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Let A be a partition of a set, and B a refinement of A. Fill in the blanks: A is a __________ of B. I know that A is coarser than B, but how does one turn that into a noun?

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  • $\begingroup$ Good question. It's possible that they want quotient, though that's a slightly sloppy usage. $\endgroup$ Mar 27, 2015 at 12:56
  • $\begingroup$ Approximation may be viable in some contexts. Not this one, I'm afraid. $\endgroup$
    – AlexR
    Mar 27, 2015 at 12:56
  • $\begingroup$ coarsification? $\endgroup$
    – JMP
    Mar 27, 2015 at 13:00
  • $\begingroup$ but how does one turn that into a noun? - drop the first 't' to get 'hat' $\endgroup$
    – JMP
    Mar 27, 2015 at 13:02
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    $\begingroup$ Just found this. "Coarsening" does exist on the literature. $\endgroup$ Mar 27, 2015 at 13:11

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The term I would use is "coarsening," as mentioned in the comments. This shows up, for example, in discussions of common knowledge and Aumann's agreement theorem.

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  • $\begingroup$ +1 for the Aumann reference. This is an old question... $\endgroup$ Nov 7, 2017 at 2:18

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