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Summary

Description	English: Illustration that the signum function is not continuous at the point $x=0$ with $\epsilon ={\tfrac {1}{2}}$ and $\delta ={\tfrac {1}{2}}$ .
Date	17 February 2017
Source	Own work
Author	Who2010
Other versions	$ϵ = 1 2 {\displaystyle \epsilon ={\tfrac {1}{2}}} and δ = 1 2 {\displaystyle \delta ={\tfrac {1}{2}}}$ $\epsilon ={\tfrac {1}{2}}$ and $\delta ={\tfrac {1}{2}}$ $ϵ = 1 2 {\displaystyle \epsilon ={\tfrac {1}{2}}} and δ = 1 {\displaystyle \delta =1}$ $\epsilon ={\tfrac {1}{2}}$ and $\delta =1$ $ϵ = 1 2 {\displaystyle \epsilon ={\tfrac {1}{2}}} and δ = 1 2 {\displaystyle \delta ={\tfrac {1}{2}}} and marked x = δ 2 {\displaystyle x={\tfrac {\delta }{2}}}$ $\epsilon ={\tfrac {1}{2}}$ and $\delta ={\tfrac {1}{2}}$ and marked $x={\tfrac {\delta }{2}}$ $ϵ = 3 2 {\displaystyle \epsilon ={\tfrac {3}{2}}} and δ = 1 {\displaystyle \delta =1}$ $\epsilon ={\tfrac {3}{2}}$ and $\delta =1$
SVG development InfoField	The SVG code is valid. This plot was created with Matplotlib. Category:Valid SVG created with Matplotlib code#Illustration%20of%20discontinuity%20with%20sgn(x).svg
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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Category:CC-Zero#Illustration%20of%20discontinuity%20with%20sgn(x).svg Category:Self-published work

Category:Continuity (functions) Category:Signum function

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

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