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"A definition is a statement of the meaning of a term... In mathematics, a definition is used to give a precise meaning to a new term, instead of describing a pre-existing term." - Wikipedia.

Suppose, I have mentioned a standard definition of a mathmatical term, exactly copied from a textbook, in my research article. May it be considered as a plagarism?

Similarly, I use an earlier proved theorem in my article. I mentioned its statement exactly as it is stated in the original artile along with its proper reference. May it be considered as a plagarism?

Is there any standard rule regarding plagarism?

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  • Whenever I read about the topic of plagiarism, my thought goes to the legions of mathematicians who had to come up with a different way of expressing the definition of topological space :-)
    – Massimo Ortolano
    Commented Nov 15, 2016 at 19:29

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Suppose, I have mentioned a standard definition of a mathematical term, exactly copied from a textbook, in my research article. May it be considered as a plagarism?

If the term is really standard, no plagiarism has been committed. But cite the source you got the definition from. Even such a standard term as the set of natural numbers can be introduced differently: either including zero or not. There are also notational reasons: as an extreme example, there are researchers in the wild who don't associate ℕ₀ with the former and ℕ₊ with the latter (or at least, they say they cannot parse these symbols and reject your paper on these grounds).

Similarly, I use an earlier proved theorem in my article. I mentioned its statement exactly as it is stated in the original article along with its proper reference. May it be considered as a plagarism?

The same applies here. If the theorem is really standard, no plagiarism has been committed. Again, cite the source. Some theorems have subtleties (the zero, the empty set, up to isomorphism, etc.) which you understand only when you dig deep into the cited paper.

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Plagiarism is passing someone's text as your own. If you quote the sentence and cite the source, you are fine. If you quote a very standard definition or a very famous theorem (e.g. Pythagoras), you are fine as well. Make sure your writing clearly separates the facts you borrow (and cite), and the things you propose yourself. If this simple rule is followed, you will have no problems with plagiarism.

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