Upside-down letters, as in ∀, and left-side-right letters, as in ∃, are used in mathematics and logic to indicate for all and there exists. Do you know other examples of such inversions in other fields. Is there a name for the practice?
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2∃ can be considered a 180-degree rotation, the same as ∀. Phonetic symbols frequently rotate or invert letters, as well. The most common vowel in English, for instance, is shwa /ə/, as in the, a, fun, double, and summer. The symbol is a 180-degree-rotated lower-case e. And the symbol for the vowel of saw is /ɔ/, a 180-degree-rotated lower-case c.– John LawlerCommented Jun 16, 2016 at 19:07
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1Are mathematics symbols really "English"? Presumably, questions and answers on this site should relate to their use in the English language, which requires limiting the list somewhat.– CatijaCommented Jun 16, 2016 at 19:39
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1When typesetting mathematical expressions, typesetters use whatever pieces of type seem to fit the need. Prior to digital typesetting this meant physical pieces of metal. Using existing English characters (if necessary, upside-down) would be an obvious approach, if the type case didn't contain enough "special" characters. Even once digital typesetting became common, typesetters would obviously use existing defined characters before crafting new ones. I think the name for the practice is "typesetting", though typesetters may have their own jargon term.– Hot LicksCommented Sep 18, 2016 at 18:30
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2 Answers
LaTeX, used by mathematicians for typesetting, has \mho \Game \Finv meaning respectively Ω G F rotated 180°. Presumably these are used in mathematics...
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2The mho, ℧, is an obsolete unit of electrical conductance (the reciprocal of the ohm, Ω . It has been officially renamed the Siemens, but is apparently still used in electronics. The quantifier Ⅎ means few, and is used along with ∀ and ∃ in mathematical logic. The last symbol, ⅁, is supposedly used in mathematical game theory. I couldn't find it in any actual mathematics papers, though. Commented Jun 16, 2016 at 20:33
There are many other examples in mathematics alone, and the answer will depend on what transformation you allow and what font you choose. For example do / and \ count as transformed I's? The schwa (ə) for phonetics comes to mind. You might want to check out the full IPA symbol list and the unicode block of letter-like symbols, U+2100 through U+214F, which contains several turned letters. Various languages use transformed Roman characters. For example Cherokee has a backwards J.
