The function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:\mathbb {R} \to \mathbb {R} }"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo>:</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow><mo stretchy="false">→<!-- → --></mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle f:\mathbb {R} \to \mathbb {R} }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e3a10a3ad05781f5cf9c2d875a02227e21a8448" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:10.186ex; height:2.509ex;" alt="{\displaystyle f:\mathbb {R} \to \mathbb {R} }"></span> with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={\begin{cases}\sin \left({\tfrac {1}{x}}\right)&amp;x\neq 0\\0&amp;x=0\end{cases}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mi>sin</mi><mo>⁡<!-- ⁡ --></mo><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mi>x</mi></mfrac></mstyle></mrow><mo>)</mo></mrow></mtd><mtd><mi>x</mi><mo>≠<!-- ≠ --></mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>x</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle f(x)={\begin{cases}\sin \left({\tfrac {1}{x}}\right)&amp;x\neq 0\\0&amp;x=0\end{cases}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3343d675c76f3d781fa0efd79c131b4519858c67" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:24.686ex; height:6.176ex;" alt="{\displaystyle f(x)={\begin{cases}\sin \left({\tfrac {1}{x}}\right)&amp;x\neq 0\\0&amp;x=0\end{cases}}}"></span> together with a rectangle around <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (0,0)}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle (0,0)}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d630d3e781a53b0a3559ae7e5b45f9479a3141a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:5.168ex; height:2.843ex;" alt="{\displaystyle (0,0)}"></span> with width <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\delta }"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>2</mn><mi>δ<!-- δ --></mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle 2\delta }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1eb07ea6b418948bdfb59fcfd066dec83d281f7f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.211ex; height:2.343ex;" alt="{\displaystyle 2\delta }"></span> and height <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\epsilon }"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>2</mn><mi>ϵ<!-- ϵ --></mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle 2\epsilon }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c92b38f8fa5386a30fab561c41b983c3384cd52" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.107ex; height:2.176ex;" alt="{\displaystyle 2\epsilon }"></span> for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon ={\tfrac {1}{2}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ϵ<!-- ϵ --></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \epsilon ={\tfrac {1}{2}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9dadb650510651fed5ba23f7adc2cc42172b99b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.171ex; width:5.701ex; height:3.509ex;" alt="{\displaystyle \epsilon ={\tfrac {1}{2}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta ={\tfrac {1}{5}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>δ<!-- δ --></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>5</mn></mfrac></mstyle></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \delta ={\tfrac {1}{5}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21abba11e04c9db522e4324f52749a599790aaf2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.338ex; width:5.805ex; height:3.676ex;" alt="{\displaystyle \delta ={\tfrac {1}{5}}}"></span>.
<a rel="nofollow" class="external text" href="http://kulla.me">Stephan Kulla</a> (<a href="//commons.wikimedia.org/wiki/User:Stephan_Kulla" title="User:Stephan Kulla">User:Stephan Kulla</a>)
2017-04-10
<span class="int-own-work" lang="en">Own work</span>