1<?xml version="1.0" encoding="UTF-8"?> 2 3<!--*********************************************************** 4 * 5 * Licensed to the Apache Software Foundation (ASF) under one 6 * or more contributor license agreements. See the NOTICE file 7 * distributed with this work for additional information 8 * regarding copyright ownership. The ASF licenses this file 9 * to you under the Apache License, Version 2.0 (the 10 * "License"); you may not use this file except in compliance 11 * with the License. You may obtain a copy of the License at 12 * 13 * http://www.apache.org/licenses/LICENSE-2.0 14 * 15 * Unless required by applicable law or agreed to in writing, 16 * software distributed under the License is distributed on an 17 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY 18 * KIND, either express or implied. See the License for the 19 * specific language governing permissions and limitations 20 * under the License. 21 * 22 ***********************************************************--> 23 24<helpdocument version="1.0"> 25<meta> 26<topic id="textsmath0103091503xml" indexer="include" status="PUBLISH"> 27<title id="tit" xml-lang="en-US">Set Operators</title> 28<filename>/text/smath/01/03091503.xhp</filename> 29</topic> 30</meta> 31<body> 32<bookmark xml-lang="en-US" branch="index" id="bm_id3157991"> 33<bookmark_value>set operators;list of</bookmark_value> 34</bookmark> 35<paragraph role="heading" id="hd_id4201178" xml-lang="en-US" level="1" l10n="NEW"><variable id="set"><link href="text/smath/01/03091503.xhp" name="set">Set Operators</link> 36</variable></paragraph> 37<table id="tbl_id3145680"> 38<tablerow> 39<tablecell colspan="" rowspan=""> 40<paragraph role="tablehead" id="par_idN1130F" xml-lang="en-US" l10n="NEW">Typed command(s)</paragraph> 41</tablecell> 42<tablecell colspan="" rowspan=""> 43<paragraph role="tablehead" id="par_id3145724" xml-lang="en-US" l10n="U">Symbol in Elements Window</paragraph> 44</tablecell> 45<tablecell colspan="" rowspan=""> 46<paragraph role="tablehead" id="par_id3158137" xml-lang="en-US" l10n="U">Meaning</paragraph> 47</tablecell> 48</tablerow> 49<tablerow> 50<tablecell colspan="" rowspan=""> 51<paragraph role="tablecontent" id="par_idN1146D" xml-lang="en-US" l10n="NEW" localize="false"> 52<item type="literal">aleph</item> 53</paragraph> 54</tablecell> 55<tablecell colspan="" rowspan=""> 56<paragraph role="tablecontent" id="par_id3146505" xml-lang="en-US" l10n="E"> 57<image id="img_id3146512" src="starmath/res/op22001.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3146512" xml-lang="en-US">Icon</alt></image></paragraph></tablecell> 58<tablecell colspan="" rowspan=""> 59<paragraph role="tablecontent" id="par_id3146625" xml-lang="en-US" l10n="U">Cardinal number</paragraph> 60</tablecell> 61</tablerow> 62<tablerow> 63<tablecell colspan="" rowspan=""> 64<paragraph role="tablecontent" id="par_idN1131F" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">emptyset</item></paragraph> 65</tablecell> 66<tablecell colspan="" rowspan=""> 67<paragraph role="tablecontent" id="par_id3159379" xml-lang="en-US" l10n="E"> 68<image id="img_id3159386" src="starmath/res/op22002.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3159386" xml-lang="en-US">Icon</alt> 69</image></paragraph> 70</tablecell> 71<tablecell colspan="" rowspan=""> 72<paragraph role="tablecontent" id="par_id3152374" xml-lang="en-US" l10n="U">Empty set</paragraph> 73</tablecell> 74</tablerow> 75<tablerow> 76<tablecell colspan="" rowspan=""> 77<paragraph role="tablecontent" id="par_id8198065" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">in</item></paragraph> 78</tablecell> 79<tablecell colspan="" rowspan=""> 80<paragraph role="tablecontent" id="par_id3158166" xml-lang="en-US" l10n="E"> 81<image id="img_id3158173" src="starmath/res/op21401.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3158173" xml-lang="en-US">Icon</alt> 82</image></paragraph> 83</tablecell> 84<tablecell colspan="" rowspan=""> 85<paragraph role="tablecontent" id="par_id3155037" xml-lang="en-US" l10n="U">is contained in</paragraph> 86</tablecell> 87</tablerow> 88<tablerow> 89<tablecell colspan="" rowspan=""> 90<paragraph role="tablecontent" id="par_idN11361" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">intersection</item></paragraph> 91</tablecell> 92<tablecell colspan="" rowspan=""> 93<paragraph role="tablecontent" id="par_id3152402" xml-lang="en-US" l10n="E"> 94<image id="img_id3152408" src="starmath/res/op21405.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3152408" xml-lang="en-US">Icon</alt> 95</image></paragraph> 96</tablecell> 97<tablecell colspan="" rowspan=""> 98<paragraph role="tablecontent" id="par_id3152522" xml-lang="en-US" l10n="U">Intersection of sets</paragraph> 99</tablecell> 100</tablerow> 101<tablerow> 102<tablecell colspan="" rowspan=""> 103<paragraph role="tablecontent" id="par_idN11297" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">notin</item></paragraph> 104</tablecell> 105<tablecell colspan="" rowspan=""> 106<paragraph role="tablecontent" id="par_id3158212" xml-lang="en-US" l10n="E"> 107<image id="img_id3158218" src="starmath/res/op21402.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3158218" xml-lang="en-US">Icon</alt> 108</image></paragraph> 109</tablecell> 110<tablecell colspan="" rowspan=""> 111<paragraph role="tablecontent" id="par_id3158332" xml-lang="en-US" l10n="U">is not contained in</paragraph> 112</tablecell> 113</tablerow> 114<tablerow> 115<tablecell colspan="" rowspan=""> 116<paragraph role="tablecontent" id="par_idN115B7" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">nsubset</item></paragraph> 117</tablecell> 118<tablecell colspan="" rowspan=""> 119<paragraph role="tablecontent" id="par_id3158819" xml-lang="en-US" l10n="E"> 120<image id="img_id3158825" src="starmath/res/op21413.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3158825" xml-lang="en-US">Icon</alt> 121</image></paragraph> 122</tablecell> 123<tablecell colspan="" rowspan=""> 124<paragraph role="tablecontent" id="par_id3158939" xml-lang="en-US" l10n="U">Not subset to</paragraph> 125</tablecell> 126</tablerow> 127<tablerow> 128<tablecell colspan="" rowspan=""> 129<paragraph role="tablecontent" id="par_idN115F9" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">nsubseteq</item></paragraph> 130</tablecell> 131<tablecell colspan="" rowspan=""> 132<paragraph role="tablecontent" id="par_id3158966" xml-lang="en-US" l10n="E"> 133<image id="img_id3158973" src="starmath/res/op21414.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3158973" xml-lang="en-US">Icon</alt> 134</image></paragraph> 135</tablecell> 136<tablecell colspan="" rowspan=""> 137<paragraph role="tablecontent" id="par_id3159086" xml-lang="en-US" l10n="U">Not subset or equal to</paragraph> 138</tablecell> 139</tablerow> 140<tablerow> 141<tablecell colspan="" rowspan=""> 142<paragraph role="tablecontent" id="par_idN1163B" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">nsupset</item></paragraph> 143</tablecell> 144<tablecell colspan="" rowspan=""> 145<paragraph role="tablecontent" id="par_id3159114" xml-lang="en-US" l10n="E"> 146<image id="img_id3159120" src="starmath/res/op21415.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3159120" xml-lang="en-US">Icon</alt> 147</image></paragraph> 148</tablecell> 149<tablecell colspan="" rowspan=""> 150<paragraph role="tablecontent" id="par_id3162974" xml-lang="en-US" l10n="U">Not superset</paragraph> 151</tablecell> 152</tablerow> 153<tablerow> 154<tablecell colspan="" rowspan=""> 155<paragraph role="tablecontent" id="par_idN1167D" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">nsupseteq</item></paragraph> 156</tablecell> 157<tablecell colspan="" rowspan=""> 158<paragraph role="tablecontent" id="par_id3163002" xml-lang="en-US" l10n="E"> 159<image id="img_id3163008" src="starmath/res/op21416.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3163008" xml-lang="en-US">Icon</alt> 160</image></paragraph> 161</tablecell> 162<tablecell colspan="" rowspan=""> 163<paragraph role="tablecontent" id="par_id3163122" xml-lang="en-US" l10n="U">Not superset or equal to</paragraph> 164</tablecell> 165</tablerow> 166<tablerow> 167<tablecell colspan="" rowspan=""> 168<paragraph role="tablecontent" id="par_idN112D9" xml-lang="en-US" l10n="NEW"> 169<item type="literal">owns</item> or <item type="literal">ni</item> 170</paragraph> 171</tablecell> 172<tablecell colspan="" rowspan=""> 173<paragraph role="tablecontent" id="par_id3158359" xml-lang="en-US" l10n="E"> 174<image id="img_id3158366" src="starmath/res/op21403.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3158366" xml-lang="en-US">Icon</alt> 175</image></paragraph> 176</tablecell> 177<tablecell colspan="" rowspan=""> 178<paragraph role="tablecontent" id="par_id3159352" xml-lang="en-US" l10n="U">Contains</paragraph> 179</tablecell> 180</tablerow> 181<tablerow> 182<tablecell colspan="" rowspan=""> 183<paragraph role="tablecontent" id="par_idN117C7" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">setc</item></paragraph> 184</tablecell> 185<tablecell colspan="" rowspan=""> 186<paragraph role="tablecontent" id="par_id3156480" xml-lang="en-US" l10n="E"> 187<image id="img_id3156486" src="starmath/res/op21421.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3156486" xml-lang="en-US">Icon</alt> 188</image></paragraph> 189</tablecell> 190<tablecell colspan="" rowspan=""> 191<paragraph role="tablecontent" id="par_id3156600" xml-lang="en-US" l10n="U">Complex number</paragraph> 192</tablecell> 193</tablerow> 194<tablerow> 195<tablecell colspan="" rowspan=""> 196<paragraph role="tablecontent" id="par_idN113E5" xml-lang="en-US" l10n="NEW"><item type="literal">setminus</item> or <item type="literal">bslash</item></paragraph> 197</tablecell> 198<tablecell colspan="" rowspan=""> 199<paragraph role="tablecontent" id="par_id3145932" xml-lang="en-US" l10n="E"> 200<image id="img_id3145938" src="starmath/res/op21407.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3145938" xml-lang="en-US">Icon</alt> 201</image></paragraph> 202</tablecell> 203<tablecell colspan="" rowspan=""> 204<paragraph role="tablecontent" id="par_id3146052" xml-lang="en-US" l10n="U">Difference between sets</paragraph> 205</tablecell> 206</tablerow> 207<tablerow> 208<tablecell colspan="" rowspan=""> 209<paragraph role="tablecontent" id="par_idN116BF" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">setn</item></paragraph> 210</tablecell> 211<tablecell colspan="" rowspan=""> 212<paragraph role="tablecontent" id="par_id3163149" xml-lang="en-US" l10n="E"> 213<image id="img_id3163156" src="starmath/res/op21417.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3163156" xml-lang="en-US">Icon</alt> 214</image></paragraph> 215</tablecell> 216<tablecell colspan="" rowspan=""> 217<paragraph role="tablecontent" id="par_id3163269" xml-lang="en-US" l10n="U">Natural number</paragraph> 218</tablecell> 219</tablerow> 220<tablerow> 221<tablecell colspan="" rowspan=""> 222<paragraph role="tablecontent" id="par_idN11743" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">setq</item></paragraph> 223</tablecell> 224<tablecell colspan="" rowspan=""> 225<paragraph role="tablecontent" id="par_id3163444" xml-lang="en-US" l10n="E"> 226<image id="img_id3163450" src="starmath/res/op21419.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3163450" xml-lang="en-US">Icon</alt> 227</image></paragraph> 228</tablecell> 229<tablecell colspan="" rowspan=""> 230<paragraph role="tablecontent" id="par_id3163564" xml-lang="en-US" l10n="U">Rational number</paragraph> 231</tablecell> 232</tablerow> 233<tablerow> 234<tablecell colspan="" rowspan=""> 235<paragraph role="tablecontent" id="par_idN11785" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">setr</item></paragraph> 236</tablecell> 237<tablecell colspan="" rowspan=""> 238<paragraph role="tablecontent" id="par_id3163591" xml-lang="en-US" l10n="E"> 239<image id="img_id3163598" src="starmath/res/op21420.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3163598" xml-lang="en-US">Icon</alt> 240</image></paragraph> 241</tablecell> 242<tablecell colspan="" rowspan=""> 243<paragraph role="tablecontent" id="par_id3156453" xml-lang="en-US" l10n="U">Real number</paragraph> 244</tablecell> 245</tablerow> 246<tablerow> 247<tablecell colspan="" rowspan=""> 248<paragraph role="tablecontent" id="par_idN11701" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">setz</item></paragraph> 249</tablecell> 250<tablecell colspan="" rowspan=""> 251<paragraph role="tablecontent" id="par_id3163296" xml-lang="en-US" l10n="E"> 252<image id="img_id3163303" src="starmath/res/op21418.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3163303" xml-lang="en-US">Icon</alt> 253</image></paragraph> 254</tablecell> 255<tablecell colspan="" rowspan=""> 256<paragraph role="tablecontent" id="par_id3163416" xml-lang="en-US" l10n="U">Integer</paragraph> 257</tablecell> 258</tablerow> 259<tablerow> 260<tablecell colspan="" rowspan=""> 261<paragraph role="tablecontent" id="par_idN1142B" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">slash</item></paragraph> 262</tablecell> 263<tablecell colspan="" rowspan=""> 264<paragraph role="tablecontent" id="par_id3146357" xml-lang="en-US" l10n="E"> 265<image id="img_id3146363" src="starmath/res/op21408.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3146363" xml-lang="en-US">Icon</alt> 266</image></paragraph> 267</tablecell> 268<tablecell colspan="" rowspan=""> 269<paragraph role="tablecontent" id="par_id3146477" xml-lang="en-US" l10n="U">Slash / for quotient set (slash) between characters</paragraph> 270</tablecell> 271</tablerow> 272<tablerow> 273<tablecell colspan="" rowspan=""> 274<paragraph role="tablecontent" id="par_idN114AF" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">subset</item></paragraph> 275</tablecell> 276<tablecell colspan="" rowspan=""> 277<paragraph role="tablecontent" id="par_id3146652" xml-lang="en-US" l10n="E"> 278<image id="img_id3146659" src="starmath/res/op21409.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3146659" xml-lang="en-US">Icon</alt> 279</image></paragraph> 280</tablecell> 281<tablecell colspan="" rowspan=""> 282<paragraph role="tablecontent" id="par_id3146772" xml-lang="en-US" l10n="U">Subset</paragraph> 283</tablecell> 284</tablerow> 285<tablerow> 286<tablecell colspan="" rowspan=""> 287<paragraph role="tablecontent" id="par_idN114F1" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">subseteq</item></paragraph> 288</tablecell> 289<tablecell colspan="" rowspan=""> 290<paragraph role="tablecontent" id="par_id3146800" xml-lang="en-US" l10n="E"> 291<image id="img_id3146806" src="starmath/res/op21410.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3146806" xml-lang="en-US">Icon</alt> 292</image></paragraph> 293</tablecell> 294<tablecell colspan="" rowspan=""> 295<paragraph role="tablecontent" id="par_id3158496" xml-lang="en-US" l10n="U">Subset or equal to</paragraph> 296</tablecell> 297</tablerow> 298<tablerow> 299<tablecell colspan="" rowspan=""> 300<paragraph role="tablecontent" id="par_idN11533" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">supset</item></paragraph> 301</tablecell> 302<tablecell colspan="" rowspan=""> 303<paragraph role="tablecontent" id="par_id3158524" xml-lang="en-US" l10n="E"> 304<image id="img_id3158530" src="starmath/res/op21411.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3158530" xml-lang="en-US">Icon</alt> 305</image></paragraph> 306</tablecell> 307<tablecell colspan="" rowspan=""> 308<paragraph role="tablecontent" id="par_id3158644" xml-lang="en-US" l10n="U">Superset</paragraph> 309</tablecell> 310</tablerow> 311<tablerow> 312<tablecell colspan="" rowspan=""> 313<paragraph role="tablecontent" id="par_idN11575" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">supseteq</item></paragraph> 314</tablecell> 315<tablecell colspan="" rowspan=""> 316<paragraph role="tablecontent" id="par_id3158671" xml-lang="en-US" l10n="E"> 317<image id="img_id3158678" src="starmath/res/op21412.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3158678" xml-lang="en-US">Icon</alt> 318</image></paragraph> 319</tablecell> 320<tablecell colspan="" rowspan=""> 321<paragraph role="tablecontent" id="par_id3158791" xml-lang="en-US" l10n="U">Superset or equal to</paragraph> 322</tablecell> 323</tablerow> 324<tablerow> 325<tablecell colspan="" rowspan=""> 326<paragraph role="tablecontent" id="par_idN113A3" xml-lang="en-US" l10n="NEW" localize="false"><item type="literal">union</item></paragraph> 327</tablecell> 328<tablecell colspan="" rowspan=""> 329<paragraph role="tablecontent" id="par_id3152548" xml-lang="en-US" l10n="E"> 330<image id="img_id3152555" src="starmath/res/op21406.png" width="0.3335inch" height="0.3335inch"><alt id="alt_id3152555" xml-lang="en-US">Icon</alt> 331</image></paragraph> 332</tablecell> 333<tablecell colspan="" rowspan=""> 334<paragraph role="tablecontent" id="par_id3145904" xml-lang="en-US" l10n="U">Union of sets</paragraph> 335</tablecell> 336</tablerow> 337</table> 338<section id="relatedtopics"> 339<embed href="text/smath/01/03090800.xhp#mengenop"/> 340<embed href="text/smath/01/03091500.xhp#reference"/> 341</section> 342</body> 343</helpdocument> 344
