File:Illustration of discontinuity with sgn(x).svg

Summary

Description	English: Illustration that the signum function is not continuous at the point $x = 0$ with $ϵ = \frac{1}{2}$ and $δ = \frac{1}{2}$ .
Date	17 February 2017
Source	Own work
Author	Who2010
Other versions	$ϵ = \frac{1}{2}$ and $δ = \frac{1}{2}$ $ϵ = \frac{1}{2}$ and $δ = 1$ $ϵ = \frac{1}{2}$ and $δ = \frac{1}{2}$ and marked $x = \frac{δ}{2}$ $ϵ = \frac{3}{2}$ and $δ = 1$
SVG development InfoField	The SVG code is valid. This plot was created with Matplotlib.
Source code InfoField	Python code from matplotlib.patches import Rectangle import matplotlib.pyplot as plt import numpy as np def save_plot(filename, bound, eps, delta): f, ax = plt.subplots() ax.axhline(color="black") ax.axvline(color="black") ax.set_xlim(-bound,bound) ax.set_ylim(-2,2) ax.add_patch( Rectangle((-delta,-eps), 2delta, 2eps, edgecolor="black", alpha=0.6, linestyle="solid", facecolor="#dddddd", lw=1.5)) ax.plot([-bound,0],[-1,-1], color="blue") ax.plot([0,bound],[1,1], color="blue") ax.plot([-delta,0],[-1,-1], color="red", lw=2) ax.plot([0,delta],[1,1], color="red", lw=2) ax.plot([0,0],[1,-1], "o", color="white") ax.plot([0], [0], "o", color="green") plt.savefig(filename) save_plot("Illustration of discontinuity with sgn(x).svg", bound=2, eps=0.5, delta=0.5) save_plot("Illustration of discontinuity with sgn(x) (version 2).svg", bound=2, eps=0.5, delta=1)

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