In brief, I’ve had virtually no mathematical education prior to seven months ago. What I did know had largely been the result of watching Khan Academy. Seven months ago I began a precalculus textbook, and now I am almost done with Larson’s Calculus. I love math far more than I ever would have imagined. However, every time I try to get into another textbook, something more advanced than Larson’s books, I get totally flummoxed by the notation.
It seems to me that every book I can find is written for people who already know the notation; those books that do define the notation do so with great paucity of detail. In other words, if you don’t know it, you’re screwed.
The most perplexing notation is thus
Definition 2.1 Let $fcolon Dsubseteqmathbb{R}tomathbb{R}$ be a function. Then $f$ is uniformly continuous if for every $epsilon>0$, there exists a $delta$ depending only on $epsilon$ such that if $|x-y|<delta$ then $|f(x)-f(y)|<epsilon$.
I’ve scoured dozens of books, but none want to explain what is meant by this. The arrow symbol does not appear in lists of symbols, nor can I find a clear explanation online. This is just about the biggest hurdle preventing me from moving on to real – and hopefully very soon, complex – analysis textbooks. Please, keep in mind that I’ve never really had any mathematical experience beyond the books I’ve read. Please explain how I can interpret this symbol.