On how Weierstrass Functions lack a derivative, have infinite arc length on finite intervals, have  graphs of Hausdorff Dimension strictly greater than 1, and, are not monotonic on any interval

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Entertainment: Work I did, proving Weierstrass Functions lacks a derivative, at any point. Are not monotonic, on any interval. On any finite interval, have infinite arc length. And, their graphs are of Hausdorff Dimension strictly greater than one, which conflicts with the view most of us have about the graphs of functions.

Wrote this in a simplistic fashion, so as to be understood by undergrads in STEM fields, and not just math undergrads, grad students.

  • My proof that Weierstrass Functions lacks a derivative, as a .docx file. 

  • My proof that Weierstrass Functions lacks a derivative, as a .pdf file. For reasons I do not know, images came out funky.
A graph of the Weierstrass Function, though as it oscillates infinitely, a "perfect" graph does not exist.


A graph I made, of the Weierstrass Function. Had to cut the sum, at 250. Software makes it impossible for a sum to go to infinity.

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© dino 2018