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<p>Perhaps. I find the constant ambiguity in mathematical “definitions” obnoxious. I can think of 5 definitions off of the top of my head that can be defined in multiple ways. It’s the same thing for names of theorems - how many theorems are named the “Lebesgue Theorem”? Even names that would seem to be very specific, such as the Riesz-Fischer Theorem, are different theorems depending on the source. We need some kind of committee that would officially determine definitions and names of theorems. (I must admit that definitions that are equivalent, such as the multiple defs for compactness, don’t bother me as much.)</p>
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<p>I wouldn’t send in any extra recs unless they’re really strong and lend something to your application that previous recs wouldn’t have.</p>