![]() The proof I found (which I do not understand) says: Let f_n be a uniform Cauchy sequence of functions, if we fix X=c in A, then f_n(c) is a simple Cauchy sequence of real numbers, and so it does converge. Now, for the question: my book states that a sequence of functions defined on a nonempty subset of the reals converges uniformly on A if an only if for every e>0, there exist a natural number N (which depends only on e), such that if m,n≥N, then |f_n(X)-f_m(X)| f_n is uniform Cauchy on A), my problem lies in the backwards one. Sorry if my question is going to be written without the usuals formal symbols, but I don't have any idea of how to write them. Compilation of Free online math resources.If your browser is so outdated or unusual that the linked advice doesn't work, consider these ideas.You will need to install a UserScript loader first.You will see formatted as in a textbook if the MathJax UserScript is installed and working. ![]() Type this as an example (replace the [- with [ when typing):
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