[kccqzy]

Polynomials with large degrees are continuous. It's just that they can still change by a large amount (i.e. having a large derivative) when the input is changed by a small amount.

I invite you to construct the Lagrange polynomial (i.e. interpolating polynomial) for points on a nice, simple curve with some noise. They will, by definition, pass through every point given, and yet it will likely behave very badly outside the range of the given points.

[tylerhou]

There is nothing wrong with using a non-linear model, though; x^2 or x^3 regressions make sense on many datasets.

Non-continuous is also not the perfect terminology, but I argue that it is more precise than non-linear: the chief idea being that the model "changes unpredictably."

[kccqzy]

Sure you can argue things however you want, if you also decide to ignore hundreds of years of mathematical terminology.