1<?xml version="1.0" encoding="UTF-8"?> 2 3 4 5<!--*********************************************************** 6 * 7 * Licensed to the Apache Software Foundation (ASF) under one 8 * or more contributor license agreements. See the NOTICE file 9 * distributed with this work for additional information 10 * regarding copyright ownership. The ASF licenses this file 11 * to you under the Apache License, Version 2.0 (the 12 * "License"); you may not use this file except in compliance 13 * with the License. You may obtain a copy of the License at 14 * 15 * http://www.apache.org/licenses/LICENSE-2.0 16 * 17 * Unless required by applicable law or agreed to in writing, 18 * software distributed under the License is distributed on an 19 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY 20 * KIND, either express or implied. See the License for the 21 * specific language governing permissions and limitations 22 * under the License. 23 * 24 ***********************************************************--> 25 26 27 28 29 <helpdocument version="1.0"> 30<meta> 31<topic id="textsmath0103091503xml" indexer="include" status="PUBLISH"> 32<title id="tit" xml-lang="en-US">Set Operators</title> 33<filename>/text/smath/01/03091503.xhp</filename> 34</topic> 35</meta> 36<body> 37<bookmark xml-lang="en-US" branch="index" id="bm_id3157991"><bookmark_value>set operators;list of</bookmark_value> 38</bookmark> 39<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> 40</variable></paragraph> 41<table id="tbl_id3145680"> 42<tablerow> 43<tablecell colspan="" rowspan=""> 44<paragraph role="tablehead" id="par_idN1130F" xml-lang="en-US" l10n="NEW">Typed command(s)</paragraph> 45</tablecell> 46<tablecell colspan="" rowspan=""> 47<paragraph role="tablehead" id="par_id3145724" xml-lang="en-US" l10n="U" oldref="478">Symbol in Elements Window</paragraph> 48</tablecell> 49<tablecell colspan="" rowspan=""> 50<paragraph role="tablehead" id="par_id3158137" xml-lang="en-US" l10n="U" oldref="480">Meaning</paragraph> 51</tablecell> 52</tablerow> 53<tablerow> 54<tablecell colspan="" rowspan=""> 55<paragraph role="tablecontent" id="par_idN1146D" xml-lang="en-US" l10n="NEW" localize="false"> 56<item type="literal">aleph</item> 57</paragraph> 58</tablecell> 59<tablecell colspan="" rowspan=""> 60<paragraph role="tablecontent" id="par_id3146505" xml-lang="en-US" l10n="E"> 61<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> 62 </image></paragraph> 63</tablecell> 64<tablecell colspan="" rowspan=""> 65<paragraph role="tablecontent" id="par_id3146625" xml-lang="en-US" l10n="U" oldref="214">Cardinal number</paragraph> 66</tablecell> 67</tablerow> 68<tablerow> 69<tablecell colspan="" rowspan=""> 70<paragraph role="tablecontent" id="par_idN1131F" xml-lang="en-US" l10n="NEW" localize="false"> 71<item type="literal">emptyset</item> 72</paragraph> 73</tablecell> 74<tablecell colspan="" rowspan=""> 75<paragraph role="tablecontent" id="par_id3159379" xml-lang="en-US" l10n="E"> 76<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> 77 </image></paragraph> 78</tablecell> 79<tablecell colspan="" rowspan=""> 80<paragraph role="tablecontent" id="par_id3152374" xml-lang="en-US" l10n="U" oldref="218">Empty set</paragraph> 81</tablecell> 82</tablerow> 83<tablerow> 84<tablecell colspan="" rowspan=""> 85<paragraph role="tablecontent" id="par_id8198065" xml-lang="en-US" l10n="NEW" localize="false"> 86<item type="literal">in</item> 87</paragraph> 88</tablecell> 89<tablecell colspan="" rowspan=""> 90<paragraph role="tablecontent" id="par_id3158166" xml-lang="en-US" l10n="E"> 91<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> 92 </image></paragraph> 93</tablecell> 94<tablecell colspan="" rowspan=""> 95<paragraph role="tablecontent" id="par_id3155037" xml-lang="en-US" l10n="U" oldref="102">is contained in</paragraph> 96</tablecell> 97</tablerow> 98<tablerow> 99<tablecell colspan="" rowspan=""> 100<paragraph role="tablecontent" id="par_idN11361" xml-lang="en-US" l10n="NEW" localize="false"> 101<item type="literal">intersection</item> 102</paragraph> 103</tablecell> 104<tablecell colspan="" rowspan=""> 105<paragraph role="tablecontent" id="par_id3152402" xml-lang="en-US" l10n="E"> 106<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> 107 </image></paragraph> 108</tablecell> 109<tablecell colspan="" rowspan=""> 110<paragraph role="tablecontent" id="par_id3152522" xml-lang="en-US" l10n="U" oldref="126">Intersection of sets</paragraph> 111</tablecell> 112</tablerow> 113<tablerow> 114<tablecell colspan="" rowspan=""> 115<paragraph role="tablecontent" id="par_idN11297" xml-lang="en-US" l10n="NEW" localize="false"> 116<item type="literal">notin</item> 117</paragraph> 118</tablecell> 119<tablecell colspan="" rowspan=""> 120<paragraph role="tablecontent" id="par_id3158212" xml-lang="en-US" l10n="E"> 121<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> 122 </image></paragraph> 123</tablecell> 124<tablecell colspan="" rowspan=""> 125<paragraph role="tablecontent" id="par_id3158332" xml-lang="en-US" l10n="U" oldref="104">is not contained in</paragraph> 126</tablecell> 127</tablerow> 128<tablerow> 129<tablecell colspan="" rowspan=""> 130<paragraph role="tablecontent" id="par_idN115B7" xml-lang="en-US" l10n="NEW" localize="false"> 131<item type="literal">nsubset</item> 132</paragraph> 133</tablecell> 134<tablecell colspan="" rowspan=""> 135<paragraph role="tablecontent" id="par_id3158819" xml-lang="en-US" l10n="E"> 136<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> 137 </image></paragraph> 138</tablecell> 139<tablecell colspan="" rowspan=""> 140<paragraph role="tablecontent" id="par_id3158939" xml-lang="en-US" l10n="U" oldref="110">Not subset to</paragraph> 141</tablecell> 142</tablerow> 143<tablerow> 144<tablecell colspan="" rowspan=""> 145<paragraph role="tablecontent" id="par_idN115F9" xml-lang="en-US" l10n="NEW" localize="false"> 146<item type="literal">nsubseteq</item> 147</paragraph> 148</tablecell> 149<tablecell colspan="" rowspan=""> 150<paragraph role="tablecontent" id="par_id3158966" xml-lang="en-US" l10n="E"> 151<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> 152 </image></paragraph> 153</tablecell> 154<tablecell colspan="" rowspan=""> 155<paragraph role="tablecontent" id="par_id3159086" xml-lang="en-US" l10n="U" oldref="112">Not subset or equal to</paragraph> 156</tablecell> 157</tablerow> 158<tablerow> 159<tablecell colspan="" rowspan=""> 160<paragraph role="tablecontent" id="par_idN1163B" xml-lang="en-US" l10n="NEW" localize="false"> 161<item type="literal">nsupset</item> 162</paragraph> 163</tablecell> 164<tablecell colspan="" rowspan=""> 165<paragraph role="tablecontent" id="par_id3159114" xml-lang="en-US" l10n="E"> 166<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> 167 </image></paragraph> 168</tablecell> 169<tablecell colspan="" rowspan=""> 170<paragraph role="tablecontent" id="par_id3162974" xml-lang="en-US" l10n="U" oldref="118">Not superset</paragraph> 171</tablecell> 172</tablerow> 173<tablerow> 174<tablecell colspan="" rowspan=""> 175<paragraph role="tablecontent" id="par_idN1167D" xml-lang="en-US" l10n="NEW" localize="false"> 176<item type="literal">nsupseteq</item> 177</paragraph> 178</tablecell> 179<tablecell colspan="" rowspan=""> 180<paragraph role="tablecontent" id="par_id3163002" xml-lang="en-US" l10n="E"> 181<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> 182 </image></paragraph> 183</tablecell> 184<tablecell colspan="" rowspan=""> 185<paragraph role="tablecontent" id="par_id3163122" xml-lang="en-US" l10n="U" oldref="120">Not superset or equal to</paragraph> 186</tablecell> 187</tablerow> 188<tablerow> 189<tablecell colspan="" rowspan=""> 190<paragraph role="tablecontent" id="par_idN112D9" xml-lang="en-US" l10n="NEW"> 191<item type="literal">owns</item> or <item type="literal">ni</item> 192</paragraph> 193</tablecell> 194<tablecell colspan="" rowspan=""> 195<paragraph role="tablecontent" id="par_id3158359" xml-lang="en-US" l10n="E"> 196<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> 197 </image></paragraph> 198</tablecell> 199<tablecell colspan="" rowspan=""> 200<paragraph role="tablecontent" id="par_id3159352" xml-lang="en-US" l10n="U" oldref="122">Contains</paragraph> 201</tablecell> 202</tablerow> 203<tablerow> 204<tablecell colspan="" rowspan=""> 205<paragraph role="tablecontent" id="par_idN117C7" xml-lang="en-US" l10n="NEW" localize="false"> 206<item type="literal">setc</item> 207</paragraph> 208</tablecell> 209<tablecell colspan="" rowspan=""> 210<paragraph role="tablecontent" id="par_id3156480" xml-lang="en-US" l10n="E"> 211<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> 212 </image></paragraph> 213</tablecell> 214<tablecell colspan="" rowspan=""> 215<paragraph role="tablecontent" id="par_id3156600" xml-lang="en-US" l10n="U" oldref="405">Complex number</paragraph> 216</tablecell> 217</tablerow> 218<tablerow> 219<tablecell colspan="" rowspan=""> 220<paragraph role="tablecontent" id="par_idN113E5" xml-lang="en-US" l10n="NEW"> 221<item type="literal">setminus</item> or <item type="literal">bslash</item> 222</paragraph> 223</tablecell> 224<tablecell colspan="" rowspan=""> 225<paragraph role="tablecontent" id="par_id3145932" xml-lang="en-US" l10n="E"> 226<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> 227 </image></paragraph> 228</tablecell> 229<tablecell colspan="" rowspan=""> 230<paragraph role="tablecontent" id="par_id3146052" xml-lang="en-US" l10n="U" oldref="128">Difference between sets</paragraph> 231</tablecell> 232</tablerow> 233<tablerow> 234<tablecell colspan="" rowspan=""> 235<paragraph role="tablecontent" id="par_idN116BF" xml-lang="en-US" l10n="NEW" localize="false"> 236<item type="literal">setn</item> 237</paragraph> 238</tablecell> 239<tablecell colspan="" rowspan=""> 240<paragraph role="tablecontent" id="par_id3163149" xml-lang="en-US" l10n="E"> 241<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> 242 </image></paragraph> 243</tablecell> 244<tablecell colspan="" rowspan=""> 245<paragraph role="tablecontent" id="par_id3163269" xml-lang="en-US" l10n="U" oldref="397">Natural number</paragraph> 246</tablecell> 247</tablerow> 248<tablerow> 249<tablecell colspan="" rowspan=""> 250<paragraph role="tablecontent" id="par_idN11743" xml-lang="en-US" l10n="NEW" localize="false"> 251<item type="literal">setq</item> 252</paragraph> 253</tablecell> 254<tablecell colspan="" rowspan=""> 255<paragraph role="tablecontent" id="par_id3163444" xml-lang="en-US" l10n="E"> 256<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> 257 </image></paragraph> 258</tablecell> 259<tablecell colspan="" rowspan=""> 260<paragraph role="tablecontent" id="par_id3163564" xml-lang="en-US" l10n="U" oldref="401">Rational number</paragraph> 261</tablecell> 262</tablerow> 263<tablerow> 264<tablecell colspan="" rowspan=""> 265<paragraph role="tablecontent" id="par_idN11785" xml-lang="en-US" l10n="NEW" localize="false"> 266<item type="literal">setr</item> 267</paragraph> 268</tablecell> 269<tablecell colspan="" rowspan=""> 270<paragraph role="tablecontent" id="par_id3163591" xml-lang="en-US" l10n="E"> 271<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> 272 </image></paragraph> 273</tablecell> 274<tablecell colspan="" rowspan=""> 275<paragraph role="tablecontent" id="par_id3156453" xml-lang="en-US" l10n="U" oldref="403">Real number</paragraph> 276</tablecell> 277</tablerow> 278<tablerow> 279<tablecell colspan="" rowspan=""> 280<paragraph role="tablecontent" id="par_idN11701" xml-lang="en-US" l10n="NEW" localize="false"> 281<item type="literal">setz</item> 282</paragraph> 283</tablecell> 284<tablecell colspan="" rowspan=""> 285<paragraph role="tablecontent" id="par_id3163296" xml-lang="en-US" l10n="E"> 286<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> 287 </image></paragraph> 288</tablecell> 289<tablecell colspan="" rowspan=""> 290<paragraph role="tablecontent" id="par_id3163416" xml-lang="en-US" l10n="U" oldref="399">Integer</paragraph> 291</tablecell> 292</tablerow> 293<tablerow> 294<tablecell colspan="" rowspan=""> 295<paragraph role="tablecontent" id="par_idN1142B" xml-lang="en-US" l10n="NEW" localize="false"> 296<item type="literal">slash</item> 297</paragraph> 298</tablecell> 299<tablecell colspan="" rowspan=""> 300<paragraph role="tablecontent" id="par_id3146357" xml-lang="en-US" l10n="E"> 301<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> 302 </image></paragraph> 303</tablecell> 304<tablecell colspan="" rowspan=""> 305<paragraph role="tablecontent" id="par_id3146477" xml-lang="en-US" l10n="U" oldref="54">Slash / for quotient set (slash) between characters</paragraph> 306</tablecell> 307</tablerow> 308<tablerow> 309<tablecell colspan="" rowspan=""> 310<paragraph role="tablecontent" id="par_idN114AF" xml-lang="en-US" l10n="NEW" localize="false"> 311<item type="literal">subset</item> 312</paragraph> 313</tablecell> 314<tablecell colspan="" rowspan=""> 315<paragraph role="tablecontent" id="par_id3146652" xml-lang="en-US" l10n="E"> 316<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> 317 </image></paragraph> 318</tablecell> 319<tablecell colspan="" rowspan=""> 320<paragraph role="tablecontent" id="par_id3146772" xml-lang="en-US" l10n="U" oldref="106">Subset</paragraph> 321</tablecell> 322</tablerow> 323<tablerow> 324<tablecell colspan="" rowspan=""> 325<paragraph role="tablecontent" id="par_idN114F1" xml-lang="en-US" l10n="NEW" localize="false"> 326<item type="literal">subseteq</item> 327</paragraph> 328</tablecell> 329<tablecell colspan="" rowspan=""> 330<paragraph role="tablecontent" id="par_id3146800" xml-lang="en-US" l10n="E"> 331<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> 332 </image></paragraph> 333</tablecell> 334<tablecell colspan="" rowspan=""> 335<paragraph role="tablecontent" id="par_id3158496" xml-lang="en-US" l10n="U" oldref="108">Subset or equal to</paragraph> 336</tablecell> 337</tablerow> 338<tablerow> 339<tablecell colspan="" rowspan=""> 340<paragraph role="tablecontent" id="par_idN11533" xml-lang="en-US" l10n="NEW" localize="false"> 341<item type="literal">supset</item> 342</paragraph> 343</tablecell> 344<tablecell colspan="" rowspan=""> 345<paragraph role="tablecontent" id="par_id3158524" xml-lang="en-US" l10n="E"> 346<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> 347 </image></paragraph> 348</tablecell> 349<tablecell colspan="" rowspan=""> 350<paragraph role="tablecontent" id="par_id3158644" xml-lang="en-US" l10n="U" oldref="114">Superset</paragraph> 351</tablecell> 352</tablerow> 353<tablerow> 354<tablecell colspan="" rowspan=""> 355<paragraph role="tablecontent" id="par_idN11575" xml-lang="en-US" l10n="NEW" localize="false"> 356<item type="literal">supseteq</item> 357</paragraph> 358</tablecell> 359<tablecell colspan="" rowspan=""> 360<paragraph role="tablecontent" id="par_id3158671" xml-lang="en-US" l10n="E"> 361<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> 362 </image></paragraph> 363</tablecell> 364<tablecell colspan="" rowspan=""> 365<paragraph role="tablecontent" id="par_id3158791" xml-lang="en-US" l10n="U" oldref="116">Superset or equal to</paragraph> 366</tablecell> 367</tablerow> 368<tablerow> 369<tablecell colspan="" rowspan=""> 370<paragraph role="tablecontent" id="par_idN113A3" xml-lang="en-US" l10n="NEW" localize="false"> 371<item type="literal">union</item> 372</paragraph> 373</tablecell> 374<tablecell colspan="" rowspan=""> 375<paragraph role="tablecontent" id="par_id3152548" xml-lang="en-US" l10n="E"> 376<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> 377 </image></paragraph> 378</tablecell> 379<tablecell colspan="" rowspan=""> 380<paragraph role="tablecontent" id="par_id3145904" xml-lang="en-US" l10n="U" oldref="124">Union of sets</paragraph> 381</tablecell> 382</tablerow> 383</table> 384<section id="relatedtopics"> 385<embed href="text/smath/01/03090800.xhp#mengenop"/> 386<embed href="text/smath/01/03091500.xhp#reference"/> 387</section> 388</body> 389</helpdocument> 390
