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I want to write a private research paper, which aims to have an academic level. I'm not yet a participant of academia, that's why the paper is "private", in case you wondered. Anyways, since I have chosen an authors suggestions for further research as main topic, I'm going to use their definitions. So not same text, but same math symbols. (a bit more formal, though) Nevertheless, there is very much to define and it feels just wrong to "copy", even thought you can't really define it in another reasonable way. How do you deal with somewhat equal introductions? Should I care if I use almost all predefined terms of another paper? Should I write the possibly huge boilerplate or just reference the paper X?

Overall it's just one question: What's the proper way of writing a following paper?

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Just tell up front that the terminology/notation used comes from the source you used (probably they do have a book or summarizing paper which explains it clearly). Nothing wrong with that.

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