Nonlinear operators might not be compatible with addition, i.e. we find arguments <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 v_{3}=v_{1}+v_{2}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msub><mo>=</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle v_{3}=v_{1}+v_{2}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4697a1d51155b78f0d6d22737b92e189b9cd32ca" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:12.484ex; height:2.343ex;" alt="{\displaystyle v_{3}=v_{1}+v_{2}}"></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(v_{3})\neq f(v_{1})+f(v_{2})}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msub><mo stretchy="false">)</mo><mo>≠<!-- ≠ --></mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle f(v_{3})\neq f(v_{1})+f(v_{2})}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/970b7f6ec1b8058cb132c515bf0136c5fe7f11f0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:21.748ex; height:2.843ex;" alt="{\displaystyle f(v_{3})\neq f(v_{1})+f(v_{2})}"></span>. This property can be condensed in <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(v_{1}+v_{2})\neq f(v_{1})+f(v_{2})}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo>≠<!-- ≠ --></mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle f(v_{1}+v_{2})\neq f(v_{1})+f(v_{2})}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/812284a7105b475d65a0c09436e0ec6c88e784f3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:26.77ex; height:2.843ex;" alt="{\displaystyle f(v_{1}+v_{2})\neq f(v_{1})+f(v_{2})}"></span> for some vectors <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 v_{1},v_{2}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle v_{1},v_{2}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77e8c76551eb136c37e15ec127089c2a0e6d1a77" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:5.398ex; height:2.009ex;" alt="{\displaystyle v_{1},v_{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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