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WaterPoloGoat
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Homework Statement
We know that f is uniformly continuous.
For each n in N, we define fn(x)=f(x+1/n) (for all x in R).
Show that fn converges uniformly to f.
Homework Equations
http://en.wikipedia.org/wiki/Uniform_convergence
The Attempt at a Solution
I know that as n approaches infinity, that fn(x)=f(x), which implies that fn converges to f.
I'm currently trying to apply the fact that if fn is uniformly convergent, then
limn->infinity Sup {fn(x): x in R}=0.
But I keep getting stuck on the fact that there's an function in the definition of fn i.e., fn(x)=f(x+1/n). Is there a way to work with it?
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