I remarked that there does not seem to be a general rule whether one should use or not an "s" apostrophe for inequalities For example, we can encounter Hölder's inequality, but Minkowski or Sobolev inequality, Cauchy's inequality, but Cauchy-Schwarz inequality, etc. There seems however to be a rule to remove the "s" when there is more than one person referred to in the inequality, but the first example suggests that for simple names, the general rule is not obvious, if there is any. The same question could be addressed to for theorems, identities, or laws, but I do not know an example contradicting the $\textit{a priori}$ rule : one name, use "s", two or more names, do not use "s".
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asked Feb 23, 2016 at 9:02
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6$\begingroup$ I fear this is a duplicate of some other question. As a rule, I'd say "The Cauchy inequality" or "Cauchy's inequality", but I'm no native speaker. $\endgroup$– Loïc TeyssierFeb 23, 2016 at 9:14
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$\begingroup$ Several of the examples mentioned in this question are grammatically incorrect. As it stands, this does not seem related to math, but simply to English grammar (it should for example be the Cauchy-Schwartz inequality). $\endgroup$– Tobias KildetoftFeb 23, 2016 at 9:32
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2$\begingroup$ @TobiasKildetoft Nevertheless, Wikipedia uses "Poincare duality" without "the". $\endgroup$– Alex DegtyarevFeb 23, 2016 at 9:39
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1$\begingroup$ I'd say you may find a better answer in english.stackexchange.com $\endgroup$– Fernando MuroFeb 23, 2016 at 9:40
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1$\begingroup$ @AlexDegtyarev That is because "duality" is a concept. One can also just refer to "by duality", whereas it is not possible to just say "by inequality". $\endgroup$– Tobias KildetoftFeb 23, 2016 at 9:41
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