File:Illustration of discontinuity with sgn(x) (version 4).svg

Summary

Description	English: This Illustration shows that signum function can fulfil the $ϵ$ - $δ$ -criterion at the point $x_{0} = 0$ when $ϵ$ is big enough. Here $ϵ = \frac{3}{2}$ is choosen.
Date	13 March 2017
Source	Own work
Author	Stephan Kulla (User:Stephan Kulla)
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 bound=2 eps=1.5 delta=1 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="green", lw=2) ax.plot([0,delta],[1,1], color="green", lw=2) ax.plot([0,0],[1,-1], "o", color="white") ax.plot([0], [0], "o", color="green") plt.savefig("Illustration of discontinuity with sgn(x) (version 4).svg")

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