Lexicography
The swung dash is often used in dictionaries to represent a word that was mentioned before and is understood, to save space:
[edit] Punctuation
The swung dash (~) is used in various ways in punctuation:
[edit] Range
In some languages (though not 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 type-set documents, as a wavy dash preceding a number sometimes represents an approximation (see the Mathematics section, below).
[edit] Japanese
Further information: Japanese punctuation
The wave dash (波ダッシュ, nami dasshu?), (Unicode U+301C) is used for various purposes in Japanese.
In Japanese, 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] or, in East Asia, as an extension of the final syllable to produce the same effect as “whyyyyyy” with “why〜〜”. Used at the end of a word or sentence in text communications, it often denotes something said in a sing-song voice, or similar to the use in instant messengers and email, depending on context.
[edit] Mathematics
In mathematics, the tilde operator (Unicode U+223C), sometimes pronounced “twiddle”, is often used to denote an equivalence relation between two objects. Thus “x ~ y” means “x is equivalent to y”. (Note that this is usually quite different from 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”.
There are two common contexts in which “~” is used to denote particular equivalence relations: It can be used to denote the asymptotical equality of two functions. For example, f(x) ~ g(x), means that limx→∞ f(x)/g(x) = 1. Additionally, in statistics and probability theory, ~ means “is distributed as”. See random variable.
There is also a triple-tilde, (≋) which is often used to show congruence, an equivalence relation in geometry.
A tilde can also be used to represent Similarity. In modern Geometry, polygons can be similar to one another, and similarity can be expressed as e.g. Triangle ABC ~ (is similar to) Triangle DEF. This is often used to relate polygons that have a geometric similarity to others, such as when using ratios and proportions to compare polygons.
In English it is sometimes used to represent approximation, for example ~10 would mean “approximately 10”. Similar symbols are used in mathematics, such as in π ≈ 3.14, “π is about equal to 3.14”. Since the double-tilde (≈) is not available from the keyboard except on the Macintosh (where it is Option-x on English layouts), the tilde (~) has become a substitute for use in typed entry.
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 or loop in the middle or, sometimes, a tilde. [Also see Approximation]. The symbol "≈" is also used for this purpose.
A tilde can be used on its own between two expressions (e.g. a ~ 0.1) to state that the two are of the same order of magnitude.
A tilde placed below a letter in mathematics can represent a vector quantity.
[edit] Logic
In written mathematical logic, it represents negation (e.g. “~p” equals “not p”). Modern use has been replacing the tilde with the negation symbol (¬) for this purpose, to avoid confusion with equivalence relations.
