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In publications the wording often resembles the following: "We found that our results followed what we found in our previous research." I am now writing a publication alone, with no co-authors. Is it bad form to use "my" in place of "our" in such cases?

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In my field, it is not common to use first singular personal pronoun even when the paper has only one author. Using 'we' and 'our' in this case means that the author refers to the reader and him/herself.

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    Along those lines, the only cases I have seen "I" or "my" used in publications in my field (mathematics) were when including the reader would be condescending. For example [assuming there is only one author] "We believe a stronger statement holds, but I have been unable to prove it using the methods of this paper." – Tom Bachmann Jun 26 '14 at 8:04
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    Also "I" should be used in the acknowledgements, as in "I thank X for A and Y for B...". The reason is the same, it's a personal statement by the author, where including the reader would be inappropriate. – Jan Johannsen Jun 26 '14 at 9:20
  • A common alternative to the above cases is to use 'the author' instead of 'I'. – adipro Jun 26 '14 at 10:34

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