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Continuing Should the name of a capital Greek letter also be capitalized when the upper case is important? with the answer https://ell.stackexchange.com/a/109096/37810, which did emphasize the importance of the capitalization of proper names, should we still write Little Omega (alternatively, Little-Omega for the the hyphenized variant) when speaking about

ω: (ℕ→ℕ)→𝔓(ℕ→ℕ),

f ↦ { g: ℕ→ℕ | ∀ c∈ℕ ∃ n∈ℕ ∀ m∈ℕ: mng(m) > c f(m) }

?

By the way, this definition of ω is fixed for the whole complexity theory.

Or, perhaps, be satisfied with Little omega (alternatively, Little-omega for the the hyphenized variant)?

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    I would say don't capitalise it at all: "We use ω (little omega) to represent angular frequency." – Mick Dec 7 '16 at 17:46
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    Statements such as these are not in English but in the notation of specific discipline, and should follow the rules of that discipline. I imagine that if the difference between Ω and ω is significant you should employ the whichever form is meant; but that is not a matter which can be authoritatively addressed here. ... By the way, we do not use resp. or respectively to represent German bzw. in the sense "or as the case may be"-- see this. – StoneyB on hiatus Dec 7 '16 at 17:51
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    If I understand you correctly, you're talking about the Big O and little o notations (en.wikipedia.org/wiki/Big_O_notation). FWIW, I've seen them written in almost all possible ways (i.e., [Bb]ig[ -]([Oo]h?|[Oo]mega, [Ll]ittle[ -]([Oo]h?|[Oo]mega). In other words, the spelling is perhaps not the most important thing in your paper/report/essay. Perhaps you might want to consult your style manual if you want to be on the safe side. – Damkerng T. Dec 7 '16 at 18:00
  • @LeonMeier Ah well.. I only did enough maths to study physics. – Mick Dec 7 '16 at 18:11
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    It does appear that resp. is often used that way by German and French speakers writing in English; but the English word "respectively" does not express that meaning of German beziehungsweise. – StoneyB on hiatus Dec 7 '16 at 18:34
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Just because you are describing a lower-case letter doesn't mean that you have to express the name in lower case. If I was writing about upper-case letters, I would write it like I just did there, in lower case. I wouldn't write, "Let us now discuss UPPER CASE LETTERS" just because the letters being discussed are upper case.

The name of a thing isn't normally expected to be an example of that thing. It's perfectly reasonable to say that "diminutive" means "small", even though the word is long. Or to say, "He spoke in German" and to use the English word for German and not the German word for German.

If you are discussing a name in some technical context, like computers, case may be critical. HTML entity names, for example, use case to express whether the character represented is upper or lower case: "&aacute" is a small "a" with an acute accent while "&Aacute" is a capital "A" with an acute accent. But that's a special case. It's not that way because of grammar: it's that way because the inventors of the name thought it would be easier to use and remember that way.

  • Wasn't that clear? Sorry. The name does not have to be an example of the thing. It is perfectly valid to say "Small Omega". Just like it's perfectly valid to write "upper case letters" just like that, in lower case. Or to write the word "blood" with ink and not with blood. – Jay Dec 8 '16 at 5:21
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My opinion (i.e., I'm not an authority, and my opinion is not backed by references), I would say that the same rules for capitalization apply to both Big Omega and Little Omega. The reason you choose to capitalize or not capitalize the expression is not based on the case of the item you are referencing. You are choosing to capitalize or not capitalize because it is the title of a thing, and the context indicates whether the title of a thing should capitalized. So anywhere you would type "Big Omega" you should type "Little Omega", and anywhere you would type "big omega" you would type "little omega". The capitalization of the omega character itself is irrelevant.

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The noun gamma for the (capital) letter gamma and the noun gamma for the (minuscule) letter gamma are nouns of the same class, so formally they should be either both capitalised or not in running text. Of course if you are talking about both of them in context it is somewhat helpful for the reader to refer to them as Gamma and gamma respectively, even if that is not correct. You can justify either choice if needed. (Speaking with no authority at all, not even as a speaker of proper English.)

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