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" oldref="478">Symbol in Elements Window</paragraph> 44</tablecell> 45<tablecell colspan="" rowspan=""> 46<paragraph role="tablehead" id="par_id3158137" xml-lang="en-US" l10n="U" oldref="480">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> 58</image></paragraph> 59</tablecell> 60<tablecell colspan="" rowspan=""> 61<paragraph role="tablecontent" id="par_id3146625" xml-lang="en-US" l10n="U" oldref="214">Cardinal number</paragraph> 62</tablecell> 63</tablerow> 64<tablerow> 65<tablecell colspan="" rowspan=""> 66<paragraph role="tablecontent" id="par_idN1131F" xml-lang="en-US" l10n="NEW" localize="false"> 67<item type="literal">emptyset</item> 68</paragraph> 69</tablecell> 70<tablecell colspan="" rowspan=""> 71<paragraph role="tablecontent" id="par_id3159379" xml-lang="en-US" l10n="E"> 72<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> 73</image></paragraph> 74</tablecell> 75<tablecell colspan="" rowspan=""> 76<paragraph role="tablecontent" id="par_id3152374" xml-lang="en-US" l10n="U" oldref="218">Empty set</paragraph> 77</tablecell> 78</tablerow> 79<tablerow> 80<tablecell colspan="" rowspan=""> 81<paragraph role="tablecontent" id="par_id8198065" xml-lang="en-US" l10n="NEW" localize="false"> 82<item type="literal">in</item> 83</paragraph> 84</tablecell> 85<tablecell colspan="" rowspan=""> 86<paragraph role="tablecontent" id="par_id3158166" xml-lang="en-US" l10n="E"> 87<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> 88</image></paragraph> 89</tablecell> 90<tablecell colspan="" rowspan=""> 91<paragraph role="tablecontent" id="par_id3155037" xml-lang="en-US" l10n="U" oldref="102">is contained in</paragraph> 92</tablecell> 93</tablerow> 94<tablerow> 95<tablecell colspan="" rowspan=""> 96<paragraph role="tablecontent" id="par_idN11361" xml-lang="en-US" l10n="NEW" localize="false"> 97<item type="literal">intersection</item> 98</paragraph> 99</tablecell> 100<tablecell colspan="" rowspan=""> 101<paragraph role="tablecontent" id="par_id3152402" xml-lang="en-US" l10n="E"> 102<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> 103</image></paragraph> 104</tablecell> 105<tablecell colspan="" rowspan=""> 106<paragraph role="tablecontent" id="par_id3152522" xml-lang="en-US" l10n="U" oldref="126">Intersection of sets</paragraph> 107</tablecell> 108</tablerow> 109<tablerow> 110<tablecell colspan="" rowspan=""> 111<paragraph role="tablecontent" id="par_idN11297" xml-lang="en-US" l10n="NEW" localize="false"> 112<item type="literal">notin</item> 113</paragraph> 114</tablecell> 115<tablecell colspan="" rowspan=""> 116<paragraph role="tablecontent" id="par_id3158212" xml-lang="en-US" l10n="E"> 117<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> 118</image></paragraph> 119</tablecell> 120<tablecell colspan="" rowspan=""> 121<paragraph role="tablecontent" id="par_id3158332" xml-lang="en-US" l10n="U" oldref="104">is not contained in</paragraph> 122</tablecell> 123</tablerow> 124<tablerow> 125<tablecell colspan="" rowspan=""> 126<paragraph role="tablecontent" id="par_idN115B7" xml-lang="en-US" l10n="NEW" localize="false"> 127<item type="literal">nsubset</item> 128</paragraph> 129</tablecell> 130<tablecell colspan="" rowspan=""> 131<paragraph role="tablecontent" id="par_id3158819" xml-lang="en-US" l10n="E"> 132<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> 133</image></paragraph> 134</tablecell> 135<tablecell colspan="" rowspan=""> 136<paragraph role="tablecontent" id="par_id3158939" xml-lang="en-US" l10n="U" oldref="110">Not subset to</paragraph> 137</tablecell> 138</tablerow> 139<tablerow> 140<tablecell colspan="" rowspan=""> 141<paragraph role="tablecontent" id="par_idN115F9" xml-lang="en-US" l10n="NEW" localize="false"> 142<item type="literal">nsubseteq</item> 143</paragraph> 144</tablecell> 145<tablecell colspan="" rowspan=""> 146<paragraph role="tablecontent" id="par_id3158966" xml-lang="en-US" l10n="E"> 147<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> 148</image></paragraph> 149</tablecell> 150<tablecell colspan="" rowspan=""> 151<paragraph role="tablecontent" id="par_id3159086" xml-lang="en-US" l10n="U" oldref="112">Not subset or equal to</paragraph> 152</tablecell> 153</tablerow> 154<tablerow> 155<tablecell colspan="" rowspan=""> 156<paragraph role="tablecontent" id="par_idN1163B" xml-lang="en-US" l10n="NEW" localize="false"> 157<item type="literal">nsupset</item> 158</paragraph> 159</tablecell> 160<tablecell colspan="" rowspan=""> 161<paragraph role="tablecontent" id="par_id3159114" xml-lang="en-US" l10n="E"> 162<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> 163</image></paragraph> 164</tablecell> 165<tablecell colspan="" rowspan=""> 166<paragraph role="tablecontent" id="par_id3162974" xml-lang="en-US" l10n="U" oldref="118">Not superset</paragraph> 167</tablecell> 168</tablerow> 169<tablerow> 170<tablecell colspan="" rowspan=""> 171<paragraph role="tablecontent" id="par_idN1167D" xml-lang="en-US" l10n="NEW" localize="false"> 172<item type="literal">nsupseteq</item> 173</paragraph> 174</tablecell> 175<tablecell colspan="" rowspan=""> 176<paragraph role="tablecontent" id="par_id3163002" xml-lang="en-US" l10n="E"> 177<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> 178</image></paragraph> 179</tablecell> 180<tablecell colspan="" rowspan=""> 181<paragraph role="tablecontent" id="par_id3163122" xml-lang="en-US" l10n="U" oldref="120">Not superset or equal to</paragraph> 182</tablecell> 183</tablerow> 184<tablerow> 185<tablecell colspan="" rowspan=""> 186<paragraph role="tablecontent" id="par_idN112D9" xml-lang="en-US" l10n="NEW"> 187<item type="literal">owns</item> or <item type="literal">ni</item> 188</paragraph> 189</tablecell> 190<tablecell colspan="" rowspan=""> 191<paragraph role="tablecontent" id="par_id3158359" xml-lang="en-US" l10n="E"> 192<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> 193</image></paragraph> 194</tablecell> 195<tablecell colspan="" rowspan=""> 196<paragraph role="tablecontent" id="par_id3159352" xml-lang="en-US" l10n="U" oldref="122">Contains</paragraph> 197</tablecell> 198</tablerow> 199<tablerow> 200<tablecell colspan="" rowspan=""> 201<paragraph role="tablecontent" id="par_idN117C7" xml-lang="en-US" l10n="NEW" localize="false"> 202<item type="literal">setc</item> 203</paragraph> 204</tablecell> 205<tablecell colspan="" rowspan=""> 206<paragraph role="tablecontent" id="par_id3156480" xml-lang="en-US" l10n="E"> 207<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> 208</image></paragraph> 209</tablecell> 210<tablecell colspan="" rowspan=""> 211<paragraph role="tablecontent" id="par_id3156600" xml-lang="en-US" l10n="U" oldref="405">Complex number</paragraph> 212</tablecell> 213</tablerow> 214<tablerow> 215<tablecell colspan="" rowspan=""> 216<paragraph role="tablecontent" id="par_idN113E5" xml-lang="en-US" l10n="NEW"> 217<item type="literal">setminus</item> or <item type="literal">bslash</item> 218</paragraph> 219</tablecell> 220<tablecell colspan="" rowspan=""> 221<paragraph role="tablecontent" id="par_id3145932" xml-lang="en-US" l10n="E"> 222<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> 223</image></paragraph> 224</tablecell> 225<tablecell colspan="" rowspan=""> 226<paragraph role="tablecontent" id="par_id3146052" xml-lang="en-US" l10n="U" oldref="128">Difference between sets</paragraph> 227</tablecell> 228</tablerow> 229<tablerow> 230<tablecell colspan="" rowspan=""> 231<paragraph role="tablecontent" id="par_idN116BF" xml-lang="en-US" l10n="NEW" localize="false"> 232<item type="literal">setn</item> 233</paragraph> 234</tablecell> 235<tablecell colspan="" rowspan=""> 236<paragraph role="tablecontent" id="par_id3163149" xml-lang="en-US" l10n="E"> 237<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> 238</image></paragraph> 239</tablecell> 240<tablecell colspan="" rowspan=""> 241<paragraph role="tablecontent" id="par_id3163269" xml-lang="en-US" l10n="U" oldref="397">Natural number</paragraph> 242</tablecell> 243</tablerow> 244<tablerow> 245<tablecell colspan="" rowspan=""> 246<paragraph role="tablecontent" id="par_idN11743" xml-lang="en-US" l10n="NEW" localize="false"> 247<item type="literal">setq</item> 248</paragraph> 249</tablecell> 250<tablecell colspan="" rowspan=""> 251<paragraph role="tablecontent" id="par_id3163444" xml-lang="en-US" l10n="E"> 252<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> 253</image></paragraph> 254</tablecell> 255<tablecell colspan="" rowspan=""> 256<paragraph role="tablecontent" id="par_id3163564" xml-lang="en-US" l10n="U" oldref="401">Rational number</paragraph> 257</tablecell> 258</tablerow> 259<tablerow> 260<tablecell colspan="" rowspan=""> 261<paragraph role="tablecontent" id="par_idN11785" xml-lang="en-US" l10n="NEW" localize="false"> 262<item type="literal">setr</item> 263</paragraph> 264</tablecell> 265<tablecell colspan="" rowspan=""> 266<paragraph role="tablecontent" id="par_id3163591" xml-lang="en-US" l10n="E"> 267<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> 268</image></paragraph> 269</tablecell> 270<tablecell colspan="" rowspan=""> 271<paragraph role="tablecontent" id="par_id3156453" xml-lang="en-US" l10n="U" oldref="403">Real number</paragraph> 272</tablecell> 273</tablerow> 274<tablerow> 275<tablecell colspan="" rowspan=""> 276<paragraph role="tablecontent" id="par_idN11701" xml-lang="en-US" l10n="NEW" localize="false"> 277<item type="literal">setz</item> 278</paragraph> 279</tablecell> 280<tablecell colspan="" rowspan=""> 281<paragraph role="tablecontent" id="par_id3163296" xml-lang="en-US" l10n="E"> 282<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> 283</image></paragraph> 284</tablecell> 285<tablecell colspan="" rowspan=""> 286<paragraph role="tablecontent" id="par_id3163416" xml-lang="en-US" l10n="U" oldref="399">Integer</paragraph> 287</tablecell> 288</tablerow> 289<tablerow> 290<tablecell colspan="" rowspan=""> 291<paragraph role="tablecontent" id="par_idN1142B" xml-lang="en-US" l10n="NEW" localize="false"> 292<item type="literal">slash</item> 293</paragraph> 294</tablecell> 295<tablecell colspan="" rowspan=""> 296<paragraph role="tablecontent" id="par_id3146357" xml-lang="en-US" l10n="E"> 297<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> 298</image></paragraph> 299</tablecell> 300<tablecell colspan="" rowspan=""> 301<paragraph role="tablecontent" id="par_id3146477" xml-lang="en-US" l10n="U" oldref="54">Slash / for quotient set (slash) between characters</paragraph> 302</tablecell> 303</tablerow> 304<tablerow> 305<tablecell colspan="" rowspan=""> 306<paragraph role="tablecontent" id="par_idN114AF" xml-lang="en-US" l10n="NEW" localize="false"> 307<item type="literal">subset</item> 308</paragraph> 309</tablecell> 310<tablecell colspan="" rowspan=""> 311<paragraph role="tablecontent" id="par_id3146652" xml-lang="en-US" l10n="E"> 312<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> 313</image></paragraph> 314</tablecell> 315<tablecell colspan="" rowspan=""> 316<paragraph role="tablecontent" id="par_id3146772" xml-lang="en-US" l10n="U" oldref="106">Subset</paragraph> 317</tablecell> 318</tablerow> 319<tablerow> 320<tablecell colspan="" rowspan=""> 321<paragraph role="tablecontent" id="par_idN114F1" xml-lang="en-US" l10n="NEW" localize="false"> 322<item type="literal">subseteq</item> 323</paragraph> 324</tablecell> 325<tablecell colspan="" rowspan=""> 326<paragraph role="tablecontent" id="par_id3146800" xml-lang="en-US" l10n="E"> 327<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> 328</image></paragraph> 329</tablecell> 330<tablecell colspan="" rowspan=""> 331<paragraph role="tablecontent" id="par_id3158496" xml-lang="en-US" l10n="U" oldref="108">Subset or equal to</paragraph> 332</tablecell> 333</tablerow> 334<tablerow> 335<tablecell colspan="" rowspan=""> 336<paragraph role="tablecontent" id="par_idN11533" xml-lang="en-US" l10n="NEW" localize="false"> 337<item type="literal">supset</item> 338</paragraph> 339</tablecell> 340<tablecell colspan="" rowspan=""> 341<paragraph role="tablecontent" id="par_id3158524" xml-lang="en-US" l10n="E"> 342<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> 343</image></paragraph> 344</tablecell> 345<tablecell colspan="" rowspan=""> 346<paragraph role="tablecontent" id="par_id3158644" xml-lang="en-US" l10n="U" oldref="114">Superset</paragraph> 347</tablecell> 348</tablerow> 349<tablerow> 350<tablecell colspan="" rowspan=""> 351<paragraph role="tablecontent" id="par_idN11575" xml-lang="en-US" l10n="NEW" localize="false"> 352<item type="literal">supseteq</item> 353</paragraph> 354</tablecell> 355<tablecell colspan="" rowspan=""> 356<paragraph role="tablecontent" id="par_id3158671" xml-lang="en-US" l10n="E"> 357<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> 358</image></paragraph> 359</tablecell> 360<tablecell colspan="" rowspan=""> 361<paragraph role="tablecontent" id="par_id3158791" xml-lang="en-US" l10n="U" oldref="116">Superset or equal to</paragraph> 362</tablecell> 363</tablerow> 364<tablerow> 365<tablecell colspan="" rowspan=""> 366<paragraph role="tablecontent" id="par_idN113A3" xml-lang="en-US" l10n="NEW" localize="false"> 367<item type="literal">union</item> 368</paragraph> 369</tablecell> 370<tablecell colspan="" rowspan=""> 371<paragraph role="tablecontent" id="par_id3152548" xml-lang="en-US" l10n="E"> 372<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> 373</image></paragraph> 374</tablecell> 375<tablecell colspan="" rowspan=""> 376<paragraph role="tablecontent" id="par_id3145904" xml-lang="en-US" l10n="U" oldref="124">Union of sets</paragraph> 377</tablecell> 378</tablerow> 379</table> 380<section id="relatedtopics"> 381<embed href="text/smath/01/03090800.xhp#mengenop"/> 382<embed href="text/smath/01/03091500.xhp#reference"/> 383</section> 384</body> 385</helpdocument> 386
