Application Essay and Cantor Sets

[CesareBorgia]

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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.)

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<p>Yeah, I hear you. Euler is even more problematic than Lebesgue.</p>

<p>The biggest problem is when mathematicians can’t even agree on equivalent definitions for something (e.g. rings a.k.a rings with unity a.k.a associative rings).</p>

<p>Multiple equivalent definitions are usually very interesting, as they link 2 often completely different ways of thinking of something (e.g. Heine-Borel or construction of R by Cauchy sequences and construction of R by Dedekind cuts.)</p>