Jump to navigation
Jump to search


General
Display information for equation id:math.228714.3 on revision:228714
* Page found: Pointwise convergence (eq math.228714.3)
(force rerendering)Cannot find the equation data in the database. Fetching from revision text.
Occurrences on the following pages:
Hash: e4b3c72b72bd32f819c8ecc477bc2c78
TeX (original user input):
\lim_{n\rightarrow\infty}\,\sup\{\,\left|f_n(x)-f(x)\right|: x\in\mbox{the domain}\,\}=0.
TeX (checked):
\lim _{n\rightarrow \infty }\,\sup\{\,\left|f_{n}(x)-f(x)\right|:x\in {\mbox{the domain}}\,\}=0.
LaTeXML (experimental; uses MathML) rendering
MathML (6.031 KB / 1.231 KB) :

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\lim_{{n\rightarrow\infty}}\,\sup\{\,\left|f_{n}(x)-f(x)\right|:% x\in{\mbox{the domain}}\,\}=0.}" display="inline">
<semantics id="p1.1.m1.1a">
<mrow id="p1.1.m1.1b">
<mpadded width="+1.7pt" id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">
<munder id="p1.1.m1.1.28a" xref="p1.1.m1.1.28.cmml">
<mo movablelimits="false" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">lim</mo>
<mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
<mi id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">n</mi>
<mo id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml">→</mo>
<mi mathvariant="normal" id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml">∞</mi>
</mrow>
</munder>
</mpadded>
<mo movablelimits="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">sup</mo>
<mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
<mo rspace="4.2pt" stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">{</mo>
<mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">|</mo>
<msub id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">
<mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">f</mi>
<mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">n</mi>
</msub>
<mrow id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
<mo stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">(</mo>
<mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">x</mi>
<mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">-</mo>
<mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">f</mi>
<mrow id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
<mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">(</mo>
<mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">x</mi>
<mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">)</mo>
</mrow>
<mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">|</mo>
<mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">:</mo>
<mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">x</mi>
<mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">∈</mo>
<mpadded width="+1.7pt" id="p1.1.m1.1.22" xref="p1.1.m1.1.22b.cmml">
<mtext id="p1.1.m1.1.22a" xref="p1.1.m1.1.22b.cmml">the domain</mtext>
</mpadded>
<mo stretchy="false" id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">}</mo>
</mrow>
<mo id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">=</mo>
<mn id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">0</mn>
<mo id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">.</mo>
</mrow>
<annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
<cerror id="p1.1.m1.1d">
<csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
<apply id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">
<csymbol cd="ambiguous" id="p1.1.m1.1.28.1.cmml" xref="p1.1.m1.1.28">subscript</csymbol>
<limit id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
<apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
<ci id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2">→</ci>
<ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">𝑛</ci>
<infinity id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3"/>
</apply>
</apply>
<csymbol cd="latexml" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">supremum</csymbol>
<cerror id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
<csymbol cd="ambiguous" id="p1.1.m1.1.6a.cmml" xref="p1.1.m1.1.6">fragments</csymbol>
<ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">{</ci>
<ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">|</ci>
<apply id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">
<csymbol cd="ambiguous" id="p1.1.m1.1.29.1.cmml" xref="p1.1.m1.1.29">subscript</csymbol>
<ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝑓</ci>
<ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">𝑛</ci>
</apply>
<cerror id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
<csymbol cd="ambiguous" id="p1.1.m1.1.2a.cmml" xref="p1.1.m1.1.2">fragments</csymbol>
<ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">(</ci>
<csymbol cd="unknown" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">x</csymbol>
<ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">)</ci>
</cerror>
<minus id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
<csymbol cd="unknown" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">f</csymbol>
<cerror id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
<csymbol cd="ambiguous" id="p1.1.m1.1.3a.cmml" xref="p1.1.m1.1.3">fragments</csymbol>
<ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">(</ci>
<csymbol cd="unknown" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">x</csymbol>
<ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">)</ci>
</cerror>
<ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">|</ci>
<ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">:</ci>
<csymbol cd="unknown" id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">x</csymbol>
<in id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
<ci id="p1.1.m1.1.22b.cmml" xref="p1.1.m1.1.22">
<mpadded width="+1.7pt" id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">
<mtext id="p1.1.m1.1.22a.cmml" xref="p1.1.m1.1.22">the domain</mtext>
</mpadded>
</ci>
<ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">}</ci>
</cerror>
<eq id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25"/>
<cn type="integer" id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">0</cn>
<ci id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">.</ci>
</cerror>
</annotation-xml>
<annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle\lim_{{n\rightarrow\infty}}\,\sup\{\,\left|f_{n}(x)-f(x)\right|:%
x\in{\mbox{the domain}}\,\}=0.}</annotation>
</semantics>
</math>
SVG (18.104 KB / 6.544 KB) :
SVG with PNG fallback (MathML can be enabled via browser plugin) rendering
MathML (1.862 KB / 587 B) :

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \lim _{n\rightarrow \infty }\,\sup\{\,\left|f_{n}(x)-f(x)\right|:x\in {\mbox{the domain}}\,\}=0.}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<munder>
<mo movablelimits="true" form="prefix">lim</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
<mo stretchy="false">→<!-- → --></mo>
<mi mathvariant="normal">∞<!-- ∞ --></mi>
</mrow>
</munder>
<mspace width="thinmathspace" />
<mo movablelimits="true" form="prefix">sup</mo>
<mo fence="false" stretchy="false">{</mo>
<mspace width="thinmathspace" />
<mrow>
<mo>|</mo>
<mrow>
<msub>
<mi>f</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>n</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>−<!-- − --></mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>|</mo>
</mrow>
<mo>:</mo>
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mtext>the domain</mtext>
</mstyle>
</mrow>
<mspace width="thinmathspace" />
<mo fence="false" stretchy="false">}</mo>
<mo>=</mo>
<mn>0.</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \lim _{n\rightarrow \infty }\,\sup\{\,\left|f_{n}(x)-f(x)\right|:x\in {\mbox{the domain}}\,\}=0.}</annotation>
</semantics>
</math>
SVG (16.115 KB / 6.214 KB) :
PNG (0 B / 8 B) :
Translations to Computer Algebra Systems
Translation to Maple
In Maple:
Translation to Mathematica
In Mathematica:
Similar pages
Calculated based on the variables occurring on the entire Pointwise convergence page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results