Visualization of the epsilon-delta-continuity with 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} :x\mapsto {\tfrac {1}{3}}x}"><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><mo>:</mo><mi>x</mi><mo stretchy="false">↦<!-- ↦ --></mo><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle></mrow><mi>x</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle f:\mathbb {R} \to \mathbb {R} :x\mapsto {\tfrac {1}{3}}x}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2d5a6fa501c18d354340d5a8855af9fba3eb9b5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.338ex; width:20.055ex; height:3.676ex;" alt="{\displaystyle f:\mathbb {R} \to \mathbb {R} :x\mapsto {\tfrac {1}{3}}x}"></span> and the point <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 x_{0}=1}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn></mrow></msub><mo>=</mo><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle x_{0}=1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dd9ebf815134d1288a48491ff1529f06f477112" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:6.645ex; height:2.509ex;" alt="{\displaystyle x_{0}=1}"></span>. The 2epsilon-2delta-rectangle is drawn 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 \epsilon =1}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ϵ<!-- ϵ --></mi><mo>=</mo><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \epsilon =1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6cea33fb1374a6510eb3a7062b52245de1b33ee" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:5.205ex; height:2.176ex;" alt="{\displaystyle \epsilon =1}"></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 =2}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>δ<!-- δ --></mi><mo>=</mo><mn>2</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \delta =2}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/301eb57c3fb2851d0ddde618d93bcbdad410400a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:5.31ex; height:2.343ex;" alt="{\displaystyle \delta =2}"></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>)
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