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Perhaps this question fits on an English Language wiki, but it is more likely a question that mathematicians would know the answer to.

I know that all uses of the words "Theorem" and "Lemma" should be capitalized, but what about the word "lemmata"?

My thinking is that if you make the analogy that each Lemma is behaving like a pronoun (so you have Lemma Bob and Lemma Cthulhu), then "lemmata" is like the word people, which wouldn't be capitalized.

Thanks!

user139388
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    In Dr. Seuss, you've got Thing One and Thing Two. I think you'd say, "Call in Things One and Two," wouldn't you? It's not true that all uses of the words "theorem" and "lemma" should be capitalized; just those cases where they refer to a particular named theorem or lemma. – mjqxxxx Apr 06 '14 at 18:30
  • @mjqxxx I enjoyed that colorful response! But thinking about the word "university", several sources seem to indicate that it not be capitalized when appearing alone, but that it should when appearing as part of a name like "University of Atlantis". What would the convention be for "universities of Atlantis and Valhalla", since in this case the word functions as a descriptor more than a name component. Certainly, if we can determine what Dr. Seuss would have thought I shant argue with it! – user139388 Apr 06 '14 at 18:35
  • @user139388 The convention there should be to capitalize "universities," but for a different reason: uncapitalized, it is ambiguous whether the phrase refers to all universities within Atlantis and Valhalla, or just the pair. Unfortunately having a possessive in the phrase ruins the exact analogy. "Lemmas 1 and 2" or "Lemmata 1 and 2" are not so ambiguous. – Gyu Eun Lee Apr 06 '14 at 18:54
  • @kigen Ah, I see your point. If the phrase is "the following lemmata", what would the approach be? Thanks! – user139388 Apr 06 '14 at 18:56
  • @user139388 Uncapitalized. "lemmata" (or "lemmas") in that context is not a proper noun. You need to give a name (typically a number, a label in any case) to your lemmas/lemmata to make reference to distinct ones and to use them as proper nouns. – Gyu Eun Lee Apr 06 '14 at 19:01
  • Okay, that makes sense. Thanks :) – user139388 Apr 06 '14 at 19:03

1 Answers1

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We may define "lemmata" as the plural of lemma. It is "a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself". However, nowhere is it mentioned if "lemma" is a proper noun.

Let us explore that from a purely English perspective. Wikipedia: "A proper noun is a noun that in its primary application refers to a unique entity". Is a lemma a unique entity? Consider Zorn's Lemma. We capitalize the "l" in "Zorn's Lemma" since it is unique. However, when referring to a general lemma, we don't capitalize the "l". Therefore, we may conclude that a lemma is a proper noun if it is unique. Lemmata in general are not unique. For example, we may consider the set $\{\text{Lemmata in Mathematics}\}$. An arbitrary choice of two lemmas would allow us to write "Lemmata", since the chosen lemmas are two unique lemmas in $\{\text{Lemmata in Mathematics}\}$. If we were to consider the set of lemmata proposed by a single person, say Darth Vader, then we would capitalize the lemmata to get "Varth's Lemmata $\subset\{\text{Lemmata in Mathematics}\}$", the reason being that lemmata are proper nouns if they are unique, in this case meaning made by Vader. In your example, you've got Lemma Bob and Lemma Cthulhu, which you can rewrite as Cthulhu and Bob's Lemmata.

  • Okay, I think I see. So any time I refer to something like "Lemma 6.2", I'm precisely specifying a unique entity, and should capitalize. If I say, "the following Lemmata", I'm uniquely specifying the collection of Lemmata that follow, say Darth's, and should also capitalize. Is that right? Thanks for the well thought out answer btw! – user139388 Apr 06 '14 at 19:01
  • @user139388 Yes, that's right. –  Apr 06 '14 at 19:01