarcastically.^[15]

Range

In some languages (though not generally in English), a tilde-like wavy dash may be used as punctuation (instead of an unspaced hyphen or en-dash) between two numbers, to indicate a range rather than 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". Japanese and other East Asian languages almost always use this convention, but it is often done for clarity in some other languages as well. Chinese uses the wavy 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".^[16]

Japanese

The wave dash (波ダッシュ, nami dasshu) is used for various purposes in Japanese, including to denote ranges of numbers, 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.

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

Unicode and Shift JIS encoding of wave dash

In practice the full-width tilde (全角チルダ, zenkaku chiruda), Unicode U+FF5E, is often used instead of the wave dash (波ダッシュ, nami dasshu), Unicode U+301C, because the Shift JIS code for the wave dash, 0x8160, which is supposed to be mapped to U+301C,^[17][18] is not mapped to U+301C but mapped to U+FF5E^[19] in code page 932 (Microsoft's code page for Japanese), a widely used extension of Shift JIS, in order to avoid the shape definition error in Unicode: the wave dash glyph in JIS/Shift JIS^[20] is identical to the Unicode reference glyph for U+FF5E,^[21] while the reference glyph for U+301C^[22] was incorrectly turned upside down when Unicode imported the JIS wave dash. In other platforms such as Mac OS and Mac OS X, 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.

Nevertheless, the Japanese wave dash is still formally mapped to U+301C as of JIS X 0213. Those two code points have the identical or very similar 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" 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 has been replacing the tilde with the negation symbol (¬) for this purpose, to avoid confusion with equivalence relations.

As a relational operator

In mathematics, the tilde operator (Unicode U+223C), 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".^[23]

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 lim_{x → ∞} f( x) ∕ g(x) = 1.^[4]

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.^[4]

In statistics and probability theory, the tilde means "is distributed as";^[4] see random variable.

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.

As an accent

The symbol "" is often pronounced "eff twiddle" or, particularly in American English, "eff wiggle".^[24] 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. ).

In statistics and probability theory, a tilde placed on top of a variable is sometimes used to represent the median of that variable; thus would indicate the median of the variable . A tilde over the letter n () is sometimes used to indicate the harmonic mean.

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 ) a substitution can be made, where is the equilibrium part and 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.

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.

Computing

Directories and URLs

On Unix-like operating systems (including AIX, BSD, Linux and Mac OS X), tilde normally indicates the current user's home directory. For example, if the current user's home directory is /home/bloggsj, then the command cd ~ is equivalent to cd /home/bloggsj, 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. 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).^[25]

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 web site 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.^[26]

In URLs, the characters ~ (or %7e) may substitute for tilde if an input device lacks a tilde key.^[27] 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.

In the C, C++ and C# programming languages, the tilde character is used as bitwise NOT operator, following the notation in logic (an ! causes a logical NOT, instead). 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 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.^[28] Given a String the method will produce a java.util.regex.Pattern. Given an integer it will negate the integer bitwise like in different C variants. =~ and ==~ can in Groovy be used to match a regular expression.^[29][30]

In Haskell, the tilde is used in type constraints to indicate type equality.^[31] Also, in pattern-matching, the tilde is used to indicate a lazy pattern match.^[32]

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.^[33] 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 Microsoft's SQL Server Transact-SQL (T-SQL) language, the tilde is a unary Bitwise NOT operator.

In JavaScript, the tilde is used as a unary bitwise complement (or bitwise negation) operation (~number). 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 ~~number as a shorthand for the mathematical floor function (numbers are stripped of their decimal part and changed into their complement, and then back. The net result is thus only the removal of the decimal part).

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.

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 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, probably because version control software does this better.

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.

Other uses

Computer programmers use the tilde in various ways and sometimes call the symbol (as opposed to the diacritic) a squiggle, squiggly, or twiddle. According to the Jargon File, other synonyms sometimes used in programming include not, approx, wiggle, enyay (after eñe) and (humorously) sqiggle /ˈskɪɡəl/. It is used in many languages as a binary inversion operator, swapping a number's binary 1's and 0's for example ~10 (binary ~1010) is equal to 5 (binary 0101).

In Perl 6, "~~" is used instead of "=~".

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)*.^[34]

Keyboards

Where a tilde is on the keyboard depends on the computer's language settings according to the following chart. On many keyboards it is primarily available through a dead key that makes it possible to produce a variety of precomposed characters with the diacritic. In that case, a single tilde can typically be inserted with the dead key followed by the space bar, or alternatively by striking the dead key twice in a row.

To insert a tilde with the dead key, it is often necessary to simultaneously hold down the Alt Gr key. On the keyboard layouts that include an Alt Gr key, it typically takes the place of the right-hand Alt key. With a Macintosh either of the Alt/Option keys function similarly.

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

For Mac use option+'n' key

Keyboard	Insert a single tilde (~)	Insert a precomposed character with tilde (e.g. ã)
Arabic (Saudi)	⇧ Shift+`ذّ
Croatian	Alt Gr+1
Danish	Alt Gr+¨ followed by Space	Alt Gr+¨ followed by the relevant letter
Dvorak	Alt Gr+= followed by Space, or Alt Gr+⇧ Shift+' followed by Space	Alt Gr+= followed by the relevant letter, or Alt Gr+⇧ Shift+' followed by the relevant letter
English (Australia)	⇧ Shift+`
English (Canada)	⇧ Shift+`
English (UK)	⇧ Shift+#
English (US)	⇧ Shift+`	Ctrl+~ followed by the relevant letter
Faroese	Alt Gr+ð followed by Space	Alt Gr+ð followed by the relevant letter
Finnish	Alt Gr+¨ followed by Space, or Alt Gr+¨¨	Alt Gr+¨ followed by the relevant letter
French (Canada)	Alt Gr+ç followed by Space, or Alt Gr+çç	Alt Gr+ç followed by the relevant letter
French (France)	Alt Gr+é followed by Space, or Alt Gr+éé ⌥ Option+n (on Mac OS X)	Alt Gr+é followed by the relevant letter
French (Switzerland)	Alt Gr+^ followed by Space, or Alt Gr+^^	Alt Gr+^ followed by the relevant letter
Bépo (French Dvorak)	Alt Gr+N followed by Space, or Alt Gr+K	Alt Gr+N followed by the relevant letter
German (Germany)	Alt Gr++
German (Switzerland)	Alt Gr+^ followed by Space, or Alt Gr+^^	Alt Gr+^ followed by the relevant letter
Hebrew (Israel)	⇧ Shift+~	Ctrl+⇧ Shift+~ followed by the relevant letter
Hindi (India)	Alt Gr+⇧ Shift+ the key to the left of 1
Hungarian	Alt Gr+1
Icelandic	Alt Gr+' (the same key as ?)
Italian	⌥ Option+5 (on Mac OS X) Alt Gr+ì (on Linux)
Norwegian	Alt Gr+¨ followed by Space, or Alt Gr+¨¨. On Mac: Ctrl+⌥ Option+¨, or ⌥ Option+¨ followed by Space.	Alt Gr+¨ followed by the relevant letter. On Mac: ⌥ Option+¨ followed by the relevant letter.
Polish	⇧ Shift+` followed by Space, or ⇧ Shift+``	The dead key is not generally used for inserting characters with tilde; when followed by {a|c|e|l|n|o|s|x|z}, it results in {ą|ć|ę|ł|ń|ó|ś|ź|ż} instead.
Portuguese	~ followed by Space	~ followed by the relevant letter
Slovak	Alt Gr+1
Spanish (Spain)	Alt Gr+4 followed by Space, or Alt Gr+44	Alt Gr+4 followed by the relevant letter
Spanish (Latin America)	Alt Gr++
Swedish	Alt Gr+¨ followed by Space, or Alt Gr+¨¨	Alt Gr+¨ followed by the relevant letter
Turkish	Alt Gr+ü followed by Space, or Alt Gr+üü	Alt Gr+ü followed by the relevant letter

See also

• Circumflex
• Tittle

References

External links

• Diacritics Project, CZ: Typo .
• Keyboard Help: Learn to create accent marks and other diacritics on a computer, Starr .