1*b1cdbd2cSJim Jagielski<?xml version="1.0" encoding="UTF-8"?> 2*b1cdbd2cSJim Jagielski 3*b1cdbd2cSJim Jagielski 4*b1cdbd2cSJim Jagielski<!--*********************************************************** 5*b1cdbd2cSJim Jagielski * 6*b1cdbd2cSJim Jagielski * Licensed to the Apache Software Foundation (ASF) under one 7*b1cdbd2cSJim Jagielski * or more contributor license agreements. See the NOTICE file 8*b1cdbd2cSJim Jagielski * distributed with this work for additional information 9*b1cdbd2cSJim Jagielski * regarding copyright ownership. The ASF licenses this file 10*b1cdbd2cSJim Jagielski * to you under the Apache License, Version 2.0 (the 11*b1cdbd2cSJim Jagielski * "License"); you may not use this file except in compliance 12*b1cdbd2cSJim Jagielski * with the License. You may obtain a copy of the License at 13*b1cdbd2cSJim Jagielski * 14*b1cdbd2cSJim Jagielski * http://www.apache.org/licenses/LICENSE-2.0 15*b1cdbd2cSJim Jagielski * 16*b1cdbd2cSJim Jagielski * Unless required by applicable law or agreed to in writing, 17*b1cdbd2cSJim Jagielski * software distributed under the License is distributed on an 18*b1cdbd2cSJim Jagielski * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY 19*b1cdbd2cSJim Jagielski * KIND, either express or implied. See the License for the 20*b1cdbd2cSJim Jagielski * specific language governing permissions and limitations 21*b1cdbd2cSJim Jagielski * under the License. 22*b1cdbd2cSJim Jagielski * 23*b1cdbd2cSJim Jagielski ***********************************************************--> 24*b1cdbd2cSJim Jagielski 25*b1cdbd2cSJim Jagielski 26*b1cdbd2cSJim Jagielski 27*b1cdbd2cSJim Jagielski<helpdocument version="1.0"> 28*b1cdbd2cSJim Jagielski<meta> 29*b1cdbd2cSJim Jagielski<topic id="textsmath0103090200xml" indexer="include" status="PUBLISH"> 30*b1cdbd2cSJim Jagielski<title id="tit" xml-lang="en-US">Relations</title> 31*b1cdbd2cSJim Jagielski<filename>/text/smath/01/03090200.xhp</filename> 32*b1cdbd2cSJim Jagielski</topic> 33*b1cdbd2cSJim Jagielski<history> 34*b1cdbd2cSJim Jagielski<created date="2003-10-31T00:00:00">Sun Microsystems, Inc.</created> 35*b1cdbd2cSJim Jagielski<lastedited date="2004-09-06T11:25:01">converted from old format - fpe</lastedited> 36*b1cdbd2cSJim Jagielski</history> 37*b1cdbd2cSJim Jagielski</meta> 38*b1cdbd2cSJim Jagielski<body> 39*b1cdbd2cSJim Jagielski<section id="relationen"> 40*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="index" id="bm_id3156316"><bookmark_value>relations; in $[officename] Math</bookmark_value> 41*b1cdbd2cSJim Jagielski<bookmark_value>$[officename] Math; relations</bookmark_value> 42*b1cdbd2cSJim Jagielski<bookmark_value>equal sign</bookmark_value> 43*b1cdbd2cSJim Jagielski<bookmark_value>inequation</bookmark_value> 44*b1cdbd2cSJim Jagielski<bookmark_value>unequal sign</bookmark_value> 45*b1cdbd2cSJim Jagielski<bookmark_value>identical to relation</bookmark_value> 46*b1cdbd2cSJim Jagielski<bookmark_value>congruent relation</bookmark_value> 47*b1cdbd2cSJim Jagielski<bookmark_value>right angled relations</bookmark_value> 48*b1cdbd2cSJim Jagielski<bookmark_value>orthogonal relations</bookmark_value> 49*b1cdbd2cSJim Jagielski<bookmark_value>divides relation</bookmark_value> 50*b1cdbd2cSJim Jagielski<bookmark_value>does not divide relation</bookmark_value> 51*b1cdbd2cSJim Jagielski<bookmark_value>less than relations</bookmark_value> 52*b1cdbd2cSJim Jagielski<bookmark_value>approximately equal to relation</bookmark_value> 53*b1cdbd2cSJim Jagielski<bookmark_value>parallel relation</bookmark_value> 54*b1cdbd2cSJim Jagielski<bookmark_value>less than or equal to signs</bookmark_value> 55*b1cdbd2cSJim Jagielski<bookmark_value>greater than or equal to signs</bookmark_value> 56*b1cdbd2cSJim Jagielski<bookmark_value>proportional to relation</bookmark_value> 57*b1cdbd2cSJim Jagielski<bookmark_value>similar to relations</bookmark_value> 58*b1cdbd2cSJim Jagielski<bookmark_value>toward relation</bookmark_value> 59*b1cdbd2cSJim Jagielski<bookmark_value>logic symbols</bookmark_value> 60*b1cdbd2cSJim Jagielski<bookmark_value>double arrow symbols</bookmark_value> 61*b1cdbd2cSJim Jagielski<bookmark_value>much greater than relation</bookmark_value> 62*b1cdbd2cSJim Jagielski<bookmark_value>considerably greater than relation</bookmark_value> 63*b1cdbd2cSJim Jagielski<bookmark_value>greater than relations</bookmark_value> 64*b1cdbd2cSJim Jagielski<bookmark_value>much less than relation</bookmark_value> 65*b1cdbd2cSJim Jagielski<bookmark_value>considerably less than relation</bookmark_value> 66*b1cdbd2cSJim Jagielski<bookmark_value>defined as relation</bookmark_value> 67*b1cdbd2cSJim Jagielski<bookmark_value>correspondence; picture by</bookmark_value> 68*b1cdbd2cSJim Jagielski<bookmark_value>picture by correspondence</bookmark_value> 69*b1cdbd2cSJim Jagielski<bookmark_value>image of relation</bookmark_value> 70*b1cdbd2cSJim Jagielski<bookmark_value>correspondence; original by</bookmark_value> 71*b1cdbd2cSJim Jagielski<bookmark_value>original by correspondence</bookmark_value> 72*b1cdbd2cSJim Jagielski</bookmark> 73*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_RELATIONS_TBX" id="bm_id3145204" localize="false"/> 74*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_RELATIONS_CAT" id="bm_id3145207" localize="false"/> 75*b1cdbd2cSJim Jagielski<paragraph role="heading" id="hd_id3156316" xml-lang="en-US" level="1" l10n="U" oldref="1"><link href="text/smath/01/03090200.xhp" name="Relations">Relations</link></paragraph> 76*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3153152" xml-lang="en-US" l10n="U" oldref="2"><ahelp hid="HID_SMA_RELATIONS_CAT">You can choose among various relations to structure your <emph>$[officename] Math</emph> formula. The relation functions are displayed in the lower part of the Elements window.</ahelp> The list is also in the <link href="text/shared/00/00000001.xhp#kontextmenue" name="context menu">context menu</link> of the <emph>Commands</emph> window. All relations that are not contained in the Elements window or in the context menu can be typed manually in the Commands window.</paragraph> 77*b1cdbd2cSJim Jagielski</section> 78*b1cdbd2cSJim Jagielski<section id="howtoget"> 79*b1cdbd2cSJim Jagielski <embed href="text/smath/00/00000004.xhp#astbio"/> 80*b1cdbd2cSJim Jagielski</section> 81*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3147258" xml-lang="en-US" l10n="U" oldref="3">The following is a complete list of the relations. The symbol next to the name of the relation indicates that it can be accessed through the Elements window (choose <emph>View - Elements</emph>) or through the context menu of the <emph>Commands</emph> window.</paragraph> 82*b1cdbd2cSJim Jagielski<paragraph role="heading" id="hd_id3148827" xml-lang="en-US" level="3" l10n="U" oldref="4">Relations:</paragraph> 83*b1cdbd2cSJim Jagielski<table id="tbl_id3145414"> 84*b1cdbd2cSJim Jagielski<tablerow> 85*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 86*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10086" xml-lang="en-US" l10n="F"> 87*b1cdbd2cSJim Jagielski<image id="img_id3153573" src="starmath/res/bi21301.png" width="0.847cm" height="0.847cm"><alt id="alt_id3153573" xml-lang="en-US">Icon</alt> 88*b1cdbd2cSJim Jagielski </image></paragraph> 89*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XEQY" id="bm_id3153580" localize="false"/> 90*b1cdbd2cSJim Jagielski</tablecell> 91*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 92*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3154104" xml-lang="en-US" l10n="U" oldref="5">is equal</paragraph> 93*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3152947" xml-lang="en-US" l10n="U" oldref="6"><ahelp hid="HID_SMA_XEQY">Inserts an equal sign (=) with two placeholders.</ahelp> You can also directly type <emph><?> = <?></emph> in the <emph>Commands</emph> window.</paragraph> 94*b1cdbd2cSJim Jagielski</tablecell> 95*b1cdbd2cSJim Jagielski</tablerow> 96*b1cdbd2cSJim Jagielski</table> 97*b1cdbd2cSJim Jagielski 98*b1cdbd2cSJim Jagielski<table id="tbl_id3151098"> 99*b1cdbd2cSJim Jagielski<tablerow> 100*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 101*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN100BF" xml-lang="en-US" l10n="F"> 102*b1cdbd2cSJim Jagielski<image id="img_id3147523" src="starmath/res/bi21302.png" width="0.847cm" height="0.847cm"><alt id="alt_id3147523" xml-lang="en-US">Icon</alt> 103*b1cdbd2cSJim Jagielski </image></paragraph> 104*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XNEQY" id="bm_id3147529" localize="false"/> 105*b1cdbd2cSJim Jagielski</tablecell> 106*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 107*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3152959" xml-lang="en-US" l10n="U" oldref="54">does not equal</paragraph> 108*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3150976" xml-lang="en-US" l10n="U" oldref="53"><ahelp hid="HID_SMA_XNEQY">The <emph>neq</emph> icon or command inserts an <emph>inequality</emph> with two placeholders.</ahelp> You can also type <emph><?> neq <?></emph> in the <emph>Commands</emph> window.</paragraph> 109*b1cdbd2cSJim Jagielski</tablecell> 110*b1cdbd2cSJim Jagielski</tablerow> 111*b1cdbd2cSJim Jagielski</table> 112*b1cdbd2cSJim Jagielski 113*b1cdbd2cSJim Jagielski<table id="tbl_id3150831"> 114*b1cdbd2cSJim Jagielski<tablerow> 115*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 116*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10101" xml-lang="en-US" l10n="F"> 117*b1cdbd2cSJim Jagielski<image id="img_id3154196" src="starmath/res/bi21303.png" width="0.847cm" height="0.847cm"><alt id="alt_id3154196" xml-lang="en-US">Icon</alt> 118*b1cdbd2cSJim Jagielski </image></paragraph> 119*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XEQUIVY" id="bm_id3151322" localize="false"/> 120*b1cdbd2cSJim Jagielski</tablecell> 121*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 122*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3151332" xml-lang="en-US" l10n="U" oldref="56">identical to</paragraph> 123*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3155181" xml-lang="en-US" l10n="U" oldref="55"><ahelp hid="HID_SMA_XEQUIVY">Inserts a character for the <emph>identical to</emph> (congruent) relation with two placeholders.</ahelp> You can also type <emph><?> equiv <?></emph> in the <emph>Commands</emph> window.</paragraph> 124*b1cdbd2cSJim Jagielski</tablecell> 125*b1cdbd2cSJim Jagielski</tablerow> 126*b1cdbd2cSJim Jagielski</table> 127*b1cdbd2cSJim Jagielski 128*b1cdbd2cSJim Jagielski<table id="tbl_id3151256"> 129*b1cdbd2cSJim Jagielski<tablerow> 130*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 131*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10140" xml-lang="en-US" l10n="F"> 132*b1cdbd2cSJim Jagielski<image id="img_id3154835" src="starmath/res/bi21304.png" width="0.847cm" height="0.847cm"><alt id="alt_id3154835" xml-lang="en-US">Icon</alt> 133*b1cdbd2cSJim Jagielski </image></paragraph> 134*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XORTHOY" id="bm_id3147089" localize="false"/> 135*b1cdbd2cSJim Jagielski</tablecell> 136*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 137*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3147098" xml-lang="en-US" l10n="U" oldref="58">orthogonal to</paragraph> 138*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3148976" xml-lang="en-US" l10n="U" oldref="57"><ahelp hid="HID_SMA_XORTHOY">Inserts a character for an <emph>orthogonal</emph> (right angled) relation with two placeholders.</ahelp> You can also type <emph><?> ortho <?></emph> in the <emph>Commands</emph> window.</paragraph> 139*b1cdbd2cSJim Jagielski</tablecell> 140*b1cdbd2cSJim Jagielski</tablerow> 141*b1cdbd2cSJim Jagielski</table> 142*b1cdbd2cSJim Jagielski 143*b1cdbd2cSJim Jagielski<table id="tbl_id3148734"> 144*b1cdbd2cSJim Jagielski<tablerow> 145*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 146*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10182" xml-lang="en-US" l10n="F"> 147*b1cdbd2cSJim Jagielski<image id="img_id3147321" src="starmath/res/bi21322.png" width="0.847cm" height="0.847cm"><alt id="alt_id3147321" xml-lang="en-US">Icon</alt> 148*b1cdbd2cSJim Jagielski </image></paragraph> 149*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XDIVIDESY" id="bm_id3153514" localize="false"/> 150*b1cdbd2cSJim Jagielski</tablecell> 151*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 152*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3153523" xml-lang="en-US" l10n="U" oldref="80">divides</paragraph> 153*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3147079" xml-lang="en-US" l10n="U" oldref="79"><ahelp hid="HID_SMA_XDIVIDESY">Inserts the <emph>divides</emph> character.</ahelp> You can also type <emph><?> divides <?></emph> in the <emph>Commands</emph> window.</paragraph> 154*b1cdbd2cSJim Jagielski</tablecell> 155*b1cdbd2cSJim Jagielski</tablerow> 156*b1cdbd2cSJim Jagielski</table> 157*b1cdbd2cSJim Jagielski 158*b1cdbd2cSJim Jagielski<table id="tbl_id3153355"> 159*b1cdbd2cSJim Jagielski<tablerow> 160*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 161*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN101BF" xml-lang="en-US" l10n="F"> 162*b1cdbd2cSJim Jagielski<image id="img_id3151030" src="starmath/res/bi21323.png" width="0.847cm" height="0.847cm"><alt id="alt_id3151030" xml-lang="en-US">Icon</alt> 163*b1cdbd2cSJim Jagielski </image></paragraph> 164*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XNDIVIDESY" id="bm_id3156273" localize="false"/> 165*b1cdbd2cSJim Jagielski</tablecell> 166*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 167*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3149164" xml-lang="en-US" l10n="U" oldref="82">does not divide</paragraph> 168*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3149177" xml-lang="en-US" l10n="U" oldref="81"><ahelp hid="HID_SMA_XNDIVIDESY">This icon inserts the <emph>does not divide</emph> character.</ahelp> You can also type <emph><?>ndivides<?></emph> in the <emph>Commands</emph> window.</paragraph> 169*b1cdbd2cSJim Jagielski</tablecell> 170*b1cdbd2cSJim Jagielski</tablerow> 171*b1cdbd2cSJim Jagielski</table> 172*b1cdbd2cSJim Jagielski 173*b1cdbd2cSJim Jagielski<table id="tbl_id3147318"> 174*b1cdbd2cSJim Jagielski<tablerow> 175*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 176*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN101FC" xml-lang="en-US" l10n="F"> 177*b1cdbd2cSJim Jagielski<image id="img_id3155133" src="starmath/res/bi21305.png" width="0.847cm" height="0.847cm"><alt id="alt_id3155133" xml-lang="en-US">Icon</alt> 178*b1cdbd2cSJim Jagielski </image></paragraph> 179*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XLTY" id="bm_id3151381" localize="false"/> 180*b1cdbd2cSJim Jagielski</tablecell> 181*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 182*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3148877" xml-lang="en-US" l10n="U" oldref="27">less than</paragraph> 183*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3148889" xml-lang="en-US" l10n="U" oldref="28"><ahelp hid="HID_SMA_XLTY">Inserts the <emph>less than</emph> relation.</ahelp> You can also type <emph><?>lt<?></emph> or <?> < <?> in the <emph>Commands</emph> window.</paragraph> 184*b1cdbd2cSJim Jagielski</tablecell> 185*b1cdbd2cSJim Jagielski</tablerow> 186*b1cdbd2cSJim Jagielski</table> 187*b1cdbd2cSJim Jagielski 188*b1cdbd2cSJim Jagielski<table id="tbl_id3150112"> 189*b1cdbd2cSJim Jagielski<tablerow> 190*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 191*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN1023B" xml-lang="en-US" l10n="F"> 192*b1cdbd2cSJim Jagielski<image id="img_id3147468" src="starmath/res/bi21306.png" width="0.847cm" height="0.847cm"><alt id="alt_id3147468" xml-lang="en-US">Icon</alt> 193*b1cdbd2cSJim Jagielski </image></paragraph> 194*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XGTY" id="bm_id3147475" localize="false"/> 195*b1cdbd2cSJim Jagielski</tablecell> 196*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 197*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3147495" xml-lang="en-US" l10n="U" oldref="25">greater than</paragraph> 198*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3146904" xml-lang="en-US" l10n="U" oldref="26"><ahelp hid="HID_SMA_XGTY">Inserts the <emph>greater than </emph>relation.</ahelp> You can also type <emph><?> gt <?></emph> or <?> > <?> in the <emph>Commands</emph> window.</paragraph> 199*b1cdbd2cSJim Jagielski</tablecell> 200*b1cdbd2cSJim Jagielski</tablerow> 201*b1cdbd2cSJim Jagielski</table> 202*b1cdbd2cSJim Jagielski 203*b1cdbd2cSJim Jagielski<table id="tbl_id3149555"> 204*b1cdbd2cSJim Jagielski<tablerow> 205*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 206*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10279" xml-lang="en-US" l10n="F"> 207*b1cdbd2cSJim Jagielski<image id="img_id3155982" src="starmath/res/bi21307.png" width="0.847cm" height="0.847cm"><alt id="alt_id3155982" xml-lang="en-US">Icon</alt> 208*b1cdbd2cSJim Jagielski </image></paragraph> 209*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XAPPROXY" id="bm_id3153505" localize="false"/> 210*b1cdbd2cSJim Jagielski</tablecell> 211*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 212*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3149218" xml-lang="en-US" l10n="U" oldref="60">approximately equal to</paragraph> 213*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3149231" xml-lang="en-US" l10n="U" oldref="59"><ahelp hid="HID_SMA_XAPPROXY">Inserts the <emph>approximately equal</emph> relation with two placeholders.</ahelp> You can also type <emph><?> approx <?> </emph>in the <emph>Commands</emph> window.</paragraph> 214*b1cdbd2cSJim Jagielski</tablecell> 215*b1cdbd2cSJim Jagielski</tablerow> 216*b1cdbd2cSJim Jagielski</table> 217*b1cdbd2cSJim Jagielski 218*b1cdbd2cSJim Jagielski<table id="tbl_id3146338"> 219*b1cdbd2cSJim Jagielski<tablerow> 220*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 221*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN102B5" xml-lang="en-US" l10n="F"> 222*b1cdbd2cSJim Jagielski<image id="img_id3155773" src="starmath/res/bi21308.png" width="0.566cm" height="0.566cm"><alt id="alt_id3155773" xml-lang="en-US">Icon</alt> 223*b1cdbd2cSJim Jagielski </image></paragraph> 224*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XPARALLELY" id="bm_id3155780" localize="false"/> 225*b1cdbd2cSJim Jagielski</tablecell> 226*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 227*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3147598" xml-lang="en-US" l10n="U" oldref="62">parallel to</paragraph> 228*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3147449" xml-lang="en-US" l10n="U" oldref="61"><ahelp hid="HID_SMA_XPARALLELY">Inserts a <emph>parallel </emph>relation with two placeholders.</ahelp> You can also type <emph><?>parallel<?></emph> in the <emph>Commands</emph> window.</paragraph> 229*b1cdbd2cSJim Jagielski</tablecell> 230*b1cdbd2cSJim Jagielski</tablerow> 231*b1cdbd2cSJim Jagielski</table> 232*b1cdbd2cSJim Jagielski 233*b1cdbd2cSJim Jagielski<table id="tbl_id3155576"> 234*b1cdbd2cSJim Jagielski<tablerow> 235*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 236*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN102F3" xml-lang="en-US" l10n="F"> 237*b1cdbd2cSJim Jagielski<image id="img_id3148442" src="starmath/res/bi21309.png" width="0.847cm" height="0.847cm"><alt id="alt_id3148442" xml-lang="en-US">Icon</alt> 238*b1cdbd2cSJim Jagielski </image></paragraph> 239*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XLESLANTY" id="bm_id3151080" localize="false"/> 240*b1cdbd2cSJim Jagielski</tablecell> 241*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 242*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3151089" xml-lang="en-US" l10n="U" oldref="64">less than or equal to (slanted)</paragraph> 243*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3154078" xml-lang="en-US" l10n="U" oldref="63"><ahelp hid="HID_SMA_XLESLANTY">Inserts a <emph>less than or equal to</emph> relation with two placeholders.</ahelp> You can also type <emph><?> leslant <?></emph> in the <emph>Commands</emph> window.</paragraph> 244*b1cdbd2cSJim Jagielski</tablecell> 245*b1cdbd2cSJim Jagielski</tablerow> 246*b1cdbd2cSJim Jagielski</table> 247*b1cdbd2cSJim Jagielski 248*b1cdbd2cSJim Jagielski<table id="tbl_id3153806"> 249*b1cdbd2cSJim Jagielski<tablerow> 250*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 251*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10331" xml-lang="en-US" l10n="F"> 252*b1cdbd2cSJim Jagielski<image id="img_id3153299" src="starmath/res/bi21310.png" width="0.847cm" height="0.847cm"><alt id="alt_id3153299" xml-lang="en-US">Icon</alt> 253*b1cdbd2cSJim Jagielski </image></paragraph> 254*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XGESLANTY" id="bm_id3150162" localize="false"/> 255*b1cdbd2cSJim Jagielski</tablecell> 256*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 257*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3150171" xml-lang="en-US" l10n="U" oldref="66">greater than or equal to (slanted)</paragraph> 258*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3156098" xml-lang="en-US" l10n="U" oldref="65"><ahelp hid="HID_SMA_XGESLANTY">Inserts the <emph>greater than or equal to</emph> relation with two placeholders.</ahelp> You can also type <emph><?>geslant<?> </emph>in the <emph>Commands</emph> window.</paragraph> 259*b1cdbd2cSJim Jagielski</tablecell> 260*b1cdbd2cSJim Jagielski</tablerow> 261*b1cdbd2cSJim Jagielski</table> 262*b1cdbd2cSJim Jagielski 263*b1cdbd2cSJim Jagielski<table id="tbl_id3150466"> 264*b1cdbd2cSJim Jagielski<tablerow> 265*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 266*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN1036F" xml-lang="en-US" l10n="F"> 267*b1cdbd2cSJim Jagielski<image id="img_id3153976" src="starmath/res/bi21311.png" width="0.847cm" height="0.847cm"><alt id="alt_id3153976" xml-lang="en-US">Icon</alt> 268*b1cdbd2cSJim Jagielski </image></paragraph> 269*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XSIMEQY" id="bm_id3145327" localize="false"/> 270*b1cdbd2cSJim Jagielski</tablecell> 271*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 272*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3145336" xml-lang="en-US" l10n="U" oldref="68">similar or equal to</paragraph> 273*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3155580" xml-lang="en-US" l10n="U" oldref="67"><ahelp hid="HID_SMA_XSIMEQY">Inserts the <emph>similar or equal to</emph> relation with two placeholders.</ahelp> You can also type <emph><?>simeq<?></emph> in the <emph>Commands</emph> window.</paragraph> 274*b1cdbd2cSJim Jagielski</tablecell> 275*b1cdbd2cSJim Jagielski</tablerow> 276*b1cdbd2cSJim Jagielski</table> 277*b1cdbd2cSJim Jagielski 278*b1cdbd2cSJim Jagielski<table id="tbl_id3150920"> 279*b1cdbd2cSJim Jagielski<tablerow> 280*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 281*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN103AD" xml-lang="en-US" l10n="F"> 282*b1cdbd2cSJim Jagielski<image id="img_id3151195" src="starmath/res/bi21312.png" width="0.847cm" height="0.847cm"><alt id="alt_id3151195" xml-lang="en-US">Icon</alt> 283*b1cdbd2cSJim Jagielski </image></paragraph> 284*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XPROPY" id="bm_id3149250" localize="false"/> 285*b1cdbd2cSJim Jagielski</tablecell> 286*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 287*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3155076" xml-lang="en-US" l10n="U" oldref="70">proportional to</paragraph> 288*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3155088" xml-lang="en-US" l10n="U" oldref="69"><ahelp hid="HID_SMA_XPROPY">Inserts the <emph>proportional to</emph> relation with two placeholders.</ahelp> You can also type <emph><?> prop <?></emph> in the <emph>Commands</emph> window.</paragraph> 289*b1cdbd2cSJim Jagielski</tablecell> 290*b1cdbd2cSJim Jagielski</tablerow> 291*b1cdbd2cSJim Jagielski</table> 292*b1cdbd2cSJim Jagielski 293*b1cdbd2cSJim Jagielski<table id="tbl_id3146946"> 294*b1cdbd2cSJim Jagielski<tablerow> 295*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 296*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN103EB" xml-lang="en-US" l10n="F"> 297*b1cdbd2cSJim Jagielski<image id="img_id3150103" src="starmath/res/bi21313.png" width="0.847cm" height="0.847cm"><alt id="alt_id3150103" xml-lang="en-US">Icon</alt> 298*b1cdbd2cSJim Jagielski </image></paragraph> 299*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XLEY" id="bm_id3149997" localize="false"/> 300*b1cdbd2cSJim Jagielski</tablecell> 301*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 302*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3150006" xml-lang="en-US" l10n="U" oldref="31">less than or equal to</paragraph> 303*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3150033" xml-lang="en-US" l10n="U" oldref="32"><ahelp hid="HID_SMA_XLEY">Inserts the <emph>less than or equal to</emph> relation with two placeholders.</ahelp> You can also type <emph><?> le <?></emph> or <emph><?> <= <?></emph> in the <emph>Commands</emph> window.</paragraph> 304*b1cdbd2cSJim Jagielski</tablecell> 305*b1cdbd2cSJim Jagielski</tablerow> 306*b1cdbd2cSJim Jagielski</table> 307*b1cdbd2cSJim Jagielski 308*b1cdbd2cSJim Jagielski<table id="tbl_id3147234"> 309*b1cdbd2cSJim Jagielski<tablerow> 310*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 311*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN1042C" xml-lang="en-US" l10n="F"> 312*b1cdbd2cSJim Jagielski<image id="img_id3151228" src="starmath/res/bi21314.png" width="0.847cm" height="0.847cm"><alt id="alt_id3151228" xml-lang="en-US">Icon</alt> 313*b1cdbd2cSJim Jagielski </image></paragraph> 314*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XGEY" id="bm_id3153122" localize="false"/> 315*b1cdbd2cSJim Jagielski</tablecell> 316*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 317*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3153131" xml-lang="en-US" l10n="U" oldref="29">greater than or equal to</paragraph> 318*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3155379" xml-lang="en-US" l10n="U" oldref="30"><ahelp hid="HID_SMA_XGEY">Inserts the <emph>greater than or equal to</emph> relation with two placeholders.</ahelp> You can also type <emph><?> ge <?></emph> or <emph><?> >= <?></emph> in the <emph>Commands</emph> window.</paragraph> 319*b1cdbd2cSJim Jagielski</tablecell> 320*b1cdbd2cSJim Jagielski</tablerow> 321*b1cdbd2cSJim Jagielski</table> 322*b1cdbd2cSJim Jagielski 323*b1cdbd2cSJim Jagielski<table id="tbl_id3156090"> 324*b1cdbd2cSJim Jagielski<tablerow> 325*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 326*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN1046D" xml-lang="en-US" l10n="F"> 327*b1cdbd2cSJim Jagielski<image id="img_id3151003" src="starmath/res/bi21315.png" width="0.847cm" height="0.847cm"><alt id="alt_id3151003" xml-lang="en-US">Icon</alt> 328*b1cdbd2cSJim Jagielski </image></paragraph> 329*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XSIMY" id="bm_id3154365" localize="false"/> 330*b1cdbd2cSJim Jagielski</tablecell> 331*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 332*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3155935" xml-lang="en-US" l10n="U" oldref="72">similar to</paragraph> 333*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3155947" xml-lang="en-US" l10n="U" oldref="71"><ahelp hid="HID_SMA_XSIMY">This icon inserts the <emph>similar to</emph> relation with two placeholders.</ahelp> You can also type <emph><?>sim<?></emph> in the <emph>Commands</emph> window.</paragraph> 334*b1cdbd2cSJim Jagielski</tablecell> 335*b1cdbd2cSJim Jagielski</tablerow> 336*b1cdbd2cSJim Jagielski</table> 337*b1cdbd2cSJim Jagielski 338*b1cdbd2cSJim Jagielski<table id="tbl_id3147398"> 339*b1cdbd2cSJim Jagielski<tablerow> 340*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 341*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN104AB" xml-lang="en-US" l10n="F"> 342*b1cdbd2cSJim Jagielski<image id="img_id3149631" src="starmath/res/bi21316.png" width="0.847cm" height="0.847cm"><alt id="alt_id3149631" xml-lang="en-US">Icon</alt> 343*b1cdbd2cSJim Jagielski </image></paragraph> 344*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_XTOWARDY" id="bm_id3146086" localize="false"/> 345*b1cdbd2cSJim Jagielski</tablecell> 346*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 347*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3150659" xml-lang="en-US" l10n="U" oldref="73">toward</paragraph> 348*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3150670" xml-lang="en-US" l10n="U" oldref="42"><ahelp hid="HID_SMA_XTOWARDY">Inserts a <emph>toward</emph> relation symbol with two placeholders.</ahelp> You can also type <emph><?> toward <?></emph> in the <emph>Commands</emph> window.</paragraph> 349*b1cdbd2cSJim Jagielski</tablecell> 350*b1cdbd2cSJim Jagielski</tablerow> 351*b1cdbd2cSJim Jagielski</table> 352*b1cdbd2cSJim Jagielski 353*b1cdbd2cSJim Jagielski<table id="tbl_id3154675"> 354*b1cdbd2cSJim Jagielski<tablerow> 355*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 356*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN104E7" xml-lang="en-US" l10n="F"> 357*b1cdbd2cSJim Jagielski<image id="img_id3149969" src="starmath/res/bi21324.png" width="0.847cm" height="0.847cm"><alt id="alt_id3149969" xml-lang="en-US">Icon</alt> 358*b1cdbd2cSJim Jagielski </image></paragraph> 359*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_DLARROW" id="bm_id3147270" localize="false"/> 360*b1cdbd2cSJim Jagielski</tablecell> 361*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 362*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3147279" xml-lang="en-US" l10n="U" oldref="84">double arrow pointing left</paragraph> 363*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3149599" xml-lang="en-US" l10n="U" oldref="83"><ahelp hid="HID_SMA_DLARROW">Inserts the logical relation <emph>arrow with double bar pointing left</emph>.</ahelp> You can also type <emph>dlarrow</emph> in the <emph>Commands</emph> window.</paragraph> 364*b1cdbd2cSJim Jagielski</tablecell> 365*b1cdbd2cSJim Jagielski</tablerow> 366*b1cdbd2cSJim Jagielski</table> 367*b1cdbd2cSJim Jagielski 368*b1cdbd2cSJim Jagielski<table id="tbl_id3145651"> 369*b1cdbd2cSJim Jagielski<tablerow> 370*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 371*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10525" xml-lang="en-US" l10n="F"> 372*b1cdbd2cSJim Jagielski<image id="img_id3149516" src="starmath/res/bi21325.png" width="0.847cm" height="0.847cm"><alt id="alt_id3149516" xml-lang="en-US">Icon</alt> 373*b1cdbd2cSJim Jagielski </image></paragraph> 374*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_DLRARROW" id="bm_id3149204" localize="false"/> 375*b1cdbd2cSJim Jagielski</tablecell> 376*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 377*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3148707" xml-lang="en-US" l10n="U" oldref="86">double arrow pointing left and right</paragraph> 378*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3148721" xml-lang="en-US" l10n="U" oldref="85"><ahelp hid="HID_SMA_DLRARROW">Inserts the logical relation <emph>arrow with double bar pointing left and right</emph> with two operators.</ahelp> You can also type <emph>dlrarrow</emph> in the <emph>Commands</emph> window.</paragraph> 379*b1cdbd2cSJim Jagielski</tablecell> 380*b1cdbd2cSJim Jagielski</tablerow> 381*b1cdbd2cSJim Jagielski</table> 382*b1cdbd2cSJim Jagielski 383*b1cdbd2cSJim Jagielski<table id="tbl_id3155359"> 384*b1cdbd2cSJim Jagielski<tablerow> 385*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 386*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_idN10563" xml-lang="en-US" l10n="F"> 387*b1cdbd2cSJim Jagielski<image id="img_id3148697" src="starmath/res/bi21326.png" width="0.847cm" height="0.847cm"><alt id="alt_id3148697" xml-lang="en-US">Icon</alt> 388*b1cdbd2cSJim Jagielski </image></paragraph> 389*b1cdbd2cSJim Jagielski<bookmark xml-lang="en-US" branch="hid/STARMATH_HID_SMA_DRARROW" id="bm_id3150844" localize="false"/> 390*b1cdbd2cSJim Jagielski</tablecell> 391*b1cdbd2cSJim Jagielski<tablecell colspan="" rowspan=""> 392*b1cdbd2cSJim Jagielski<paragraph role="tablehead" id="par_id3150853" xml-lang="en-US" l10n="U" oldref="88">double arrow pointing right</paragraph> 393*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3150866" xml-lang="en-US" l10n="U" oldref="87"><ahelp hid="HID_SMA_DRARROW">Inserts the logical operator <emph>arrow with double bar pointing right</emph> with two placeholders.</ahelp> You can also type <emph>drarrow</emph> in the <emph>Commands</emph> window.</paragraph> 394*b1cdbd2cSJim Jagielski</tablecell> 395*b1cdbd2cSJim Jagielski</tablerow> 396*b1cdbd2cSJim Jagielski</table> 397*b1cdbd2cSJim Jagielski 398*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3153545" xml-lang="en-US" l10n="U" oldref="74">To create the <emph>much greater than</emph> relation with two placeholders, type <emph><?> gg <?> </emph>or <emph>>></emph> in the <emph>Commands</emph> window.</paragraph> 399*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3156000" xml-lang="en-US" l10n="U" oldref="75">Type <emph>ll</emph> or <emph><<</emph> in the <emph>Commands</emph> window to insert the <emph>much less than</emph> relation into the formula.</paragraph> 400*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3153749" xml-lang="en-US" l10n="U" oldref="76">The <emph>is defined as</emph> relation with two placeholders is inserted by typing <emph><?>def<?></emph>.</paragraph> 401*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3154068" xml-lang="en-US" l10n="U" oldref="77">Insert the <emph>picture by</emph> correspondence character with two placeholders by typing <emph><?> transl <?></emph> in the <emph>Commands</emph> window.</paragraph> 402*b1cdbd2cSJim Jagielski<paragraph role="paragraph" id="par_id3149592" xml-lang="en-US" l10n="U" oldref="78">The <emph><?>transr<?></emph> command inserts the <emph>original by</emph> correspondence character with two placeholders.</paragraph> 403*b1cdbd2cSJim Jagielski<paragraph role="warning" id="par_id3154735" xml-lang="en-US" l10n="U" oldref="52">When entering information manually in the <emph>Commands</emph> window, note that a number of operators require spaces for the correct structure. This is especially true if you are working with values instead of placeholders. For example, for the "is considerably greater" relation, type either <emph>10 gg 1</emph> or <emph>a gg b</emph>.</paragraph> 404*b1cdbd2cSJim Jagielski</body> 405*b1cdbd2cSJim Jagielski</helpdocument> 406
