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