I am writing a paper, in which I must include a definition of a particular mathematical structure. It's a structure with which very few people would be familiar, thus I wish to include it verbatim, as opposed to citing it. Rewriting it in my own words would only obscure the meaning. Putting a long mathematical definition (perhaps half a page) in quotes looks bizarre and messes up the type setting. Is there a standard way to indicate the definition is cited, whilst avoiding any appearance of plagiarism?

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    Read other papers in your field of mathematics - some of them must run into similar problems. – Oswald Veblen Sep 3 '14 at 1:35

Immediately before the definition, you could say "Quoting verbatim from [source], we define a [whatever-it-is] as follows:"

That is, in general, thinking in terms of honesty/forthrightness is an excellent guide.

  • Thanks, just a follow-up. Would you say this behaviour is common / standard practise? And how closely do I have to stick to the original before it's a misquote (i.e. can I change formatting, the order of the arguments, fix typos)? – jhoyla Sep 2 '14 at 21:56
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    If you fix typos and change format, then say "essentially verbatim", rather than "verbatim". And, yes, the behavior I recommend is common practice, not to mention inescapable. – paul garrett Sep 2 '14 at 22:17
  • Beware if you later put the paper on the arXiv, though. It might say "substantial text overlap with..." – Flounderer Sep 3 '14 at 1:15
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    In my experience it is not common to see math papers state "quoting verbatim from ...". One simply references the definition, as if it was not a direct quote, with an attribution to the paper where the definition originated. This is not considered plagiarism in mathematics. – Oswald Veblen Sep 3 '14 at 1:33
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    @Flounderer: if quoting a few definitions leads to the "substantial text overlap" warning, one should rethink whether the entire paper is worthwhile. Also, I wish more people would read the arXiv help document linked above to see what that automatically generated comment really is intended to mean. – Willie Wong Sep 3 '14 at 11:00

This is common practice in mathematics. Definitions are not normally thought of as containing creative content, and if you need to use exactly the same definition as the previous paper, you use the same words. As far as I know, no mathematician considers this to be plagiarism of any kind, provided an appropriate citation is given. Quotation marks or block quotes are not used, because, as you say, it would look weird.

Some phrases you might use:

We define, as in [4]:

The following definition is taken from [4]:

We follow [4] by defining:

We use the definition from [4], which we include here for the reader's convenience:

Then format the definition as you normally would. Minor paraphrases and spelling/grammar fixes that do not change the meaning are also fine. If you fix a typo that makes a mathematical difference (e.g. the original author wrote 2 but from context obviously meant 4) then you should point it out explicitly, but this is more for mathematical correctness than citation practice.

Note that if you are publishing in a non-mathematics journal, standards might vary, and you might have to use quotes or otherwise format in some way that would look weird to a mathematician.

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    Another common practice is that one usually only cites unfamiliar or recent definitions. Definitions that "everyone knows" are often stated with no citation at all. – Oswald Veblen Sep 3 '14 at 1:34
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    It might be an over-statement to claim that definitions have no creative content. In some situations, finally coming to an apt definition can be a large part of the work, depending how one couches things. – paul garrett Sep 3 '14 at 12:09

If you define terms in a "Definition" environment, then you may state the reference after the heading. For example:

Definition 2 (Noche, 2014). A real number x is said to be small if 0 < x < 1.

  • A minor point: I think it would be more typical to omit the `and only if' in a mathematical definition like this. – Shane O Rourke Sep 3 '14 at 19:51
  • I agree. I've edited the post. – Joel Reyes Noche Sep 4 '14 at 0:26

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