Tilde
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Tilde
~
Tilde
Word dividers
interpunct ·
space

### Japanese

The wave dash ( 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

Correct JIS wave dash.
Previous Unicode wave dash (incorrect).

In practice the full-width tilde ( zenkaku chiruda), Unicode U+FF5E, is often used instead of the wave dash ( nami dasshu), Unicode U+301C, because the Shift JIS code for the wave dash, 0x8160, which is supposed to be mapped to U+301C,[18][19] is instead mapped to U+FF5E[20] in Windows code page 932 (Microsoft's code page for Japanese), a widely used extension of Shift JIS.

This avoided a shape definition error in the Unicode code charts: the wave dash reference glyph in JIS / Shift JIS[21][22] matches the Unicode reference glyph for U+FF5E,[23] while the reference glyph for U+301C[24] was reflected, incorrectly,[25] 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),[26][27] while IBM and Apple map it to U+301C.[28][29][30]

The current Unicode reference glyph for U+301C has been corrected[25] to match the JIS standard[31] 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 matched the JIS reference glyph for U+301C.[32]

The JIS / Shift JIS wave dash is still formally mapped to U+301C as of JIS X 0213,[33] whereas the WHATWG Encoding Standard used by HTML5 follows Microsoft in mapping 0x8160 to U+FF5E.[34] 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" 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 (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".[35]

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 limx -> ?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 "${\displaystyle {\tilde {f}}}$" is pronounced as "eff tilde" or, informally, as "eff twiddle" or, in American English, "eff wiggle".[36][37] 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. ${\displaystyle (x_{1},x_{2},x_{3},\ldots ,x_{n})={\underset {^{\sim }}{\mathbf {x} }}}$).

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

## 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 ${\displaystyle X}$) a substitution ${\displaystyle X\to x+{\tilde {x}}}$ can be made, where ${\displaystyle x}$ is the equilibrium part and ${\displaystyle {\tilde {x}}}$ 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 ?.

## 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 //'ni:~?l+t// for kneel~knelt (the plus sign '+' indicates a morpheme boundary).[38][39]

## Computing

### 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 . 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)*.[50]

## 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 Arabia) +
Croatian +
Czech +
Danish + followed by + followed by the relevant letter
Dvorak + followed by , or

++ followed by

+ followed by the relevant letter, or

++ followed by the relevant letter

English (Australia) +
English (UK) +
English (US) + + followed by the relevant letter
Faroese + followed by + followed by the relevant letter
Finnish + followed by , or

+

+ followed by the relevant letter
French (Canada) + followed by , or

+

+ followed by the relevant letter
French (France) + followed by , or

+
+ (on Mac OS X)

+ followed by the relevant letter
French (Switzerland) + followed by , or

+

+ followed by the relevant letter
Bépo (French Dvorak) + followed by , or

+

+ followed by the relevant letter
German (Germany) +
German (Switzerland) + followed by , or

+

+ followed by the relevant letter
Hebrew (Israel) + ++ followed by the relevant letter
Hindi (India) ++ the key to the left of
Hungarian +
Icelandic + (the same key as )
Italian + (on Mac OS X)

+ (on Linux)

+ (on Windows)

Norwegian + followed by , or

+.

On Mac: ++, or + followed by .

+ followed by the relevant letter.

On Mac: + followed by the relevant letter.

Polish + followed by , or

+

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 [ ? ? ? ? ? ó ? ? ? ] instead.

Portuguese followed by followed by the relevant letter
Slovak +
Spanish (Spain) + followed by , or

+ (on Windows)

On Linux: +, or + followed by .

On Mac: ++, or + followed by .

+ (on Windows) followed by the relevant letter.

+ (on Linux) followed by the relevant letter.

On Mac: + followed by the relevant letter.

Spanish (Latin America) +
Swedish + followed by , or

+

+ followed by the relevant letter
Turkish + followed by , or

+

+ followed by the relevant letter

## References

1. ^ a b tilde in the American Heritage dictionary
2. ^ Several more or less common informal names are used for the tilde that usually describe the shape, including squiggly, squiggle(s), and flourish.
3. ^ "Swung dash", WordNet (search) (3.0 ed.)
4. "Tilde". Wolfram/MathWorld. 3 November 2011. Retrieved 2011.
5. ^ a b "All Elementary Mathematics - Mathematical symbols dictionary". Bymath. Retrieved 2011.
6. ^
7. ^ a b Quinn, Liam. "HTML 4.0 Entities for Symbols and Greek Letters". HTML help. Retrieved 2011.
8. ^ "Math Symbols... Those Most Valuable and Important: Approximately Equal Symbol". Solving Math problems. 20 September 2010. Retrieved 2011.
9. ^ "26 argumentos para seguir defendiendo la Ñ". La Razón. Retrieved 2016.
10. ^ AFP. "Batalla de la Ñ: Una aventura quijotesca para defender el alma de la lengua". Periódico ABC Paraguay. Retrieved 2016.
11. ^ Diccionario de la lengua española, Real Academia Española
12. ^ Ortografía de la lengua española. Madrid: Real Academia Española. 2010. p. 279. ISBN 978-84-670-3426-4.
13. ^ "Lema en la RAE". Real Academia Española. Retrieved 2015.
14. ^ 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].
15. ^ Lithuanian Standards Board (LST), proposal for a zigzag diacritic
16. ^ "Other symbols", Abstract Math[better source needed]
17. ^
18. ^ "Appendix 1: Shift_JIS-2004 vs Unicode mapping table", JIS X 0213:2004, X 0213.
19. ^ Shift-JIS to Unicode, Unicode.
20. ^ "Windows 932_81". Microsoft. Retrieved 2010.
21. ^ "ISO-IR-087: Japanese Graphic Character Set for Information Interchange" (PDF). JP: Information Technology Standards Commission of Japan (IPSJ/ITSCJ).
22. ^ "ISO-IR-233: Japanese Graphic Character Set for Information Interchange, Plane 1" (PDF). JP: Information Technology Standards Commission of Japan (IPSJ/ITSCJ).
23. ^ Halfwidth and Fullwidth Forms (PDF) (chart), Unicode.
24. ^ CJK Symbols and Punctuation (Unicode 6.2) (PDF) (chart), Unicode.
25. ^ a b Errata Fixed in Unicode 8.0.0, Unicode
26. ^ "windows-949-2000 (lead byte A1)". ICU Demonstration - Converter Explorer. International Components for Unicode.
27. ^ "Lead Byte A1-A2 (Code page 949)". MSDN. Microsoft.
28. ^ "ibm-1363_P110-1997 (lead byte A1)". ICU Demonstration - Converter Explorer. International Components for Unicode.
29. ^ "euc-kr (lead byte A1)". ICU Demonstration - Converter Explorer. International Components for Unicode.
30. ^
31. ^ CJK Symbols and Punctuation (PDF) (chart), Unicode
32. ^ Komatsu, Hiroyuki, L2/14-198: Proposal for the modification of the sample character layout of WAVE_DASH (U+301C) (PDF)
33. ^
34. ^ "Shift_JIS visualization", Encoding Standard, WHATWG
35. ^ Derbyshire, J (2004), Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, New York: Penguin.
36. ^ "Tilde". Wolfram Research. Retrieved 2018.
37. ^ Choy, Stephen TL; Jesudason, Judith Packer; Lee, Peng Yee (1988). Proceedings of the Analysis Conference, Singapore 1986. Elsevier. Retrieved 2011.
38. ^ Collinge (2002) An Encyclopedia of Language, §4.2.
39. ^ Hayes, Bruce (2011). Introductory Phonology. John Wiley & Sons. pp. 87-88. ISBN 9781444360134.
40. ^ "Tilde expansion", C Library Manual, The GNU project, retrieved 2010.
41. ^ "Module mod_userdir", HTTP Server Documentation (version 2.0 ed.), The Apache foundation, retrieved 2010.
42. ^ RFC 3986, IETF.
43. ^
44. ^ Groovy Regular Expression User Guide, Code haus.
45. ^ Groovy RegExp FAQ, Code haus.
46. ^ "Type Families", Haskell Wiki.
47. ^
48. ^ "CLHS: Section 22.3". Lispworks.com. 11 April 2005. Retrieved 2010.
49. ^ Emacs Manual
50. ^ "The Internet Juggling Database". Archived from the original on 28 July 2005. Retrieved 2009.