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Epsilon (US: / ˈ ɛ p s ɪ l ɒ n /, [1] UK: / ɛ p ˈ s aɪ l ə n /; [2] uppercase Ε, lowercase ε or ϵ; Greek: έψιλον) is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel IPA: or IPA:.
The symbol ϵ (U+03F5) is designated specifically for the lunate form, used as a technical symbol. The symbol ϑ ("script theta") is a cursive form of theta (θ), frequent in handwriting, and used with a specialized meaning as a technical symbol. The symbol ϰ ("kappa symbol") is a cursive form of kappa (κ), used as a technical symbol.
the Christoffel symbols that describe components of a metric connection; the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a Turing machine; the Feferman–Schütte ordinal Γ 0; represents: the specific weight of substances; the lower incomplete gamma function
Epsilon with acute and smooth breathing: Archaic letter denoting the absence of /h/ prior to the vowel, with a high pitch on a short vowel or rising pitch on a long vowel Ἒἒ: Epsilon with grave and smooth breathing: Archaic letter denoting the absence of /h/ prior to the vowel, with a normal or low pitch Ἑἑ: Epsilon with rough breathing
The normal letter epsilon (Ε) was used exclusively for the latter, while a new special symbol (or, in Sicyon, ) stood both for short /e/ and for /ɛː/. Yet another variation of the system is found in neighbouring Tiryns : it uses the letter forms of the Corinthian system, versus E, but with the functional values of the classic eta versus ...
Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations. The standard letters to denote the Levi-Civita symbol are the Greek lower case epsilon ε or ϵ , or less commonly the Latin lower case e .
The symbol's names and phonetic descriptions are described in the Handbook of the International Phonetic Association. The symbols also have nonce names in the Unicode standard. In some cases, the Unicode names and the IPA names do not agree. For example, IPA calls ɛ "epsilon", but Unicode calls it "small letter open E".
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...