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Beweis: Enthielte jedes Fach höchstens ",[575,713,715,753],{"className":714},[578],[575,716,718],{"className":717},[582],[584,719,720],{"xmlns":586},[588,721,722,750],{},[591,723,724,726,728,730,732,734,737,741,744,746,748],{},[666,725,669],{"stretchy":668},[594,727,596],{},[594,729,675],{"mathvariant":674},[594,731,635],{},[666,733,680],{"stretchy":668},[666,735,736],{},"−",[738,739,740],"mn",{},"1",[666,742,743],{},"\u003C",[594,745,596],{},[594,747,675],{"mathvariant":674},[594,749,635],{},[598,751,752],{"encoding":600},"\\lceil n\u002Fk \\rceil - 1 \u003C n\u002Fk",[575,754,756,789,810],{"className":755,"ariaHidden":605},[604],[575,757,759,762,765,768,771,774,777,782,786],{"className":758},[609],[575,760],{"className":761,"style":693},[613],[575,763,669],{"className":764},[697],[575,766,596],{"className":767},[618,619],[575,769,675],{"className":770},[618],[575,772,635],{"className":773,"style":651},[618,619],[575,775,680],{"className":776},[710],[575,778],{"className":779,"style":781},[780],"mspace","margin-right:0.2222em;",[575,783,736],{"className":784},[785],"mbin",[575,787],{"className":788,"style":781},[780],[575,790,792,796,799,803,807],{"className":791},[609],[575,793],{"className":794,"style":795},[613],"height:0.6835em;vertical-align:-0.0391em;",[575,797,740],{"className":798},[618],[575,800],{"className":801,"style":802},[780],"margin-right:0.2778em;",[575,804,743],{"className":805},[806],"mrel",[575,808],{"className":809,"style":802},[780],[575,811,813,816,819,822],{"className":812},[609],[575,814],{"className":815,"style":693},[613],[575,817,596],{"className":818},[618,619],[575,820,675],{"className":821},[618],[575,823,635],{"className":824,"style":651},[618,619]," Objekte, wären es insgesamt weniger als ",[575,827,829,857],{"className":828},[578],[575,830,832],{"className":831},[582],[584,833,834],{"xmlns":586},[588,835,836,854],{},[591,837,838,840,843,845,847,849,852],{},[594,839,635],{},[666,841,842],{},"⋅",[594,844,596],{},[594,846,675],{"mathvariant":674},[594,848,635],{},[666,850,851],{},"=",[594,853,596],{},[598,855,856],{"encoding":600},"k \\cdot n\u002Fk = n",[575,858,860,878,902],{"className":859,"ariaHidden":605},[604],[575,861,863,866,869,872,875],{"className":862},[609],[575,864],{"className":865,"style":647},[613],[575,867,635],{"className":868,"style":651},[618,619],[575,870],{"className":871,"style":781},[780],[575,873,842],{"className":874},[785],[575,876],{"className":877,"style":781},[780],[575,879,881,884,887,890,893,896,899],{"className":880},[609],[575,882],{"className":883,"style":693},[613],[575,885,596],{"className":886},[618,619],[575,888,675],{"className":889},[618],[575,891,635],{"className":892,"style":651},[618,619],[575,894],{"className":895,"style":802},[780],[575,897,851],{"className":898},[806],[575,900],{"className":901,"style":802},[780],[575,903,905,908],{"className":904},[609],[575,906],{"className":907,"style":614},[613],[575,909,596],{"className":910},[618,619],".",[564,913,914,915,918,919,948],{},"Das Prinzip ist ein ",[568,916,917],{},"Existenzbeweis",": Es sagt, dass ein volles Fach existiert, aber nicht, welches. Die Kunst liegt darin, geeignete Objekte und Fächer zu wählen, etwa Reste modulo ",[575,920,922,936],{"className":921},[578],[575,923,925],{"className":924},[582],[584,926,927],{"xmlns":586},[588,928,929,934],{},[591,930,931],{},[594,932,933],{},"m",[598,935,933],{"encoding":600},[575,937,939],{"className":938,"ariaHidden":605},[604],[575,940,942,945],{"className":941},[609],[575,943],{"className":944,"style":614},[613],[575,946,933],{"className":947},[618,619],", Teilintervalle oder Farben.",[559,950,952],{"id":951},"beispiele","Beispiele",[564,954,955,958,959,989,990,1019,1020,911],{},[568,956,957],{},"Geburtstage:"," Unter ",[575,960,962,976],{"className":961},[578],[575,963,965],{"className":964},[582],[584,966,967],{"xmlns":586},[588,968,969,974],{},[591,970,971],{},[738,972,973],{},"367",[598,975,973],{"encoding":600},[575,977,979],{"className":978,"ariaHidden":605},[604],[575,980,982,986],{"className":981},[609],[575,983],{"className":984,"style":985},[613],"height:0.6444em;",[575,987,973],{"className":988},[618]," Menschen haben mindestens zwei am selben Tag Geburtstag, denn es gibt nur ",[575,991,993,1007],{"className":992},[578],[575,994,996],{"className":995},[582],[584,997,998],{"xmlns":586},[588,999,1000,1005],{},[591,1001,1002],{},[738,1003,1004],{},"366",[598,1006,1004],{"encoding":600},[575,1008,1010],{"className":1009,"ariaHidden":605},[604],[575,1011,1013,1016],{"className":1012},[609],[575,1014],{"className":1015,"style":985},[613],[575,1017,1004],{"className":1018},[618]," mögliche Tage: ",[575,1021,1023,1050],{"className":1022},[578],[575,1024,1026],{"className":1025},[582],[584,1027,1028],{"xmlns":586},[588,1029,1030,1047],{},[591,1031,1032,1034,1036,1038,1040,1042,1044],{},[666,1033,669],{"stretchy":668},[738,1035,973],{},[594,1037,675],{"mathvariant":674},[738,1039,1004],{},[666,1041,680],{"stretchy":668},[666,1043,851],{},[738,1045,1046],{},"2",[598,1048,1049],{"encoding":600},"\\lceil 367\u002F366 \\rceil = 2",[575,1051,1053,1078],{"className":1052,"ariaHidden":605},[604],[575,1054,1056,1059,1062,1066,1069,1072,1075],{"className":1055},[609],[575,1057],{"className":1058,"style":693},[613],[575,1060,669],{"className":1061},[697],[575,1063,1065],{"className":1064},[618],"367\u002F366",[575,1067,680],{"className":1068},[710],[575,1070],{"className":1071,"style":802},[780],[575,1073,851],{"className":1074},[806],[575,1076],{"className":1077,"style":802},[780],[575,1079,1081,1084],{"className":1080},[609],[575,1082],{"className":1083,"style":985},[613],[575,1085,1046],{"className":1086},[618],[564,1088,1089,1092,1093,1122,1123,1152,1153,911],{},[568,1090,1091],{},"Socken:"," In einer Schublade liegen Socken in ",[575,1094,1096,1110],{"className":1095},[578],[575,1097,1099],{"className":1098},[582],[584,1100,1101],{"xmlns":586},[588,1102,1103,1108],{},[591,1104,1105],{},[738,1106,1107],{},"3",[598,1109,1107],{"encoding":600},[575,1111,1113],{"className":1112,"ariaHidden":605},[604],[575,1114,1116,1119],{"className":1115},[609],[575,1117],{"className":1118,"style":985},[613],[575,1120,1107],{"className":1121},[618]," Farben. Wer im Dunkeln ",[575,1124,1126,1140],{"className":1125},[578],[575,1127,1129],{"className":1128},[582],[584,1130,1131],{"xmlns":586},[588,1132,1133,1138],{},[591,1134,1135],{},[738,1136,1137],{},"4",[598,1139,1137],{"encoding":600},[575,1141,1143],{"className":1142,"ariaHidden":605},[604],[575,1144,1146,1149],{"className":1145},[609],[575,1147],{"className":1148,"style":985},[613],[575,1150,1137],{"className":1151},[618]," Socken nimmt, hat sicher zwei gleicher Farbe: ",[575,1154,1156,1182],{"className":1155},[578],[575,1157,1159],{"className":1158},[582],[584,1160,1161],{"xmlns":586},[588,1162,1163,1179],{},[591,1164,1165,1167,1169,1171,1173,1175,1177],{},[666,1166,669],{"stretchy":668},[738,1168,1137],{},[594,1170,675],{"mathvariant":674},[738,1172,1107],{},[666,1174,680],{"stretchy":668},[666,1176,851],{},[738,1178,1046],{},[598,1180,1181],{"encoding":600},"\\lceil 4\u002F3 \\rceil = 2",[575,1183,1185,1210],{"className":1184,"ariaHidden":605},[604],[575,1186,1188,1191,1194,1198,1201,1204,1207],{"className":1187},[609],[575,1189],{"className":1190,"style":693},[613],[575,1192,669],{"className":1193},[697],[575,1195,1197],{"className":1196},[618],"4\u002F3",[575,1199,680],{"className":1200},[710],[575,1202],{"className":1203,"style":802},[780],[575,1205,851],{"className":1206},[806],[575,1208],{"className":1209,"style":802},[780],[575,1211,1213,1216],{"className":1212},[609],[575,1214],{"className":1215,"style":985},[613],[575,1217,1046],{"className":1218},[618],[564,1220,1221,1224,1225,1254,1255,1323],{},[568,1222,1223],{},"Monate:"," Von ",[575,1226,1228,1242],{"className":1227},[578],[575,1229,1231],{"className":1230},[582],[584,1232,1233],{"xmlns":586},[588,1234,1235,1240],{},[591,1236,1237],{},[738,1238,1239],{},"100",[598,1241,1239],{"encoding":600},[575,1243,1245],{"className":1244,"ariaHidden":605},[604],[575,1246,1248,1251],{"className":1247},[609],[575,1249],{"className":1250,"style":985},[613],[575,1252,1239],{"className":1253},[618]," Personen haben mindestens ",[575,1256,1258,1286],{"className":1257},[578],[575,1259,1261],{"className":1260},[582],[584,1262,1263],{"xmlns":586},[588,1264,1265,1283],{},[591,1266,1267,1269,1271,1273,1276,1278,1280],{},[666,1268,669],{"stretchy":668},[738,1270,1239],{},[594,1272,675],{"mathvariant":674},[738,1274,1275],{},"12",[666,1277,680],{"stretchy":668},[666,1279,851],{},[738,1281,1282],{},"9",[598,1284,1285],{"encoding":600},"\\lceil 100\u002F12 \\rceil = 9",[575,1287,1289,1314],{"className":1288,"ariaHidden":605},[604],[575,1290,1292,1295,1298,1302,1305,1308,1311],{"className":1291},[609],[575,1293],{"className":1294,"style":693},[613],[575,1296,669],{"className":1297},[697],[575,1299,1301],{"className":1300},[618],"100\u002F12",[575,1303,680],{"className":1304},[710],[575,1306],{"className":1307,"style":802},[780],[575,1309,851],{"className":1310},[806],[575,1312],{"className":1313,"style":802},[780],[575,1315,1317,1320],{"className":1316},[609],[575,1318],{"className":1319,"style":985},[613],[575,1321,1282],{"className":1322},[618]," im selben Monat Geburtstag.",[564,1325,1326,1329,1330,1359,1360,1389,1390,1418,1419,1447,1448,1476],{},[568,1327,1328],{},"Zahlentheorie:"," Unter je ",[575,1331,1333,1347],{"className":1332},[578],[575,1334,1336],{"className":1335},[582],[584,1337,1338],{"xmlns":586},[588,1339,1340,1345],{},[591,1341,1342],{},[738,1343,1344],{},"6",[598,1346,1344],{"encoding":600},[575,1348,1350],{"className":1349,"ariaHidden":605},[604],[575,1351,1353,1356],{"className":1352},[609],[575,1354],{"className":1355,"style":985},[613],[575,1357,1344],{"className":1358},[618]," ganzen Zahlen gibt es zwei, deren Differenz durch ",[575,1361,1363,1377],{"className":1362},[578],[575,1364,1366],{"className":1365},[582],[584,1367,1368],{"xmlns":586},[588,1369,1370,1375],{},[591,1371,1372],{},[738,1373,1374],{},"5",[598,1376,1374],{"encoding":600},[575,1378,1380],{"className":1379,"ariaHidden":605},[604],[575,1381,1383,1386],{"className":1382},[609],[575,1384],{"className":1385,"style":985},[613],[575,1387,1374],{"className":1388},[618]," teilbar ist. Fächer sind die ",[575,1391,1393,1406],{"className":1392},[578],[575,1394,1396],{"className":1395},[582],[584,1397,1398],{"xmlns":586},[588,1399,1400,1404],{},[591,1401,1402],{},[738,1403,1374],{},[598,1405,1374],{"encoding":600},[575,1407,1409],{"className":1408,"ariaHidden":605},[604],[575,1410,1412,1415],{"className":1411},[609],[575,1413],{"className":1414,"style":985},[613],[575,1416,1374],{"className":1417},[618]," möglichen Reste modulo ",[575,1420,1422,1435],{"className":1421},[578],[575,1423,1425],{"className":1424},[582],[584,1426,1427],{"xmlns":586},[588,1428,1429,1433],{},[591,1430,1431],{},[738,1432,1374],{},[598,1434,1374],{"encoding":600},[575,1436,1438],{"className":1437,"ariaHidden":605},[604],[575,1439,1441,1444],{"className":1440},[609],[575,1442],{"className":1443,"style":985},[613],[575,1445,1374],{"className":1446},[618],"; zwei Zahlen mit gleichem Rest haben eine durch ",[575,1449,1451,1464],{"className":1450},[578],[575,1452,1454],{"className":1453},[582],[584,1455,1456],{"xmlns":586},[588,1457,1458,1462],{},[591,1459,1460],{},[738,1461,1374],{},[598,1463,1374],{"encoding":600},[575,1465,1467],{"className":1466,"ariaHidden":605},[604],[575,1468,1470,1473],{"className":1469},[609],[575,1471],{"className":1472,"style":985},[613],[575,1474,1374],{"className":1475},[618]," teilbare Differenz.",[559,1478,1480],{"id":1479},"typische-fehler","Typische Fehler",[1482,1483,1484,1693,1757],"ul",{},[1485,1486,1487,1490,1491,1559,1560,1588,1589,1663,1664,1692],"li",{},[568,1488,1489],{},"Abrunden statt aufrunden."," ",[575,1492,1494,1523],{"className":1493},[578],[575,1495,1497],{"className":1496},[582],[584,1498,1499],{"xmlns":586},[588,1500,1501,1520],{},[591,1502,1503,1506,1508,1510,1512,1515,1517],{},[666,1504,1505],{"stretchy":668},"⌊",[738,1507,1239],{},[594,1509,675],{"mathvariant":674},[738,1511,1275],{},[666,1513,1514],{"stretchy":668},"⌋",[666,1516,851],{},[738,1518,1519],{},"8",[598,1521,1522],{"encoding":600},"\\lfloor 100\u002F12 \\rfloor = 8",[575,1524,1526,1550],{"className":1525,"ariaHidden":605},[604],[575,1527,1529,1532,1535,1538,1541,1544,1547],{"className":1528},[609],[575,1530],{"className":1531,"style":693},[613],[575,1533,1505],{"className":1534},[697],[575,1536,1301],{"className":1537},[618],[575,1539,1514],{"className":1540},[710],[575,1542],{"className":1543,"style":802},[780],[575,1545,851],{"className":1546},[806],[575,1548],{"className":1549,"style":802},[780],[575,1551,1553,1556],{"className":1552},[609],[575,1554],{"className":1555,"style":985},[613],[575,1557,1519],{"className":1558},[618]," ist zu schwach. Mit nur ",[575,1561,1563,1576],{"className":1562},[578],[575,1564,1566],{"className":1565},[582],[584,1567,1568],{"xmlns":586},[588,1569,1570,1574],{},[591,1571,1572],{},[738,1573,1519],{},[598,1575,1519],{"encoding":600},[575,1577,1579],{"className":1578,"ariaHidden":605},[604],[575,1580,1582,1585],{"className":1581},[609],[575,1583],{"className":1584,"style":985},[613],[575,1586,1519],{"className":1587},[618]," pro Monat kämen höchstens ",[575,1590,1592,1615],{"className":1591},[578],[575,1593,1595],{"className":1594},[582],[584,1596,1597],{"xmlns":586},[588,1598,1599,1612],{},[591,1600,1601,1603,1605,1607,1609],{},[738,1602,1519],{},[666,1604,842],{},[738,1606,1275],{},[666,1608,851],{},[738,1610,1611],{},"96",[598,1613,1614],{"encoding":600},"8 \\cdot 12 = 96",[575,1616,1618,1636,1654],{"className":1617,"ariaHidden":605},[604],[575,1619,1621,1624,1627,1630,1633],{"className":1620},[609],[575,1622],{"className":1623,"style":985},[613],[575,1625,1519],{"className":1626},[618],[575,1628],{"className":1629,"style":781},[780],[575,1631,842],{"className":1632},[785],[575,1634],{"className":1635,"style":781},[780],[575,1637,1639,1642,1645,1648,1651],{"className":1638},[609],[575,1640],{"className":1641,"style":985},[613],[575,1643,1275],{"className":1644},[618],[575,1646],{"className":1647,"style":802},[780],[575,1649,851],{"className":1650},[806],[575,1652],{"className":1653,"style":802},[780],[575,1655,1657,1660],{"className":1656},[609],[575,1658],{"className":1659,"style":985},[613],[575,1661,1611],{"className":1662},[618]," Personen unter, also muss ein Monat ",[575,1665,1667,1680],{"className":1666},[578],[575,1668,1670],{"className":1669},[582],[584,1671,1672],{"xmlns":586},[588,1673,1674,1678],{},[591,1675,1676],{},[738,1677,1282],{},[598,1679,1282],{"encoding":600},[575,1681,1683],{"className":1682,"ariaHidden":605},[604],[575,1684,1686,1689],{"className":1685},[609],[575,1687],{"className":1688,"style":985},[613],[575,1690,1282],{"className":1691},[618]," haben.",[1485,1694,1695,1698,1699,1727,1728,1756],{},[568,1696,1697],{},"Gleich viele Objekte wie Fächer."," Bei ",[575,1700,1702,1715],{"className":1701},[578],[575,1703,1705],{"className":1704},[582],[584,1706,1707],{"xmlns":586},[588,1708,1709,1713],{},[591,1710,1711],{},[738,1712,1004],{},[598,1714,1004],{"encoding":600},[575,1716,1718],{"className":1717,"ariaHidden":605},[604],[575,1719,1721,1724],{"className":1720},[609],[575,1722],{"className":1723,"style":985},[613],[575,1725,1004],{"className":1726},[618]," Personen und ",[575,1729,1731,1744],{"className":1730},[578],[575,1732,1734],{"className":1733},[582],[584,1735,1736],{"xmlns":586},[588,1737,1738,1742],{},[591,1739,1740],{},[738,1741,1004],{},[598,1743,1004],{"encoding":600},[575,1745,1747],{"className":1746,"ariaHidden":605},[604],[575,1748,1750,1753],{"className":1749},[609],[575,1751],{"className":1752,"style":985},[613],[575,1754,1004],{"className":1755},[618]," Tagen ist eine Doppelung nicht garantiert. Man braucht mindestens ein Objekt mehr als Fächer.",[1485,1758,1759,1762],{},[568,1760,1761],{},"Mehr behaupten als bewiesen."," Das Prinzip sagt nicht, welches Fach voll ist, und auch nicht, dass die Objekte gleichmäßig verteilt sind.",{"title":1764,"searchDepth":1765,"depth":1765,"links":1766},"",2,[1767,1768,1769],{"id":561,"depth":1765,"text":562},{"id":951,"depth":1765,"text":952},{"id":1479,"depth":1765,"text":1480},[1771,1773,1775,1777,1779,1781],{"lhs":1772,"rhs":1046},"ceil(367\u002F366)",{"lhs":1774,"rhs":1046},"ceil(4\u002F3)",{"lhs":1776,"rhs":1282},"ceil(100\u002F12)",{"lhs":1778,"rhs":1519},"floor(100\u002F12)",{"lhs":1780,"rhs":1611},"8*12",{"lhs":1782,"rhs":1046},"ceil(6\u002F5)","n, k \\in \\mathbb{N},\\ k \\geq 1,\\ n_1, \\ldots, n_k \\in \\mathbb{N}_0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n, k \\in \\mathbb{N},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\geq 1,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8304em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>n\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsub>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n_1, \\ldots, n_k \\in \\mathbb{N}_0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","pigeonhole-principle","n_1 + \\ldots + n_k = n \\;\\Rightarrow\\; \\max_{1 \\leq j \\leq k} n_j \\geq \\left\\lceil \\frac{n}{k} \\right\\rceil","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>n\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmunder>\u003Cmrow>\u003Cmi>max\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>j\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmsub>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">⌈\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">⌉\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n_1 + \\ldots + n_k = n \\;\\Rightarrow\\; \\max_{1 \\leq j \\leq k} n_j \\geq \\left\\lceil \\frac{n}{k} \\right\\rceil\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.5242em;vertical-align:-0.8882em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.4306em;\">\u003Cspan style=\"top:-2.3479em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">≤\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">≤\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">max\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8882em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.836em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">⌈\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">⌉\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fschubfachprinzip",[],[1796,1797],"modular-arithmetic","handshake-lemma",{"title":548,"description":1764},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fschubfachprinzip","Verteilt man n Objekte auf k Fächer, liegen in mindestens einem Fach mindestens n\u002Fk aufgerundet Objekte.",[1802,1803,1804,1805],"kombinatorik","beweisverfahren","dirichlet","existenzbeweis",[1807,1810,1813,1817],{"symbol":596,"meaning":1808,"symbolHtml":1809},"Anzahl der verteilten Objekte","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":635,"meaning":1811,"symbolHtml":1812},"Anzahl der Fächer","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1814,"meaning":1815,"symbolHtml":1816},"n_j","Anzahl der Objekte im Fach j","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n_j\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7167em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1818,"meaning":1819,"symbolHtml":1820},"\\left\\lceil x \\right\\rceil","Aufrundung, die kleinste ganze Zahl größer oder gleich x","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo fence=\"true\">⌈\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo fence=\"true\">⌉\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\left\\lceil x \\right\\rceil\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">⌈\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">⌉\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","S1fLcp5snPSNGQiAFd8VXyVNtdlYoCZOy9RpDqH1PNs",[1823,1826],{"stem":1824,"title":1825,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fhandschlaglemma","Handschlaglemma",{"stem":1827,"title":1828,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Frechnen-mit-kongruenzen","Rechnen mit Kongruenzen",1793824276869]