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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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closed as off-topic by Fernando Muro, Moritz Firsching, Alex Degtyarev, abx, Carlo Beenakker Feb 23 '16 at 9:45

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Fernando Muro, Moritz Firsching, Alex Degtyarev, abx, Carlo Beenakker
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ 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 Teyssier Feb 23 '16 at 9:14
  • $\begingroup$ 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 Kildetoft Feb 23 '16 at 9:32
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    $\begingroup$ @TobiasKildetoft Nevertheless, Wikipedia uses "Poincare duality" without "the". $\endgroup$ – Alex Degtyarev Feb 23 '16 at 9:39
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    $\begingroup$ I'd say you may find a better answer in english.stackexchange.com $\endgroup$ – Fernando Muro Feb 23 '16 at 9:40
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    $\begingroup$ @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 Kildetoft Feb 23 '16 at 9:41