Answer to Question #336753 in Real Analysis for Uju

Question

(Cauchy criterion for limits of functions) Let D be a subset of R2 and (x0,y0) € R2 be such that D contains r nhbd of (x0, y0) \ {(x0, y0)} for some r >0 and let f: D to R be a function. Then the limit of f(x,y) as (x, y) tends to (x0, y0) exists if for every epsilon > 0, there is delta >0 such that (x,y),(u,v) € D intersection delta nhbd of (x0, y0) \{(x0, y0)} implies |f(x,y) - f(u,v)|< epsilon.

Answer 1

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