8.2. Uniform Convergence
Example 8.2.2 (e): Uniform Convergence on R
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!