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## Main Question or Discussion Point

If I could use any polynomial up to degree ∞, then can I get a close fit to any continuous function?

I know that with a 4th degree polynomial you can get a pretty close fit to the sine function between 0 and 2pi (http://en.wikipedia.org/wiki/Curve_fitting#Fitting_lines_and_polynomial_curves_to_data_points)

So is it also true that you can fit a polynomial to any function if you use enough exponents?

I know that with a 4th degree polynomial you can get a pretty close fit to the sine function between 0 and 2pi (http://en.wikipedia.org/wiki/Curve_fitting#Fitting_lines_and_polynomial_curves_to_data_points)

So is it also true that you can fit a polynomial to any function if you use enough exponents?