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Example 8.2.2 (e): Uniform Convergence on R

Can you find a uniformly convergent sequence for all real numbers?

We saw an example of a sequence fn(x) = x/n that converges uniformly on any compact subset of R but fails to converge on all of R. Our other examples were all defined on bounded intervals, so finding a uniformly convergent sequence for all real numbers is a valid question.

Well, then ... go for it!

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