that’s because you can’t “see” the The Weierstrass function in the first place, because our eyes cannot see functions that are everywhere (or almost everywhere) nondifferentiable. When you look at a picture of the The Weierstrass function on google image search, you are looking at a piecewise linear approaximation of it. Hence, if you compare what you see on google image search with a piecewise linear approaximation of it, they will look the same…
I’m sort of annoyed by your insistence that the Weierstrass function cannot be approximated by piecewise linear functions when, after all, it is the limit of a series of piecewise linear functions.
that’s because you can’t “see” the The Weierstrass function in the first place, because our eyes cannot see functions that are everywhere (or almost everywhere) nondifferentiable. When you look at a picture of the The Weierstrass function on google image search, you are looking at a piecewise linear approaximation of it. Hence, if you compare what you see on google image search with a piecewise linear approaximation of it, they will look the same…
I’m sort of annoyed by your insistence that the Weierstrass function cannot be approximated by piecewise linear functions when, after all, it is the limit of a series of piecewise linear functions.
RTFM.