Hey, this was an interesting read for this underclassmen.Through 3 semesters of calculus, up to a first course in multi-variable calculus, one occurrence of arbitrary I’ve encountered is the allowance of arbitrary choice of axes in introductory physics, mostly concerning reference frames. Also, I recall Morris Kline’s Calculus: An Intuitive and Physical Approach as alluding often to arbitrariness when informing the reader (student) about mathematical conventions. I felt this use of “arbitrary” eased the process of coping with the way mathematics is presented by encouraging acceptance of mathematical methods before analysis. Oh and among texts I’ve come across, Sylvanus Thompson’s Calculus Made Easy is the most memorable paraphrase of “arbitrarily small.”
Looking forward to more reflections and insights Professor, cheers!

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