User:IssaRice/Adverb negative adjective: Difference between revisions

Latest revision as of 05:10, 7 February 2019

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.

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 * "[[wikipedia:Recursively inseparable sets|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)
+* <math>\omega</math>-incomplete (not <math>\omega</math>-complete) and <math>\omega</math>-inconsistent (not <math>\omega</math>-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.