This paragraph has nothing to do with numerics. It is about the fact that continuous functions can not be approximated globally by polynomials. So you need to restrict to intervals for reasons of mathematical theory. This is totally unrelated to the numerical issues, which are nowhere even acknowledged.
This paragraph has nothing to do with numerics. It is about the fact that continuous functions can not be approximated globally by polynomials. So you need to restrict to intervals for reasons of mathematical theory. This is totally unrelated to the numerical issues, which are nowhere even acknowledged.