## Example 8.2.2 (e): Uniform Convergence on R

We saw an example of a sequence *f _{n}(x) = x/n* that
converges uniformly on any compact subset of

*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.*

**R**Well, then ... go for it!