<html><head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Math.SE extracted Samples</title>
<style id="CHTML-styles">
mjx-math {
display: inline-block;
line-height: 0;
text-align: left;
text-indent: 0;
font-style: normal;
font-weight: normal;
font-size: 100%;
font-size-adjust: none;
letter-spacing: normal;
word-wrap: normal;
word-spacing: normal;
white-space: nowrap;
direction: ltr;
padding: 1px 0;
}
mjx-chtml.MJX-DISPLAY {
display: block;
text-align: center;
margin: 1em 0;
}
mjx-chtml.MJX-DISPLAY mjx-math {
padding: 0;
}
mjx-chtml[justify="left"] {
text-align: left;
}
mjx-chtml[justify="right"] {
text-align: right;
}
mjx-mrow {
display: inline-block;
}
mjx-chtml [space="1"] {
margin-left: .111em;
}
mjx-chtml [space="2"] {
margin-left: .167em;
}
mjx-chtml [space="3"] {
margin-left: .222em;
}
mjx-chtml [space="4"] {
margin-left: .278em;
}
mjx-chtml [space="5"] {
margin-left: .333em;
}
mjx-chtml [rspace="1"] {
margin-right: .111em;
}
mjx-chtml [rspace="2"] {
margin-right: .167em;
}
mjx-chtml [rspace="3"] {
margin-right: .222em;
}
mjx-chtml [rspace="4"] {
margin-right: .278em;
}
mjx-chtml [rspace="5"] {
margin-right: .333em;
}
mjx-chtml [size="s"] {
font-size: 70.7%;
}
mjx-chtml [size="ss"] {
font-size: 50%;
}
mjx-chtml [size="Tn"] {
font-size: 60%;
}
mjx-chtml [size="sm"] {
font-size: 85%;
}
mjx-chtml [size="lg"] {
font-size: 120%;
}
mjx-chtml [size="Lg"] {
font-size: 144%;
}
mjx-chtml [size="LG"] {
font-size: 173%;
}
mjx-chtml [size="hg"] {
font-size: 207%;
}
mjx-chtml [size="HG"] {
font-size: 249%;
}
mjx-chtml [width="full"] {
width: 100%;
}
mjx-box {
display: inline-block;
}
mjx-block {
display: block;
}
mjx-itable {
display: inline-table;
}
mjx-row {
display: table-row;
}
mjx-row > * {
display: table-cell;
}
mjx-mn {
display: inline-block;
}
mjx-mtext {
display: inline-block;
}
mjx-merror {
display: inline-block;
color: red;
background-color: yellow;
}
mjx-mphantom {
visibility: hidden;
}
mjx-inferredMrow {
display: inline-block;
}
mjx-mi {
display: inline-block;
}
mjx-mo {
display: inline-block;
}
mjx-stretchy-h {
display: inline-table;
width: 100%;
}
mjx-stretchy-h > mjx-beg, mjx-stretchy-h > mjx-end {
display: table-cell;
width: 0;
}
mjx-stretchy-h > mjx-ext {
display: table-cell;
overflow: hidden;
width: 100%;
}
mjx-stretchy-h > mjx-ext > mjx-c {
transform: scalex(500);
}
mjx-stretchy-h > mjx-ext > mjx-c::before {
padding: .001em 0;
}
mjx-stretchy-h > mjx-beg > mjx-c {
margin-right: -.1em;
}
mjx-stretchy-h > mjx-end > mjx-c {
margin-left: -.1em;
}
mjx-stretchy-v {
display: inline-block;
}
mjx-stretchy-v > * {
display: block;
}
mjx-stretchy-v > mjx-beg {
height: 0;
}
mjx-stretchy-v > mjx-end > mjx-c {
display: block;
}
mjx-stretchy-v > * > mjx-c {
transform: scale(1);
transform-origin: left center;
overflow: hidden;
}
mjx-stretchy-v > mjx-ext {
display: block;
height: 100%;
box-sizing: border-box;
border: 0px solid transparent;
overflow: hidden;
}
mjx-stretchy-v > mjx-ext > mjx-c {
transform: scaleY(500) translateY(.1em);
overflow: visible;
}
mjx-mark {
display: inline-block;
height: 0px;
}
mjx-ms {
display: inline-block;
}
mjx-mspace {
display: inline-block;
}
mjx-mpadded {
display: inline-block;
}
mjx-rbox {
display: inline-block;
position: relative;
}
mjx-menclose {
display: inline-block;
position: relative;
}
mjx-menclose > mjx-dstrike {
display: inline-block;
left: 0;
top: 0;
position: absolute;
border-top: 0.067em solid;
transform-origin: top left;
}
mjx-menclose > mjx-ustrike {
display: inline-block;
left: 0;
bottom: 0;
position: absolute;
border-top: 0.067em solid;
transform-origin: bottom left;
}
mjx-menclose > mjx-hstrike {
border-top: 0.067em solid;
position: absolute;
left: 0;
right: 0;
bottom: 50%;
transform: translateY(0.0335em);
}
mjx-menclose > mjx-vstrike {
border-left: 0.067em solid;
position: absolute;
top: 0;
bottom: 0;
right: 50%;
transform: translateX(0.0335em);
}
mjx-menclose > mjx-rbox {
position: absolute;
top: 0;
bottom: 0;
right: 0;
left: 0;
border: 0.067em solid;
border-radius: 0.267em;
}
mjx-menclose > svg.mjx-circle {
position: absolute;
top: 0;
bottom: 0;
right: 0;
left: 0;
width: 100%;
height: 100%;
}
mjx-menclose > svg.mjx-circle > ellipse {
stroke-width: 0.067;
stroke: currentColor;
fill: none;
}
mjx-menclose > svg.mjx-arrow {
position: absolute;
}
mjx-menclose > svg.mjx-arrow > path {
stroke: none;
fill: currentColor;
}
mjx-menclose > svg.mjx-arrow > line {
stroke: currentColor;
stroke-width: 0.067;
stroke-linecap: round;
}
mjx-menclose > svg.mjx-longdiv {
position: absolute;
top: 0;
bottom: 0;
left: 0;
right: 0;
width: 100%;
height: 100%;
}
mjx-menclose > svg.mjx-longdiv > path {
stroke: currentColor;
stroke-width: 0.067;
stroke-linecap: round;
stroke-linejoin: round;
fill: none;
}
mjx-mfrac {
display: inline-block;
}
mjx-frac {
display: inline-block;
vertical-align: 0.17em;
padding: 0 .22em;
}
mjx-frac[type="d"] {
vertical-align: .04em;
}
mjx-frac[delims] {
padding: 0 .1em;
}
mjx-frac[atop] {
padding: 0 .12em;
}
mjx-frac[atop][delims] {
padding: 0;
}
mjx-dtable {
display: inline-table;
width: 100%;
}
mjx-dtable > * {
font-size: 2000%;
}
mjx-dbox {
display: block;
font-size: 5%;
}
mjx-num {
display: block;
text-align: center;
}
mjx-den {
display: block;
text-align: center;
}
mjx-den[align="right"], mjx-num[align="right"] {
text-align: right;
}
mjx-den[align="left"], mjx-num[align="left"] {
text-align: left;
}
mjx-nstrut {
display: inline-block;
height: .054em;
width: 0;
vertical-align: -.054em;
}
mjx-nstrut[type="d"] {
height: .217em;
vertical-align: -.217em;
}
mjx-dstrut {
display: inline-block;
height: .505em;
width: 0;
}
mjx-dstrut[type="d"] {
height: .726em;
}
mjx-line {
display: block;
box-sizing: border-box;
min-height: 1px;
height: .06em;
border-top: .06em solid;
margin: .06em -.1em;
overflow: hidden;
}
mjx-line[type="d"] {
margin: .18em -.1em;
}
mjx-msqrt {
display: inline-block;
}
mjx-root {
display: inline-block;
white-space: nowrap;
}
mjx-surd {
display: inline-block;
vertical-align: top;
}
mjx-sqrt {
display: inline-block;
padding-top: .07em;
}
mjx-sqrt > mjx-box {
border-top: .07em solid;
}
mjx-sqrt.mjx-tall > mjx-box {
padding-left: .3em;
margin-left: -.3em;
}
mjx-mroot {
display: inline-block;
}
mjx-msub {
display: inline-block;
}
mjx-msup {
display: inline-block;
}
mjx-msubsup {
display: inline-block;
}
mjx-script {
display: inline-block;
padding-right: .05em;
}
mjx-script > * {
display: block;
}
mjx-munder {
display: inline-block;
}
mjx-over {
text-align: left;
}
mjx-munder:not([limits="false"]) {
display: inline-table;
}
mjx-munder > mjx-row {
text-align: left;
}
mjx-under {
padding-bottom: .1em;
}
mjx-mover {
display: inline-block;
}
mjx-mover:not([limits="false"]) {
padding-top: .1em;
}
mjx-mover:not([limits="false"]) > * {
display: block;
text-align: left;
}
mjx-munderover {
display: inline-block;
}
mjx-munderover:not([limits="false"]) {
padding-top: .1em;
}
mjx-munderover:not([limits="false"]) > * {
display: block;
}
mjx-mmultiscripts {
display: inline-block;
}
mjx-prescripts {
display: inline-table;
padding-left: .05em;
}
mjx-scripts {
display: inline-table;
padding-right: .05em;
}
mjx-prescripts > mjx-row > mjx-cell {
text-align: right;
}
mjx-mfenced {
display: inline-block;
}
mjx-mtable {
display: inline-block;
vertical-align: .25em;
text-align: center;
position: relative;
box-sizing: border-box;
}
mjx-mtable > mjx-itable {
vertical-align: middle;
text-align: left;
box-sizing: border-box;
}
mjx-labels {
display: inline-table;
position: absolute;
top: 0;
}
mjx-mtable[justify="left"][side="left"] {
text-align: left;
padding-right: 0 ! important;
}
mjx-mtable[justify="left"][side="right"] {
text-align: left;
padding-left: 0 ! important;
}
mjx-mtable[justify="right"][side="left"] {
text-align: right;
padding-right: 0 ! important;
}
mjx-mtable[justify="right"][side="right"] {
text-align: right;
padding-left: 0 ! important;
}
mjx-mtable[align] {
vertical-align: baseline;
}
mjx-mtable[align="top"] > mjx-itable {
vertical-align: top;
}
mjx-mtable[align="bottom"] > mjx-itable {
vertical-align: bottom;
}
mjx-mtable[align="center"] > mjx-itable {
vertical-align: middle;
}
mjx-mtable[align="baseline"] > mjx-itable {
vertical-align: middle;
}
mjx-mtr {
display: table-row;
}
mjx-mtr[rowalign="top"] > mjx-mtd {
vertical-align: top;
}
mjx-mtr[rowalign="center"] > mjx-mtd {
vertical-align: middle;
}
mjx-mtr[rowalign="bottom"] > mjx-mtd {
vertical-align: bottom;
}
mjx-mtr[rowalign="baseline"] > mjx-mtd {
vertical-align: baseline;
}
mjx-mtr[rowalign="axis"] > mjx-mtd {
vertical-align: .25em;
}
mjx-mlabeledtr {
display: table-row;
}
mjx-mlabeledtr[rowalign="top"] > mjx-mtd {
vertical-align: top;
}
mjx-mlabeledtr[rowalign="center"] > mjx-mtd {
vertical-align: middle;
}
mjx-mlabeledtr[rowalign="bottom"] > mjx-mtd {
vertical-align: bottom;
}
mjx-mlabeledtr[rowalign="baseline"] > mjx-mtd {
vertical-align: baseline;
}
mjx-mlabeledtr[rowalign="axis"] > mjx-mtd {
vertical-align: .25em;
}
mjx-mtd {
display: table-cell;
text-align: center;
padding: .215em .4em;
}
mjx-mtd:first-child {
padding-left: 0;
}
mjx-mtd:last-child {
padding-right: 0;
}
mjx-mtable > mjx-itable > *:first-child > mjx-mtd {
padding-top: 0;
}
mjx-mtable > mjx-itable > *:last-child > mjx-mtd {
padding-bottom: 0;
}
mjx-mtable > mjx-labels > *:first-child > mjx-mtd {
padding-top: 0;
}
mjx-mtable > mjx-labels > *:last-child > mjx-mtd {
padding-bottom: 0;
}
mjx-tstrut {
display: inline-block;
height: 1em;
vertical-align: -.25em;
}
mjx-labels[align="left"] > mjx-mtr > mjx-mtd {
text-align: left;
}
mjx-labels[align="right"] > mjx-mtr > mjx-mtd {
text-align: right;
}
mjx-mtr mjx-mtd[rowalign="top"], mjx-mlabeledtr mjx-mtd[rowalign="top"] {
vertical-align: top;
}
mjx-mtr mjx-mtd[rowalign="center"], mjx-mlabeledtr mjx-mtd[rowalign="center"] {
vertical-align: middle;
}
mjx-mtr mjx-mtd[rowalign="bottom"], mjx-mlabeledtr mjx-mtd[rowalign="bottom"] {
vertical-align: bottom;
}
mjx-mtr mjx-mtd[rowalign="baseline"], mjx-mlabeledtr mjx-mtd[rowalign="baseline"] {
vertical-align: baseline;
}
mjx-mtr mjx-mtd[rowalign="axis"], mjx-mlabeledtr mjx-mtd[rowalign="axis"] {
vertical-align: .25em;
}
mjx-maction {
display: inline-block;
position: relative;
}
mjx-maction > mjx-tool {
display: none;
position: absolute;
bottom: -.33em;
right: 0;
width: 0;
height: 0;
}
mjx-tool > mjx-tip {
display: inline-block;
padding: .2em;
border: 1px solid #888;
font-size: 70%;
background-color: #F8F8F8;
color: black;
box-shadow: 2px 2px 5px #AAAAAA;
}
mjx-maction[toggle] {
cursor: pointer;
}
mjx-status {
display: block;
position: fixed;
left: 1em;
bottom: 1em;
min-width: 25%;
padding: .2em .4em;
border: 1px solid #888;
font-size: 90%;
background-color: #F8F8F8;
color: black;
}
mjx-mglyph {
display: inline-block;
}
mjx-mglyph > img {
display: inline-block;
border: 0;
padding: 0;
}
mjx-semantics {
display: inline-block;
}
mjx-annotation {
display: inline-block;
}
mjx-annotation-xml {
display: inline-block;
}
mjx-TeXAtom {
display: inline-block;
}
mjx-c, mjx-c::before {
display: inline-block;
}
.MJX-TEX .mjx-n mjx-c {
font-family: MJXZERO, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-i mjx-c {
font-family: MJXZERO, MJXTEX-I, MJXTEX, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-b mjx-c {
font-family: MJXZERO, MJXTEX-B, MJXTEX-BI, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-b.mjx-i mjx-c {
font-family: MJXZERO, MJXTEX-BI, MJXTEX-B, MJXTEX-I, MJXTEX, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-cal mjx-c {
font-family: MJXZERO, MJXTEX-C, MJXTEX-I, MJXTEX, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-cal.mjx-b mjx-c {
font-family: MJXZERO, MJXTEX-C-B, MJXTEX-C, MJXTEX-B, MJXTEX-BI, MJXTEX, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-ds mjx-c {
font-family: MJXZERO, MJXTEX-A, MJXTEX-B, MJXTEX-BI, MJXTEX, MJXTEX-I, MJXTEX-S1;
}
.MJX-TEX .mjx-fr mjx-c {
font-family: MJXZERO, MJXTEX-FR, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-fr.mjx-b mjx-c {
font-family: MJXZERO, MJXTEX-FR-B, MJXTEX-FR, MJXTEX-B, MJXTEX-BI, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-sc mjx-c {
font-family: MJXZERO, MJXTEX-SC, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-sc.mjx-b mjx-c {
font-family: MJXZERO, MJXTEX-SC-B, MJXTEX-SC, MJXTEX-B, MJXTEX-BI, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-ss mjx-c {
font-family: MJXZERO, MJXTEX-SS, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-ss.mjx-b mjx-c {
font-family: MJXZERO, MJXTEX-SS-B, MJXTEX-SS, MJXTEX-B, MJXTEX-BI, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-ss.mjx-i mjx-c {
font-family: MJXZERO, MJXTEX-SS-I, MJXTEX-I, MJXTEX, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-ss.mjx-b.mjx-i mjx-c {
font-family: MJXZERO, MJXTEX-SS-B, MJXTEX-SS-I, MJXTEX-BI, MJXTEX-B, MJXTEX-I, MJXTEX, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-ty mjx-c {
font-family: MJXZERO, MJXTEX-T, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-var mjx-c {
font-family: MJXZERO, MJXTEX-A, MJXTEX, MJXTEX-I, MJXTEX-S1;
}
.MJX-TEX .mjx-os mjx-c {
font-family: MJXZERO, MJXTEX-C, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-os.mjx-b mjx-c {
font-family: MJXZERO, MJXTEX-C-B, MJXTEX-C, MJXTEX-B, MJXTEX-BI, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-mit mjx-c {
font-family: MJXZERO, MJXTEX-MI, MJXTEX-I, MJXTEX, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-lop mjx-c {
font-family: MJXZERO, MJXTEX-S2, MJXTEX-S1, MJXTEX, MJXTEX-I, MJXTEX-A;
}
.MJX-TEX .mjx-sop mjx-c {
font-family: MJXZERO, MJXTEX-S1, MJXTEX, MJXTEX-I, MJXTEX-A;
}
.MJX-TEX .mjx-s3 mjx-c {
font-family: MJXZERO, MJXTEX-S3, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX .mjx-s4 mjx-c {
font-family: MJXZERO, MJXTEX-S4, MJXTEX, MJXTEX-I, MJXTEX-S1, MJXTEX-A;
}
.MJX-TEX {
font-family: MJXZERO;
}
.MJX-TEX mjx-stretchy-v mjx-c, .MJX-TEX mjx-stretchy-h mjx-c {
font-family: MJXZERO, MJXTEX, MJXTEX-S4 ! important;
}
@font-face /* 0 */ {
font-family: MJXZERO;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/otf/MathJax_Zero.otf") format("opentype");
}
@font-face /* 1 */ {
font-family: MJXTEX;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Main-Regular.woff") format("woff");
}
@font-face /* 2 */ {
font-family: MJXTEX-B;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Main-Bold.woff") format("woff");
}
@font-face /* 3 */ {
font-family: MJXTEX-MI;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Main-Italic.woff") format("woff");
}
@font-face /* 4 */ {
font-family: MJXTEX-I;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Math-Italic.woff") format("woff");
}
@font-face /* 5 */ {
font-family: MJXTEX-BI;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Math-BoldItalic.woff") format("woff");
}
@font-face /* 6 */ {
font-family: MJXTEX-S1;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Size1-Regular.woff") format("woff");
}
@font-face /* 7 */ {
font-family: MJXTEX-S2;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Size2-Regular.woff") format("woff");
}
@font-face /* 8 */ {
font-family: MJXTEX-S3;
src: url("https://cdn.rawgit.com/mathjax/mathjax-v3/3.0.0-beta.1/mathjax2/css/woff/MathJax_Size3-Regular.woff") format("woff");
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border-bottom-width: 1.769em;
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border-bottom-width: 0.879em;
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padding: 0.525em 0 0.024em;
}
.MJX-TEX mjx-stretchy-h[c="21D0"] mjx-ext mjx-c::before {
content: "=";
}
.MJX-TEX mjx-stretchy-v[c="21D1"] mjx-beg mjx-c::before {
content: "\21D1";
padding: 0.694em 0 0.194em;
}
.MJX-TEX mjx-stretchy-v[c="21D1"] mjx-ext mjx-c::before {
content: "\2016";
}
.MJX-TEX mjx-stretchy-v[c="21D1"] > mjx-ext {
border-top-width: 0.858em;
}
.MJX-TEX mjx-stretchy-h[c="21D2"] mjx-ext mjx-c::before {
content: "=";
}
.MJX-TEX mjx-stretchy-h[c="21D2"] mjx-end mjx-c::before {
content: "\21D2";
padding: 0.525em 0 0.024em;
}
.MJX-TEX mjx-stretchy-v[c="21D3"] mjx-ext mjx-c::before {
content: "\2016";
}
.MJX-TEX mjx-stretchy-v[c="21D3"] mjx-end mjx-c::before {
content: "\21D3";
padding: 0.694em 0 0.194em;
}
.MJX-TEX mjx-stretchy-v[c="21D3"] > mjx-end {
margin-top: -0.888em;
}
.MJX-TEX mjx-stretchy-v[c="21D3"] > mjx-ext {
border-bottom-width: 0.858em;
}
.MJX-TEX mjx-stretchy-h[c="21D4"] mjx-beg mjx-c::before {
content: "\21D0";
padding: 0.525em 0 0.024em;
}
.MJX-TEX mjx-stretchy-h[c="21D4"] mjx-ext mjx-c::before {
content: "=";
}
.MJX-TEX mjx-stretchy-h[c="21D4"] mjx-end mjx-c::before {
content: "\21D2";
padding: 0.525em 0 0.024em;
}
.MJX-TEX mjx-stretchy-v[c="21D5"] mjx-beg mjx-c::before {
content: "\21D1";
padding: 0.694em 0 0.194em;
}
.MJX-TEX mjx-stretchy-v[c="21D5"] mjx-ext mjx-c::before {
content: "\2016";
}
.MJX-TEX mjx-stretchy-v[c="21D5"] mjx-end mjx-c::before {
content: "\21D3";
padding: 0.694em 0 0.194em;
}
.MJX-TEX mjx-stretchy-v[c="21D5"] > mjx-end {
margin-top: -0.888em;
}
.MJX-TEX mjx-stretchy-v[c="21D5"] > mjx-ext {
border-top-width: 0.858em;
border-bottom-width: 0.858em;
}
.MJX-TEX mjx-stretchy-h[c="21DA"] mjx-beg mjx-c::before {
content: "\21DA";
padding: 0.611em 0 0.111em;
}
.MJX-TEX mjx-stretchy-h[c="21DA"] mjx-ext mjx-c::before {
content: "\2261";
}
.MJX-TEX mjx-stretchy-h[c="21DB"] mjx-ext mjx-c::before {
content: "\2261";
}
.MJX-TEX mjx-stretchy-h[c="21DB"] mjx-end mjx-c::before {
content: "\21DB";
padding: 0.611em 0 0.111em;
}
.MJX-TEX mjx-stretchy-h[c="2212"] mjx-ext mjx-c::before {
content: "\2212";
padding: 0.583em 0 0.082em;
}
.MJX-TEX .mjx-stretched mjx-c[c="2215"]::before {
content: "/";
}
.MJX-TEX mjx-stretchy-v[c="221A"] mjx-beg mjx-c::before {
content: "\E001";
padding: 0.605em 0 0.014em;
}
.MJX-TEX mjx-stretchy-v[c="221A"] mjx-ext mjx-c::before {
content: "\E000";
}
.MJX-TEX mjx-stretchy-v[c="221A"] mjx-end mjx-c::before {
content: "\23B7";
padding: 0.935em 0 0.885em;
}
.MJX-TEX mjx-stretchy-v[c="221A"] > mjx-end {
margin-top: -1.82em;
}
.MJX-TEX mjx-stretchy-v[c="221A"] > mjx-ext {
border-top-width: 0.589em;
border-bottom-width: 1.79em;
}
.MJX-TEX mjx-stretchy-v[c="2223"] mjx-ext mjx-c::before {
content: "\2223";
}
.MJX-TEX mjx-stretchy-v[c="2225"] mjx-ext mjx-c::before {
content: "\2225";
}
.MJX-TEX mjx-stretchy-v[c="2308"] mjx-beg mjx-c::before {
content: "\23A1";
padding: 1.154em 0 0.645em;
}
.MJX-TEX mjx-stretchy-v[c="2308"] mjx-ext mjx-c::before {
content: "\23A2";
}
.MJX-TEX mjx-stretchy-v[c="2308"] > mjx-ext {
border-top-width: 1.769em;
}
.MJX-TEX mjx-stretchy-v[c="2309"] mjx-beg mjx-c::before {
content: "\23A4";
padding: 1.154em 0 0.645em;
}
.MJX-TEX mjx-stretchy-v[c="2309"] mjx-ext mjx-c::before {
content: "\23A5";
}
.MJX-TEX mjx-stretchy-v[c="2309"] > mjx-ext {
border-top-width: 1.769em;
}
.MJX-TEX mjx-stretchy-v[c="230A"] mjx-ext mjx-c::before {
content: "\23A2";
}
.MJX-TEX mjx-stretchy-v[c="230A"] mjx-end mjx-c::before {
content: "\23A3";
padding: 1.155em 0 0.644em;
}
.MJX-TEX mjx-stretchy-v[c="230A"] > mjx-end {
margin-top: -1.799em;
}
.MJX-TEX mjx-stretchy-v[c="230A"] > mjx-ext {
border-bottom-width: 1.769em;
}
.MJX-TEX mjx-stretchy-v[c="230B"] mjx-ext mjx-c::before {
content: "\23A5";
}
.MJX-TEX mjx-stretchy-v[c="230B"] mjx-end mjx-c::before {
content: "\23A6";
padding: 1.155em 0 0.644em;
}
.MJX-TEX mjx-stretchy-v[c="230B"] > mjx-end {
margin-top: -1.799em;
}
.MJX-TEX mjx-stretchy-v[c="230B"] > mjx-ext {
border-bottom-width: 1.769em;
}
.MJX-TEX .mjx-stretched mjx-c[c="2312"]::before {
content: "\23DC";
}
.MJX-TEX mjx-stretchy-h[c="2312"] mjx-beg mjx-c::before {
content: "\E150";
padding: 0.12em 0 0.213em;
}
.MJX-TEX mjx-stretchy-h[c="2312"] mjx-ext mjx-c::before {
content: "\E154";
}
.MJX-TEX mjx-stretchy-h[c="2312"] mjx-end mjx-c::before {
content: "\E151";
padding: 0.12em 0 0.213em;
}
.MJX-TEX .mjx-stretched mjx-c[c="2322"]::before {
content: "\23DC";
}
.MJX-TEX mjx-stretchy-h[c="2322"] mjx-beg mjx-c::before {
content: "\E150";
padding: 0.12em 0 0.213em;
}
.MJX-TEX mjx-stretchy-h[c="2322"] mjx-ext mjx-c::before {
content: "\E154";
}
.MJX-TEX mjx-stretchy-h[c="2322"] mjx-end mjx-c::before {
content: "\E151";
padding: 0.12em 0 0.213em;
}
.MJX-TEX .mjx-stretched mjx-c[c="2323"]::before {
content: "\23DD";
}
.MJX-TEX mjx-stretchy-h[c="2323"] mjx-beg mjx-c::before {
content: "\E152";
padding: 0.333em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="2323"] mjx-ext mjx-c::before {
content: "\E154";
}
.MJX-TEX mjx-stretchy-h[c="2323"] mjx-end mjx-c::before {
content: "\E153";
padding: 0.333em 0 0;
}
.MJX-TEX .mjx-stretched mjx-c[c="2329"]::before {
content: "\27E8";
}
.MJX-TEX .mjx-stretched mjx-c[c="232A"]::before {
content: "\27E9";
}
.MJX-TEX mjx-stretchy-v[c="23AA"] mjx-beg mjx-c::before {
content: "\23AA";
padding: 0.29em 0 0.015em;
}
.MJX-TEX mjx-stretchy-v[c="23AA"] mjx-ext mjx-c::before {
content: "\23AA";
}
.MJX-TEX mjx-stretchy-v[c="23AA"] mjx-end mjx-c::before {
content: "\23AA";
padding: 0.29em 0 0.015em;
}
.MJX-TEX mjx-stretchy-v[c="23AA"] > mjx-end {
margin-top: -0.305em;
}
.MJX-TEX mjx-stretchy-v[c="23AA"] > mjx-ext {
border-top-width: 0.275em;
border-bottom-width: 0.275em;
}
.MJX-TEX .mjx-stretched mjx-c[c="23AF"]::before {
content: "\2013";
}
.MJX-TEX mjx-stretchy-h[c="23AF"] mjx-ext mjx-c::before {
content: "\2013";
padding: 0.285em 0 0;
}
.MJX-TEX mjx-stretchy-v[c="23B0"] mjx-beg mjx-c::before {
content: "\23A7";
padding: 0.899em 0 0.01em;
}
.MJX-TEX mjx-stretchy-v[c="23B0"] mjx-ext mjx-c::before {
content: "\23AA";
}
.MJX-TEX mjx-stretchy-v[c="23B0"] mjx-end mjx-c::before {
content: "\23AD";
padding: 0.01em 0 0.899em;
}
.MJX-TEX mjx-stretchy-v[c="23B0"] > mjx-end {
margin-top: -0.909em;
}
.MJX-TEX mjx-stretchy-v[c="23B0"] > mjx-ext {
border-top-width: 0.879em;
border-bottom-width: 0.879em;
}
.MJX-TEX mjx-stretchy-v[c="23B1"] mjx-beg mjx-c::before {
content: "\23AB";
padding: 0.899em 0 0.01em;
}
.MJX-TEX mjx-stretchy-v[c="23B1"] mjx-ext mjx-c::before {
content: "\23AA";
}
.MJX-TEX mjx-stretchy-v[c="23B1"] mjx-end mjx-c::before {
content: "\23A9";
padding: 0.01em 0 0.899em;
}
.MJX-TEX mjx-stretchy-v[c="23B1"] > mjx-end {
margin-top: -0.909em;
}
.MJX-TEX mjx-stretchy-v[c="23B1"] > mjx-ext {
border-top-width: 0.879em;
border-bottom-width: 0.879em;
}
.MJX-TEX mjx-stretchy-h[c="23B4"] mjx-beg mjx-c::before {
content: "\250C";
padding: 0.694em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23B4"] mjx-ext mjx-c::before {
content: "\2212";
}
.MJX-TEX mjx-stretchy-h[c="23B4"] mjx-end mjx-c::before {
content: "\2510";
padding: 0.694em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23B5"] mjx-beg mjx-c::before {
content: "\2514";
padding: 0.366em 0 0.022em;
}
.MJX-TEX mjx-stretchy-h[c="23B5"] mjx-ext mjx-c::before {
content: "\2212";
}
.MJX-TEX mjx-stretchy-h[c="23B5"] mjx-end mjx-c::before {
content: "\2518";
padding: 0.366em 0 0.022em;
}
.MJX-TEX mjx-stretchy-v[c="23D0"] mjx-ext mjx-c::before {
content: "\2223";
}
.MJX-TEX mjx-stretchy-h[c="23DC"] mjx-beg mjx-c::before {
content: "\E150";
padding: 0.12em 0 0.213em;
}
.MJX-TEX mjx-stretchy-h[c="23DC"] mjx-ext mjx-c::before {
content: "\E154";
}
.MJX-TEX mjx-stretchy-h[c="23DC"] mjx-end mjx-c::before {
content: "\E151";
padding: 0.12em 0 0.213em;
}
.MJX-TEX mjx-stretchy-h[c="23DD"] mjx-beg mjx-c::before {
content: "\E152";
padding: 0.333em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23DD"] mjx-ext mjx-c::before {
content: "\E154";
}
.MJX-TEX mjx-stretchy-h[c="23DD"] mjx-end mjx-c::before {
content: "\E153";
padding: 0.333em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23DE"] mjx-beg mjx-c::before {
content: "\E150";
padding: 0.12em 0 0.213em;
}
.MJX-TEX mjx-stretchy-h[c="23DE"] mjx-ext mjx-c::before {
content: "\E154";
}
.MJX-TEX mjx-stretchy-h[c="23DE"] mjx-end mjx-c::before {
content: "\E151";
padding: 0.12em 0 0.213em;
}
.MJX-TEX mjx-stretchy-h[c="23DE"] mjx-mid mjx-c::before {
content: "\E153\E152";
padding: 0.333em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23DE"] > mjx-ext {
width: 50%;
}
.MJX-TEX mjx-stretchy-h[c="23DF"] mjx-beg mjx-c::before {
content: "\E152";
padding: 0.333em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23DF"] mjx-ext mjx-c::before {
content: "\E154";
}
.MJX-TEX mjx-stretchy-h[c="23DF"] mjx-end mjx-c::before {
content: "\E153";
padding: 0.333em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23DF"] mjx-mid mjx-c::before {
content: "\E151\E150";
padding: 0.12em 0 0.213em;
}
.MJX-TEX mjx-stretchy-h[c="23DF"] > mjx-ext {
width: 50%;
}
.MJX-TEX mjx-stretchy-h[c="23E0"] mjx-beg mjx-c::before {
content: "\2CA";
padding: 0.699em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23E0"] mjx-ext mjx-c::before {
content: "\2C9";
}
.MJX-TEX mjx-stretchy-h[c="23E0"] mjx-end mjx-c::before {
content: "\2CB";
padding: 0.699em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23E1"] mjx-beg mjx-c::before {
content: "\2CB";
padding: 0.699em 0 0;
}
.MJX-TEX mjx-stretchy-h[c="23E1"] mjx-ext mjx-c::before {
content: "\2C9";
}
.MJX-TEX mjx-stretchy-h[c="23E1"] mjx-end mjx-c::before {
content: "\2CA";
padding: 0.699em 0 0;
}
.MJX-TEX .mjx-stretched mjx-c[c="2500"]::before {
content: "\2013";
}
.MJX-TEX mjx-stretchy-h[c="2500"] mjx-ext mjx-c::before {
content: "\2013";
padding: 0.285em 0 0;
}
.MJX-TEX .mjx-stretched mjx-c[c="2758"]::before {
content: "\2223";
}
.MJX-TEX mjx-stretchy-v[c="2758"] mjx-ext mjx-c::before {
content: "\2223";
}
.MJX-TEX mjx-stretchy-v[c="27EE"] mjx-beg mjx-c::before {
content: "\23A7";
padding: 0.899em 0 0.01em;
}
.MJX-TEX mjx-stretchy-v[c="27EE"] mjx-ext mjx-c::before {
content: "\23AA";
}
.MJX-TEX mjx-stretchy-v[c="27EE"] mjx-end mjx-c::before {
content: "\23A9";
padding: 0.01em 0 0.899em;
}
.MJX-TEX mjx-stretchy-v[c="27EE"] > mjx-end {
margin-top: -0.909em;
}
.MJX-TEX mjx-stretchy-v[c="27EE"] > mjx-ext {
border-top-width: 0.879em;
border-bottom-width: 0.879em;
}
.MJX-TEX mjx-stretchy-v[c="27EF"] mjx-beg mjx-c::before {
content: "\23AB";
padding: 0.899em 0 0.01em;
}
.MJX-TEX mjx-stretchy-v[c="27EF"] mjx-ext mjx-c::before {
content: "\23AA";
}
.MJX-TEX mjx-stretchy-v[c="27EF"] mjx-end mjx-c::before {
content: "\23AD";
padding: 0.01em 0 0.899em;
}
.MJX-TEX mjx-stretchy-v[c="27EF"] > mjx-end {
margin-top: -0.909em;
}
.MJX-TEX mjx-stretchy-v[c="27EF"] > mjx-ext {
border-top-width: 0.879em;
border-bottom-width: 0.879em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27F5"]::before {
content: "\2190";
}
.MJX-TEX mjx-stretchy-h[c="27F5"] mjx-beg mjx-c::before {
content: "\2190";
padding: 0.511em 0 0.011em;
}
.MJX-TEX mjx-stretchy-h[c="27F5"] mjx-ext mjx-c::before {
content: "\2212";
}
.MJX-TEX .mjx-stretched mjx-c[c="27F6"]::before {
content: "\2192";
}
.MJX-TEX mjx-stretchy-h[c="27F6"] mjx-ext mjx-c::before {
content: "\2212";
}
.MJX-TEX mjx-stretchy-h[c="27F6"] mjx-end mjx-c::before {
content: "\2192";
padding: 0.511em 0 0.011em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27F7"]::before {
content: "\2194";
}
.MJX-TEX mjx-stretchy-h[c="27F7"] mjx-beg mjx-c::before {
content: "\2190";
padding: 0.511em 0 0.011em;
}
.MJX-TEX mjx-stretchy-h[c="27F7"] mjx-ext mjx-c::before {
content: "\2212";
}
.MJX-TEX mjx-stretchy-h[c="27F7"] mjx-end mjx-c::before {
content: "\2192";
padding: 0.511em 0 0.011em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27F8"]::before {
content: "\21D0";
}
.MJX-TEX mjx-stretchy-h[c="27F8"] mjx-beg mjx-c::before {
content: "\21D0";
padding: 0.525em 0 0.024em;
}
.MJX-TEX mjx-stretchy-h[c="27F8"] mjx-ext mjx-c::before {
content: "=";
}
.MJX-TEX .mjx-stretched mjx-c[c="27F9"]::before {
content: "\21D2";
}
.MJX-TEX mjx-stretchy-h[c="27F9"] mjx-ext mjx-c::before {
content: "=";
}
.MJX-TEX mjx-stretchy-h[c="27F9"] mjx-end mjx-c::before {
content: "\21D2";
padding: 0.525em 0 0.024em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27FA"]::before {
content: "\21D4";
}
.MJX-TEX mjx-stretchy-h[c="27FA"] mjx-beg mjx-c::before {
content: "\21D0";
padding: 0.525em 0 0.024em;
}
.MJX-TEX mjx-stretchy-h[c="27FA"] mjx-ext mjx-c::before {
content: "=";
}
.MJX-TEX mjx-stretchy-h[c="27FA"] mjx-end mjx-c::before {
content: "\21D2";
padding: 0.525em 0 0.024em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27FB"]::before {
content: "\21A4";
}
.MJX-TEX mjx-stretchy-h[c="27FB"] mjx-beg mjx-c::before {
content: "\2190";
padding: 0.511em 0 0.011em;
}
.MJX-TEX mjx-stretchy-h[c="27FB"] mjx-ext mjx-c::before {
content: "\2212";
}
.MJX-TEX mjx-stretchy-h[c="27FB"] mjx-end mjx-c::before {
content: "\2223";
padding: 0.75em 0 0.249em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27FC"]::before {
content: "\21A6";
}
.MJX-TEX mjx-stretchy-h[c="27FC"] mjx-beg mjx-c::before {
content: "\2223";
padding: 0.75em 0 0.249em;
}
.MJX-TEX mjx-stretchy-h[c="27FC"] mjx-ext mjx-c::before {
content: "\2212";
}
.MJX-TEX mjx-stretchy-h[c="27FC"] mjx-end mjx-c::before {
content: "\2192";
padding: 0.511em 0 0.011em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27FD"]::before {
content: "\2906";
}
.MJX-TEX mjx-stretchy-h[c="27FD"] mjx-beg mjx-c::before {
content: "\21D0";
padding: 0.525em 0 0.024em;
}
.MJX-TEX mjx-stretchy-h[c="27FD"] mjx-ext mjx-c::before {
content: "=";
}
.MJX-TEX mjx-stretchy-h[c="27FD"] mjx-end mjx-c::before {
content: "\2223";
padding: 0.75em 0 0.249em;
}
.MJX-TEX .mjx-stretched mjx-c[c="27FE"]::before {
content: "\2907";
}
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content: "=";
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padding: 0.525em 0 0.024em;
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content: "=";
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padding: 0.75em 0 0.249em;
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padding: 0.525em 0 0.024em;
}
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padding: 0.511em 0 0;
}
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content: "\2212";
}
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padding: 0.511em 0 0;
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content: "\21BE";
padding: 0.694em 0 0.194em;
}
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content: "\23D0";
}
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content: "\21C2";
padding: 0.694em 0 0.194em;
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margin-top: -0.888em;
}
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border-bottom-width: 0.858em;
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padding: 0.27em 0 0.011em;
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content: "\2212";
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padding: 0.27em 0 0.011em;
}
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content: "\23D0";
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content: "\21C3";
padding: 0.694em 0 0.194em;
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margin-top: -0.888em;
}
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border-bottom-width: 0.858em;
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padding: 0.511em 0 0;
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padding: 0.75em 0 0.249em;
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padding: 0.511em 0 0;
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content: "\21BE";
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content: "\23D0";
}
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content: "\22A5";
padding: 0.668em 0 0;
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margin-top: -0.668em;
}
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border-top-width: 0.858em;
border-bottom-width: 0.638em;
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padding: 0.668em 0 0;
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content: "\23D0";
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content: "\21C2";
padding: 0.694em 0 0.194em;
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margin-top: -0.888em;
}
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border-top-width: 0.638em;
border-bottom-width: 0.858em;
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content: "\21BD";
padding: 0.27em 0 0.011em;
}
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content: "\2212";
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content: "\2223";
padding: 0.75em 0 0.249em;
}
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content: "\2223";
padding: 0.75em 0 0.249em;
}
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content: "\2212";
}
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content: "\21C1";
padding: 0.27em 0 0.011em;
}
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content: "\21BF";
padding: 0.694em 0 0.194em;
}
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content: "\23D0";
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content: "\22A5";
padding: 0.668em 0 0;
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margin-top: -0.668em;
}
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border-top-width: 0.858em;
border-bottom-width: 0.638em;
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content: "\22A4";
padding: 0.668em 0 0;
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content: "\23D0";
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content: "\21C3";
padding: 0.694em 0 0.194em;
}
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margin-top: -0.888em;
}
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border-top-width: 0.638em;
border-bottom-width: 0.858em;
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content: "\27E9";
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padding: 0.12em 0 0.213em;
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content: "\E154";
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content: "\E151";
padding: 0.12em 0 0.213em;
}
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content: "\E153\E152";
padding: 0.333em 0 0;
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width: 50%;
}
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content: "\23DF";
}
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content: "\E152";
padding: 0.333em 0 0;
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content: "\E154";
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content: "\E153";
padding: 0.333em 0 0;
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content: "\E151\E150";
padding: 0.12em 0 0.213em;
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width: 50%;
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content: " ";
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padding: 0.716em 0 0;
content: "!";
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content: "#";
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content: "$";
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padding: 0.75em 0 0.056em;
content: "%";
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content: "\2137";
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content: "\2141";
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content: "\2195";
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content: "\2196";
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content: "\2198";
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}
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content: "\219E";
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content: "\21A9";
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content: "\21AA";
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content: "\21AB";
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content: "\21B7";
}
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content: "\21BA";
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content: "\21C3";
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content: "\21C4";
}
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padding: 0.667em 0 0;
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}
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content: "\21C7";
}
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content: "\21C8";
}
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content: "\21C9";
}
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content: "\21D0";
}
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}
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content: "\21D2";
}
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content: "\21D3";
}
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content: "\21D4";
}
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content: "\21D5";
}
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content: "\21DA";
}
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content: "\21DB";
}
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content: "\21DD";
}
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padding: 0.437em 0 0;
content: "\21E0";
}
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padding: 0.437em 0 0;
content: "\21E2";
}
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padding: 0.694em 0 0.022em;
content: "\2200";
}
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padding: 0.846em 0 0.021em;
content: "\2201";
}
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padding: 0.715em 0 0.022em;
content: "\2202";
}
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padding: 0.694em 0 0;
content: "\2203";
}
.MJX-TEX mjx-c[c="2204"]::before {
width: 0.556em;
padding: 0.716em 0 0.215em;
content: "\2203\338";
}
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width: 0.5em;
padding: 0.772em 0 0.078em;
content: "\2205";
}
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padding: 0.716em 0 0;
content: "\394";
}
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padding: 0.683em 0 0.033em;
content: "\2207";
}
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width: 0.667em;
padding: 0.54em 0 0.04em;
content: "\2208";
}
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width: 0.667em;
padding: 0.716em 0 0.215em;
content: "\2209";
}
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padding: 0.54em 0 0.04em;
content: "\220B";
}
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width: 0.667em;
padding: 0.716em 0 0.215em;
content: "\220B\338";
}
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padding: 0.44em 0 0;
content: "\220D";
}
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padding: 0.75em 0 0.25em;
content: "\220F";
}
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width: 0.944em;
padding: 0.75em 0 0.25em;
content: "\2210";
}
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width: 1.056em;
padding: 0.75em 0 0.25em;
content: "\2211";
}
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padding: 0.583em 0 0.082em;
content: "\2212";
}
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padding: 0.5em 0 0.166em;
content: "\2213";
}
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width: 0.778em;
padding: 0.766em 0 0.093em;
content: "\2214";
}
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width: 0.5em;
padding: 0.75em 0 0.25em;
content: "\2215";
}
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width: 0.778em;
padding: 0.43em 0 0.023em;
content: "\2216";
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content: "\2204";
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content: "\E006";
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content: "\E007";
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content: "\E00C";
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content: "\E00D";
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padding: 0.919em 0 0.421em;
content: "\E00E";
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padding: 0.828em 0 0.33em;
content: "\E016";
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padding: 0.828em 0 0.33em;
content: "\E018";
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content: "\E01B";
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width: 0.778em;
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width: 0.722em;
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width: 0.722em;
padding: 0.576em 0 0.019em;
}
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padding: 0.801em 0 0.303em;
content: "\E010";
}
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padding: 0.801em 0 0.303em;
content: "\E00F";
}
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padding: 0.752em 0 0.332em;
content: "\E017";
}
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padding: 0.752em 0 0.333em;
content: "\E019";
}
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}
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width: 0.734em;
}
.MJX-TEX mjx-mi:not([noIC="true"]).mjx-v mjx-c[c="E009"]:last-child::before {
width: 0.734em;
}
</style></head>
<body>
<p>Licensed under <a href="https://creativecommons.org/licenses/by-sa/3.0/" rel="license">cc by-sa 3.0</a>. Original source: <a href="http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference">meta.math.stackexchange</a> (cc by-sa 3.0), with <a href="http://blog.stackoverflow.com/2009/06/attribution-required/" rel="license">attribution required</a>.</p>
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<div><mjx-chtml class="MathJax MJX-CHTML MJX-TEX" style="font-size: 113.1%;"><mjx-math style="width: 2.731em;"><mjx-mi class="mjx-i"><mjx-c c="L"></mjx-c></mjx-mi><mjx-mspace style="margin-right: -0.325em;"></mjx-mspace><mjx-mpadded><mjx-block style="margin: 0.21em 0px 0px; position: relative;"><mjx-rbox style="left: 0px; top: -0.21em;"><mjx-texatom><mjx-mstyle size="s"><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="A"></mjx-c></mjx-mi></mjx-texatom></mjx-mstyle></mjx-texatom></mjx-rbox></mjx-block></mjx-mpadded><mjx-mspace style="margin-right: -0.17em;"></mjx-mspace><mjx-mi class="mjx-i"><mjx-c c="T"></mjx-c></mjx-mi><mjx-mspace style="margin-right: -0.14em;"></mjx-mspace><mjx-mpadded><mjx-block style="margin: -0.216em 0px 0.215em; position: relative;"><mjx-rbox style="left: 0px; top: 0.215em;"><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="E"></mjx-c></mjx-mi></mjx-texatom></mjx-rbox></mjx-block></mjx-mpadded><mjx-mspace style="margin-right: -0.115em;"></mjx-mspace><mjx-mi class="mjx-i"><mjx-c c="X"></mjx-c></mjx-mi></mjx-math></mjx-chtml></div>
<div>f(n) =
<mjx-chtml class="MathJax MJX-CHTML MJX-TEX MJX-DISPLAY" style="font-size: 113.1%;"><mjx-math display="true"><mjx-mrow><mjx-mo class="mjx-s3"><mjx-c c="{"></mjx-c></mjx-mo><mjx-mtable><mjx-itable><mjx-mtr><mjx-mtd style="text-align: left; padding-right: 0.5em; padding-bottom: 0.1em;"><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi><mjx-texatom><mjx-mo class="mjx-n"><mjx-c c="/"></mjx-c></mjx-mo></mjx-texatom><mjx-mn class="mjx-n"><mjx-c c="2"></mjx-c></mjx-mn><mjx-mo class="mjx-n"><mjx-c c=","></mjx-c></mjx-mo><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-bottom: 0.1em;"><mjx-mrow><mjx-mtext class="mjx-n"><mjx-c c="i"></mjx-c><mjx-c c="f"></mjx-c><mjx-c c="A0"></mjx-c></mjx-mtext><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi></mjx-texatom><mjx-mtext class="mjx-n"><mjx-c c="A0"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="s"></mjx-c><mjx-c c=" "></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="v"></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="n"></mjx-c></mjx-mtext></mjx-mrow><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: left; padding-right: 0.5em; padding-top: 0.1em;"><mjx-mn class="mjx-n"><mjx-c c="3"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="3"><mjx-c c="+"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c c="1"></mjx-c></mjx-mn><mjx-mo class="mjx-n"><mjx-c c=","></mjx-c></mjx-mo><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-top: 0.1em;"><mjx-mrow><mjx-mtext class="mjx-n"><mjx-c c="i"></mjx-c><mjx-c c="f"></mjx-c><mjx-c c="A0"></mjx-c></mjx-mtext><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi></mjx-texatom><mjx-mtext class="mjx-n"><mjx-c c="A0"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="s"></mjx-c><mjx-c c=" "></mjx-c><mjx-c c="o"></mjx-c><mjx-c c="d"></mjx-c><mjx-c c="d"></mjx-c></mjx-mtext></mjx-mrow><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr></mjx-itable></mjx-mtable><mjx-mo class="mjx-n" style="vertical-align: 0.25em;"></mjx-mo></mjx-mrow></mjx-math></mjx-chtml></div>
<div><mjx-chtml class="MathJax MJX-CHTML MJX-TEX MJX-DISPLAY" style="font-size: 113.1%;"><mjx-math display="true"><mjx-mrow><mjx-mo class="mjx-n" style="vertical-align: 0.25em;"></mjx-mo><mjx-mtable><mjx-itable><mjx-mtr><mjx-mtd style="text-align: left; padding-right: 0.5em; padding-bottom: 0.027em;"><mjx-mrow><mjx-mtext class="mjx-n"><mjx-c c="i"></mjx-c><mjx-c c="f"></mjx-c><mjx-c c="A0"></mjx-c></mjx-mtext><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi></mjx-texatom><mjx-mtext class="mjx-n"><mjx-c c="A0"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="s"></mjx-c><mjx-c c=" "></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="v"></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="n"></mjx-c><mjx-c c=":"></mjx-c></mjx-mtext></mjx-mrow><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-bottom: 0.027em;"><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi><mjx-texatom><mjx-mo class="mjx-n"><mjx-c c="/"></mjx-c></mjx-mo></mjx-texatom><mjx-mn class="mjx-n"><mjx-c c="2"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: left; padding-right: 0.5em; padding-top: 0.027em;"><mjx-mrow><mjx-mtext class="mjx-n"><mjx-c c="i"></mjx-c><mjx-c c="f"></mjx-c><mjx-c c="A0"></mjx-c></mjx-mtext><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi></mjx-texatom><mjx-mtext class="mjx-n"><mjx-c c="A0"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="s"></mjx-c><mjx-c c=" "></mjx-c><mjx-c c="o"></mjx-c><mjx-c c="d"></mjx-c><mjx-c c="d"></mjx-c><mjx-c c=":"></mjx-c></mjx-mtext></mjx-mrow><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-top: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="3"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="3"><mjx-c c="+"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c c="1"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr></mjx-itable></mjx-mtable><mjx-mo class="mjx-s3"><mjx-c c="}"></mjx-c></mjx-mo></mjx-mrow><mjx-mo class="mjx-n" space="4"><mjx-c c="="></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c c="f"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c c="("></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c c=")"></mjx-c></mjx-mo></mjx-math></mjx-chtml>
</div>
<div>f(n) =
<mjx-chtml class="MathJax MJX-CHTML MJX-TEX MJX-DISPLAY" style="font-size: 113.1%;"><mjx-math display="true"><mjx-mrow><mjx-mo class="mjx-s4"><mjx-c c="{"></mjx-c></mjx-mo><mjx-mtable><mjx-itable><mjx-mtr><mjx-mtd style="text-align: left; padding-right: 0.5em; padding-bottom: 0.53em;"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-mi class="mjx-i" size="s"><mjx-c c="n"></mjx-c></mjx-mi></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-mn class="mjx-n" size="s"><mjx-c c="2"></mjx-c></mjx-mn></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac><mjx-mo class="mjx-n"><mjx-c c=","></mjx-c></mjx-mo><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-bottom: 0.53em;"><mjx-mrow><mjx-mtext class="mjx-n"><mjx-c c="i"></mjx-c><mjx-c c="f"></mjx-c><mjx-c c="A0"></mjx-c></mjx-mtext><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi></mjx-texatom><mjx-mtext class="mjx-n"><mjx-c c="A0"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="s"></mjx-c><mjx-c c=" "></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="v"></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="n"></mjx-c></mjx-mtext></mjx-mrow><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="text-align: left; padding-right: 0.5em; padding-top: 0.53em;"><mjx-mn class="mjx-n"><mjx-c c="3"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="3"><mjx-c c="+"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c c="1"></mjx-c></mjx-mn><mjx-mo class="mjx-n"><mjx-c c=","></mjx-c></mjx-mo><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-top: 0.53em;"><mjx-mrow><mjx-mtext class="mjx-n"><mjx-c c="i"></mjx-c><mjx-c c="f"></mjx-c><mjx-c c="A0"></mjx-c></mjx-mtext><mjx-texatom><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi></mjx-texatom><mjx-mtext class="mjx-n"><mjx-c c="A0"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="s"></mjx-c><mjx-c c=" "></mjx-c><mjx-c c="o"></mjx-c><mjx-c c="d"></mjx-c><mjx-c c="d"></mjx-c></mjx-mtext></mjx-mrow><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr></mjx-itable></mjx-mtable><mjx-mo class="mjx-n" style="vertical-align: 0.25em;"></mjx-mo></mjx-mrow></mjx-math></mjx-chtml></div>
<div><mjx-chtml class="MathJax MJX-CHTML MJX-TEX MJX-DISPLAY" style="font-size: 113.1%;"><mjx-math display="true"><mjx-mtable><mjx-itable><mjx-mtr><mjx-mtd style="padding-right: 0.5em; padding-bottom: 0.027em;"><mjx-mi class="mjx-i"><mjx-c c="n"></mjx-c></mjx-mi><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-right: 0.5em; border-left: .07em solid; padding-bottom: 0.027em;"><mjx-mtext class="mjx-n"><mjx-c c="L"></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="f"></mjx-c><mjx-c c="t"></mjx-c></mjx-mtext><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding-left: 0.5em; padding-right: 0.5em; padding-bottom: 0.027em;"><mjx-mtext class="mjx-n"><mjx-c c="C"></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="n"></mjx-c><mjx-c c="t"></mjx-c><mjx-c c="e"></mjx-c><mjx-c c="r"></mjx-c></mjx-mtext><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: right; padding-left: 0.5em; padding-bottom: 0.027em;"><mjx-mtext class="mjx-n"><mjx-c c="R"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="g"></mjx-c><mjx-c c="h"></mjx-c><mjx-c c="t"></mjx-c></mjx-mtext><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="padding-right: 0.5em; padding-top: 0.027em; padding-bottom: 0.027em; border-top: .07em solid;"><mjx-mn class="mjx-n"><mjx-c c="1"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; border-left: .07em solid; padding: 0.027em 0.5em 0.027em 0.5em; border-top: .07em solid;"><mjx-mn class="mjx-n"><mjx-c c="0"></mjx-c><mjx-c c="."></mjx-c><mjx-c c="2"></mjx-c><mjx-c c="4"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding: 0.027em 0.5em 0.027em 0.5em; border-top: .07em solid;"><mjx-mn class="mjx-n"><mjx-c c="1"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: right; padding-left: 0.5em; padding-top: 0.027em; padding-bottom: 0.027em; border-top: .07em solid;"><mjx-mn class="mjx-n"><mjx-c c="1"></mjx-c><mjx-c c="2"></mjx-c><mjx-c c="5"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="padding-right: 0.5em; padding-top: 0.027em; padding-bottom: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="2"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; border-left: .07em solid; padding: 0.027em 0.5em 0.027em 0.5em;"><mjx-mo class="mjx-n"><mjx-c c="2212"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c c="1"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding: 0.027em 0.5em 0.027em 0.5em;"><mjx-mn class="mjx-n"><mjx-c c="1"></mjx-c><mjx-c c="8"></mjx-c><mjx-c c="9"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: right; padding-left: 0.5em; padding-top: 0.027em; padding-bottom: 0.027em;"><mjx-mo class="mjx-n"><mjx-c c="2212"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c c="8"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr><mjx-mtr><mjx-mtd style="padding-right: 0.5em; padding-top: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="3"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: left; padding-left: 0.5em; padding-right: 0.5em; border-left: .07em solid; padding-top: 0.027em;"><mjx-mo class="mjx-n"><mjx-c c="2212"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c c="2"></mjx-c><mjx-c c="0"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding-left: 0.5em; padding-right: 0.5em; padding-top: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="2"></mjx-c><mjx-c c="0"></mjx-c><mjx-c c="0"></mjx-c><mjx-c c="0"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="text-align: right; padding-left: 0.5em; padding-top: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="1"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="3"><mjx-c c="+"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c c="1"></mjx-c><mjx-c c="0"></mjx-c></mjx-mn><mjx-mi class="mjx-i"><mjx-c c="i"></mjx-c></mjx-mi><mjx-tstrut></mjx-tstrut></mjx-mtd></mjx-mtr></mjx-itable></mjx-mtable></mjx-math></mjx-chtml>
</div>
<div><mjx-chtml class="MathJax MJX-CHTML MJX-TEX MJX-DISPLAY" style="font-size: 113.1%;"><mjx-math display="true"><mjx-mtable><mjx-itable><mjx-mtr><mjx-mtd style="padding-bottom: 0.027em;"><mjx-mtable><mjx-itable><mjx-mtr><mjx-mtd style="padding-right: 0.5em;"><mjx-mtable><mjx-itable><mjx-mtr><mjx-mtd style="padding-right: 0.5em; padding-bottom: 0.027em;"><mjx-mtext class="mjx-n"><mjx-c c="m"></mjx-c><mjx-c c="i"></mjx-c><mjx-c c="n"></mjx-c></mjx-mtext><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding-left: 0.5em; padding-right: 0.5em; border-left: .07em solid; padding-bottom: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="0"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding-left: 0.5em; padding-right: 0.5em; padding-bottom: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="1"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding-left: 0.5em; padding-right: 0.5em; padding-bottom: 0.027em;"><mjx-mn class="mjx-n"><mjx-c c="2"></mjx-c></mjx-mn><mjx-tstrut></mjx-tstrut></mjx-mtd><mjx-mtd style="padding-left: 0.5em; 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