User:IssaRice/Adverb negative adjective

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Sometimes the pattern adverb followed by (negative adjective) is used in mathematical terms to mean negative followed by (adverb adjective), and I find this confusing. Here are two examples:

  • "absolutely divergent" to mean "not absolutely convergent" see this comment by Terence Tao. -- this sounds like the series does the diverging thing in an absolute manner, which makes no sense.
  • "recursively inseparable" to mean "not recursively separable" (equivalently, "not separable by a recursive set") -- this sounds like there is some recursive/computable process that "inseparates" the two sets, which makes no sense
  • "negation incomplete" to mean "not negation-complete" (see Peter Smith's Godel book)
  • \omega-incomplete (not \omega-complete) and \omega-inconsistent (not \omega-consistent), although these are a bit odd because the negation versions are defined first.

This one is slightly different:

  • "non-recursive enumerability" to mean "not (recursively enumerable)" -- see Cutland p. 130.