# Continuity problem

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• November 30th 2009, 04:41 PM
gixxer998
Continuity problem
Show that if f and g are uniformly continuous on a subset A of Reals, then f+g is uniformly continuous on A.
• November 30th 2009, 04:48 PM
Plato
Quote:

Originally Posted by gixxer998
Show that if f and g are uniformly continuous on a subset A of Reals, then f+g is uniformly continuous on A.

Note that $|(f+g)(x)-(f+g)(y)|\le |f(x)-f(y)|+|g(x)-g(y)|$