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I am currently drafting a paper and there are some bits of notation that I need for the proofs, but not to state any of the results. I am debating whether I should I introduce these bits of notation before the results and the proofs, or within the proofs themselves. These bits of notation are used in all proofs in the draft (i.e, a total of three different proofs). Hence, I can:

  1. Introduce the notation only once, before the results and the proofs.
  2. Introduce the notation only once, within the first of the three proofs.
  3. Introduce the notation three times, once within each of the three proofs.

What would you do?

EoDmnFOr3q
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    How about: 4. After results but before proofs? –  Jan 04 '23 at 21:33
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    Unless you need some context from the proof to define the notation, better to define the notation before the proof. (Context might be needing to know something is uniquely determined, so some initial result is needed for the notation to make sense.) – Thomas Andrews Jan 04 '23 at 21:34
  • Thank you for your comments. I do not like (4), is I want my proofs to directly follow the statement. I may stick to (1). – EoDmnFOr3q Jan 04 '23 at 21:41
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    I agree with @MarianoSuárez-Álvarez's comment, but I think the problem with repeating the definition can be mitigated (though not completely eliminated) by giving the definition in the first proof and then saying, when repeating the definition in later proofs, "As in the proof of Theorem 1, we define ...." I'd still prefer option 1, giving the definition just once, before the theorems, with a statement that the definition is given in advance because it will be needed several times. – Andreas Blass Jan 05 '23 at 01:51

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