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",[571,1130,1132,1197],{"className":1131},[574],[571,1133,1135],{"className":1134},[578],[580,1136,1137],{"xmlns":582},[584,1138,1139,1194],{},[587,1140,1141,1143,1151,1153,1156,1158,1164,1166,1168,1170,1176,1178,1180,1182,1184,1186,1192],{},[590,1142,878],{"mathvariant":881},[1144,1145,1146,1148],"msub",{},[590,1147,592],{},[673,1149,1150],{},"1",[664,1152,812],{},[664,1154,1155],{},"…",[664,1157,812],{},[1144,1159,1160,1162],{},[590,1161,592],{},[590,1163,1113],{},[590,1165,878],{"mathvariant":881},[664,1167,899],{},[590,1169,878],{"mathvariant":881},[1144,1171,1172,1174],{},[590,1173,592],{},[673,1175,1150],{},[590,1177,878],{"mathvariant":881},[664,1179,812],{},[664,1181,1155],{},[664,1183,812],{},[590,1185,878],{"mathvariant":881},[1144,1187,1188,1190],{},[590,1189,592],{},[590,1191,1113],{},[590,1193,878],{"mathvariant":881},[594,1195,1196],{"encoding":596},"|x_1 + \\ldots + x_n| \\leq |x_1| + \\ldots + |x_n|",[571,1198,1200,1267,1286,1345,1406,1424],{"className":1199,"ariaHidden":601},[600],[571,1201,1203,1206,1209,1258,1261,1264],{"className":1202},[605],[571,1204],{"className":1205,"style":1067},[609],[571,1207,878],{"className":1208},[614],[571,1210,1212,1215],{"className":1211},[614],[571,1213,592],{"className":1214},[614,615],[571,1216,1219],{"className":1217},[1218],"msupsub",[571,1220,1222,1249],{"className":1221},[935,936],[571,1223,1225,1246],{"className":1224},[940],[571,1226,1229],{"className":1227,"style":1228},[944],"height:0.3011em;",[571,1230,1232,1236],{"style":1231},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[571,1233],{"className":1234,"style":1235},[952],"height:2.7em;",[571,1237,1243],{"className":1238},[1239,1240,1241,1242],"sizing","reset-size6","size3","mtight",[571,1244,1150],{"className":1245},[614,1242],[571,1247,971],{"className":1248},[970],[571,1250,1252],{"className":1251},[940],[571,1253,1256],{"className":1254,"style":1255},[944],"height:0.15em;",[571,1257],{},[571,1259],{"className":1260,"style":696},[695],[571,1262,812],{"className":1263},[700],[571,1265],{"className":1266,"style":696},[695],[571,1268,1270,1273,1277,1280,1283],{"className":1269},[605],[571,1271],{"className":1272,"style":827},[609],[571,1274,1155],{"className":1275},[1276],"minner",[571,1278],{"className":1279,"style":696},[695],[571,1281,812],{"className":1282},[700],[571,1284],{"className":1285,"style":696},[695],[571,1287,1289,1292,1333,1336,1339,1342],{"className":1288},[605],[571,1290],{"className":1291,"style":1067},[609],[571,1293,1295,1298],{"className":1294},[614],[571,1296,592],{"className":1297},[614,615],[571,1299,1301],{"className":1300},[1218],[571,1302,1304,1325],{"className":1303},[935,936],[571,1305,1307,1322],{"className":1306},[940],[571,1308,1311],{"className":1309,"style":1310},[944],"height:0.1514em;",[571,1312,1313,1316],{"style":1231},[571,1314],{"className":1315,"style":1235},[952],[571,1317,1319],{"className":1318},[1239,1240,1241,1242],[571,1320,1113],{"className":1321},[614,615,1242],[571,1323,971],{"className":1324},[970],[571,1326,1328],{"className":1327},[940],[571,1329,1331],{"className":1330,"style":1255},[944],[571,1332],{},[571,1334,878],{"className":1335},[614],[571,1337],{"className":1338,"style":717},[695],[571,1340,899],{"className":1341},[721],[571,1343],{"className":1344,"style":717},[695],[571,1346,1348,1351,1354,1394,1397,1400,1403],{"className":1347},[605],[571,1349],{"className":1350,"style":1067},[609],[571,1352,878],{"className":1353},[614],[571,1355,1357,1360],{"className":1356},[614],[571,1358,592],{"className":1359},[614,615],[571,1361,1363],{"className":1362},[1218],[571,1364,1366,1386],{"className":1365},[935,936],[571,1367,1369,1383],{"className":1368},[940],[571,1370,1372],{"className":1371,"style":1228},[944],[571,1373,1374,1377],{"style":1231},[571,1375],{"className":1376,"style":1235},[952],[571,1378,1380],{"className":1379},[1239,1240,1241,1242],[571,1381,1150],{"className":1382},[614,1242],[571,1384,971],{"className":1385},[970],[571,1387,1389],{"className":1388},[940],[571,1390,1392],{"className":1391,"style":1255},[944],[571,1393],{},[571,1395,878],{"className":1396},[614],[571,1398],{"className":1399,"style":696},[695],[571,1401,812],{"className":1402},[700],[571,1404],{"className":1405,"style":696},[695],[571,1407,1409,1412,1415,1418,1421],{"className":1408},[605],[571,1410],{"className":1411,"style":827},[609],[571,1413,1155],{"className":1414},[1276],[571,1416],{"className":1417,"style":696},[695],[571,1419,812],{"className":1420},[700],[571,1422],{"className":1423,"style":696},[695],[571,1425,1427,1430,1433,1473],{"className":1426},[605],[571,1428],{"className":1429,"style":1067},[609],[571,1431,878],{"className":1432},[614],[571,1434,1436,1439],{"className":1435},[614],[571,1437,592],{"className":1438},[614,615],[571,1440,1442],{"className":1441},[1218],[571,1443,1445,1465],{"className":1444},[935,936],[571,1446,1448,1462],{"className":1447},[940],[571,1449,1451],{"className":1450,"style":1310},[944],[571,1452,1453,1456],{"style":1231},[571,1454],{"className":1455,"style":1235},[952],[571,1457,1459],{"className":1458},[1239,1240,1241,1242],[571,1460,1113],{"className":1461},[614,615,1242],[571,1463,971],{"className":1464},[970],[571,1466,1468],{"className":1467},[940],[571,1469,1471],{"className":1470,"style":1255},[944],[571,1472],{},[571,1474,878],{"className":1475},[614],[857,1477,1478,1479,1651],{},"Abschätzen über einen Zwischenpunkt: ",[571,1480,1482,1531],{"className":1481},[574],[571,1483,1485],{"className":1484},[578],[580,1486,1487],{"xmlns":582},[584,1488,1489,1528],{},[587,1490,1491,1493,1496,1498,1501,1503,1505,1507,1509,1511,1514,1516,1518,1520,1522,1524,1526],{},[590,1492,878],{"mathvariant":881},[590,1494,1495],{},"a",[664,1497,888],{},[590,1499,1500],{},"c",[590,1502,878],{"mathvariant":881},[664,1504,899],{},[590,1506,878],{"mathvariant":881},[590,1508,1495],{},[664,1510,888],{},[590,1512,1513],{},"b",[590,1515,878],{"mathvariant":881},[664,1517,812],{},[590,1519,878],{"mathvariant":881},[590,1521,1513],{},[664,1523,888],{},[590,1525,1500],{},[590,1527,878],{"mathvariant":881},[594,1529,1530],{"encoding":596},"|a - c| \\leq |a - b| + |b - c|",[571,1532,1534,1555,1576,1597,1618,1639],{"className":1533,"ariaHidden":601},[600],[571,1535,1537,1540,1543,1546,1549,1552],{"className":1536},[605],[571,1538],{"className":1539,"style":1067},[609],[571,1541,878],{"className":1542},[614],[571,1544,1495],{"className":1545},[614,615],[571,1547],{"className":1548,"style":696},[695],[571,1550,888],{"className":1551},[700],[571,1553],{"className":1554,"style":696},[695],[571,1556,1558,1561,1564,1567,1570,1573],{"className":1557},[605],[571,1559],{"className":1560,"style":1067},[609],[571,1562,1500],{"className":1563},[614,615],[571,1565,878],{"className":1566},[614],[571,1568],{"className":1569,"style":717},[695],[571,1571,899],{"className":1572},[721],[571,1574],{"className":1575,"style":717},[695],[571,1577,1579,1582,1585,1588,1591,1594],{"className":1578},[605],[571,1580],{"className":1581,"style":1067},[609],[571,1583,878],{"className":1584},[614],[571,1586,1495],{"className":1587},[614,615],[571,1589],{"className":1590,"style":696},[695],[571,1592,888],{"className":1593},[700],[571,1595],{"className":1596,"style":696},[695],[571,1598,1600,1603,1606,1609,1612,1615],{"className":1599},[605],[571,1601],{"className":1602,"style":1067},[609],[571,1604,1513],{"className":1605},[614,615],[571,1607,878],{"className":1608},[614],[571,1610],{"className":1611,"style":696},[695],[571,1613,812],{"className":1614},[700],[571,1616],{"className":1617,"style":696},[695],[571,1619,1621,1624,1627,1630,1633,1636],{"className":1620},[605],[571,1622],{"className":1623,"style":1067},[609],[571,1625,878],{"className":1626},[614],[571,1628,1513],{"className":1629},[614,615],[571,1631],{"className":1632,"style":696},[695],[571,1634,888],{"className":1635},[700],[571,1637],{"className":1638,"style":696},[695],[571,1640,1642,1645,1648],{"className":1641},[605],[571,1643],{"className":1644,"style":1067},[609],[571,1646,1500],{"className":1647},[614,615],[571,1649,878],{"className":1650},[614],". Diese Form wird in der Analysis ständig bei Grenzwertbeweisen gebraucht.",[558,1653,1655],{"id":1654},"herleitung","Herleitung",[563,1657,1658,1659,616,1758,1856],{},"Für reelle Zahlen gilt ",[571,1660,1662,1694],{"className":1661},[574],[571,1663,1665],{"className":1664},[578],[580,1666,1667],{"xmlns":582},[584,1668,1669,1691],{},[587,1670,1671,1673,1675,1677,1679,1681,1683,1685,1687,1689],{},[664,1672,888],{},[590,1674,878],{"mathvariant":881},[590,1676,592],{},[590,1678,878],{"mathvariant":881},[664,1680,899],{},[590,1682,592],{},[664,1684,899],{},[590,1686,878],{"mathvariant":881},[590,1688,592],{},[590,1690,878],{"mathvariant":881},[594,1692,1693],{"encoding":596},"-|x| \\leq x \\leq |x|",[571,1695,1697,1724,1743],{"className":1696,"ariaHidden":601},[600],[571,1698,1700,1703,1706,1709,1712,1715,1718,1721],{"className":1699},[605],[571,1701],{"className":1702,"style":1067},[609],[571,1704,888],{"className":1705},[614],[571,1707,878],{"className":1708},[614],[571,1710,592],{"className":1711},[614,615],[571,1713,878],{"className":1714},[614],[571,1716],{"className":1717,"style":717},[695],[571,1719,899],{"className":1720},[721],[571,1722],{"className":1723,"style":717},[695],[571,1725,1727,1731,1734,1737,1740],{"className":1726},[605],[571,1728],{"className":1729,"style":1730},[609],"height:0.7719em;vertical-align:-0.136em;",[571,1732,592],{"className":1733},[614,615],[571,1735],{"className":1736,"style":717},[695],[571,1738,899],{"className":1739},[721],[571,1741],{"className":1742,"style":717},[695],[571,1744,1746,1749,1752,1755],{"className":1745},[605],[571,1747],{"className":1748,"style":1067},[609],[571,1750,878],{"className":1751},[614],[571,1753,592],{"className":1754},[614,615],[571,1756,878],{"className":1757},[614],[571,1759,1761,1793],{"className":1760},[574],[571,1762,1764],{"className":1763},[578],[580,1765,1766],{"xmlns":582},[584,1767,1768,1790],{},[587,1769,1770,1772,1774,1776,1778,1780,1782,1784,1786,1788],{},[664,1771,888],{},[590,1773,878],{"mathvariant":881},[590,1775,631],{},[590,1777,878],{"mathvariant":881},[664,1779,899],{},[590,1781,631],{},[664,1783,899],{},[590,1785,878],{"mathvariant":881},[590,1787,631],{},[590,1789,878],{"mathvariant":881},[594,1791,1792],{"encoding":596},"-|y| \\leq y \\leq |y|",[571,1794,1796,1823,1841],{"className":1795,"ariaHidden":601},[600],[571,1797,1799,1802,1805,1808,1811,1814,1817,1820],{"className":1798},[605],[571,1800],{"className":1801,"style":1067},[609],[571,1803,888],{"className":1804},[614],[571,1806,878],{"className":1807},[614],[571,1809,631],{"className":1810,"style":647},[614,615],[571,1812,878],{"className":1813},[614],[571,1815],{"className":1816,"style":717},[695],[571,1818,899],{"className":1819},[721],[571,1821],{"className":1822,"style":717},[695],[571,1824,1826,1829,1832,1835,1838],{"className":1825},[605],[571,1827],{"className":1828,"style":710},[609],[571,1830,631],{"className":1831,"style":647},[614,615],[571,1833],{"className":1834,"style":717},[695],[571,1836,899],{"className":1837},[721],[571,1839],{"className":1840,"style":717},[695],[571,1842,1844,1847,1850,1853],{"className":1843},[605],[571,1845],{"className":1846,"style":1067},[609],[571,1848,878],{"className":1849},[614],[571,1851,631],{"className":1852,"style":647},[614,615],[571,1854,878],{"className":1855},[614],". Addiert man beide Ungleichungsketten, erhält man",[571,1858,1861],{"className":1859},[1860],"katex-display",[571,1862,1864,1923],{"className":1863},[574],[571,1865,1867],{"className":1866},[578],[580,1868,1870],{"xmlns":582,"display":1869},"block",[584,1871,1872,1920],{},[587,1873,1874,1876,1879,1881,1883,1885,1887,1889,1891,1893,1896,1898,1900,1902,1904,1906,1908,1910,1912,1914,1916,1918],{},[664,1875,888],{},[664,1877,1878],{"fence":601,"stretchy":601,"minsize":877,"maxsize":877},"(",[590,1880,878],{"mathvariant":881},[590,1882,592],{},[590,1884,878],{"mathvariant":881},[664,1886,812],{},[590,1888,878],{"mathvariant":881},[590,1890,631],{},[590,1892,878],{"mathvariant":881},[664,1894,1895],{"fence":601,"stretchy":601,"minsize":877,"maxsize":877},")",[664,1897,899],{},[590,1899,592],{},[664,1901,812],{},[590,1903,631],{},[664,1905,899],{},[590,1907,878],{"mathvariant":881},[590,1909,592],{},[590,1911,878],{"mathvariant":881},[664,1913,812],{},[590,1915,878],{"mathvariant":881},[590,1917,631],{},[590,1919,878],{"mathvariant":881},[594,1921,1922],{"encoding":596},"-\\bigl(|x| + |y|\\bigr) \\leq x + y \\leq |x| + |y|",[571,1924,1926,1960,1990,2008,2026,2050],{"className":1925,"ariaHidden":601},[600],[571,1927,1929,1932,1935,1942,1945,1948,1951,1954,1957],{"className":1928},[605],[571,1930],{"className":1931,"style":922},[609],[571,1933,888],{"className":1934},[614],[571,1936,1938],{"className":1937},[926],[571,1939,1878],{"className":1940},[930,1941],"size1",[571,1943,878],{"className":1944},[614],[571,1946,592],{"className":1947},[614,615],[571,1949,878],{"className":1950},[614],[571,1952],{"className":1953,"style":696},[695],[571,1955,812],{"className":1956},[700],[571,1958],{"className":1959,"style":696},[695],[571,1961,1963,1966,1969,1972,1975,1981,1984,1987],{"className":1962},[605],[571,1964],{"className":1965,"style":922},[609],[571,1967,878],{"className":1968},[614],[571,1970,631],{"className":1971,"style":647},[614,615],[571,1973,878],{"className":1974},[614],[571,1976,1978],{"className":1977},[1017],[571,1979,1895],{"className":1980},[930,1941],[571,1982],{"className":1983,"style":717},[695],[571,1985,899],{"className":1986},[721],[571,1988],{"className":1989,"style":717},[695],[571,1991,1993,1996,1999,2002,2005],{"className":1992},[605],[571,1994],{"className":1995,"style":827},[609],[571,1997,592],{"className":1998},[614,615],[571,2000],{"className":2001,"style":696},[695],[571,2003,812],{"className":2004},[700],[571,2006],{"className":2007,"style":696},[695],[571,2009,2011,2014,2017,2020,2023],{"className":2010},[605],[571,2012],{"className":2013,"style":710},[609],[571,2015,631],{"className":2016,"style":647},[614,615],[571,2018],{"className":2019,"style":717},[695],[571,2021,899],{"className":2022},[721],[571,2024],{"className":2025,"style":717},[695],[571,2027,2029,2032,2035,2038,2041,2044,2047],{"className":2028},[605],[571,2030],{"className":2031,"style":1067},[609],[571,2033,878],{"className":2034},[614],[571,2036,592],{"className":2037},[614,615],[571,2039,878],{"className":2040},[614],[571,2042],{"className":2043,"style":696},[695],[571,2045,812],{"className":2046},[700],[571,2048],{"className":2049,"style":696},[695],[571,2051,2053,2056,2059,2062],{"className":2052},[605],[571,2054],{"className":2055,"style":1067},[609],[571,2057,878],{"className":2058},[614],[571,2060,631],{"className":2061,"style":647},[614,615],[571,2063,878],{"className":2064},[614],[563,2066,2067,2068,1095],{},"und das bedeutet genau ",[571,2069,2071,2109],{"className":2070},[574],[571,2072,2074],{"className":2073},[578],[580,2075,2076],{"xmlns":582},[584,2077,2078,2106],{},[587,2079,2080,2082,2084,2086,2088,2090,2092,2094,2096,2098,2100,2102,2104],{},[590,2081,878],{"mathvariant":881},[590,2083,592],{},[664,2085,812],{},[590,2087,631],{},[590,2089,878],{"mathvariant":881},[664,2091,899],{},[590,2093,878],{"mathvariant":881},[590,2095,592],{},[590,2097,878],{"mathvariant":881},[664,2099,812],{},[590,2101,878],{"mathvariant":881},[590,2103,631],{},[590,2105,878],{"mathvariant":881},[594,2107,2108],{"encoding":596},"|x + y| \\leq |x| + |y|",[571,2110,2112,2133,2154,2178],{"className":2111,"ariaHidden":601},[600],[571,2113,2115,2118,2121,2124,2127,2130],{"className":2114},[605],[571,2116],{"className":2117,"style":1067},[609],[571,2119,878],{"className":2120},[614],[571,2122,592],{"className":2123},[614,615],[571,2125],{"className":2126,"style":696},[695],[571,2128,812],{"className":2129},[700],[571,2131],{"className":2132,"style":696},[695],[571,2134,2136,2139,2142,2145,2148,2151],{"className":2135},[605],[571,2137],{"className":2138,"style":1067},[609],[571,2140,631],{"className":2141,"style":647},[614,615],[571,2143,878],{"className":2144},[614],[571,2146],{"className":2147,"style":717},[695],[571,2149,899],{"className":2150},[721],[571,2152],{"className":2153,"style":717},[695],[571,2155,2157,2160,2163,2166,2169,2172,2175],{"className":2156},[605],[571,2158],{"className":2159,"style":1067},[609],[571,2161,878],{"className":2162},[614],[571,2164,592],{"className":2165},[614,615],[571,2167,878],{"className":2168},[614],[571,2170],{"className":2171,"style":696},[695],[571,2173,812],{"className":2174},[700],[571,2176],{"className":2177,"style":696},[695],[571,2179,2181,2184,2187,2190],{"className":2180},[605],[571,2182],{"className":2183,"style":1067},[609],[571,2185,878],{"className":2186},[614],[571,2188,631],{"className":2189,"style":647},[614,615],[571,2191,878],{"className":2192},[614],[563,2194,2195,2196,2303,2304,2429,2430,2555],{},"Die umgekehrte Form folgt, indem man die Ungleichung auf ",[571,2197,2199,2231],{"className":2198},[574],[571,2200,2202],{"className":2201},[578],[580,2203,2204],{"xmlns":582},[584,2205,2206,2228],{},[587,2207,2208,2210,2213,2216,2218,2220,2222,2224,2226],{},[590,2209,592],{},[664,2211,2212],{},"=",[664,2214,1878],{"stretchy":2215},"false",[590,2217,592],{},[664,2219,888],{},[590,2221,631],{},[664,2223,1895],{"stretchy":2215},[664,2225,812],{},[590,2227,631],{},[594,2229,2230],{"encoding":596},"x = (x - y) + y",[571,2232,2234,2252,2273,2294],{"className":2233,"ariaHidden":601},[600],[571,2235,2237,2240,2243,2246,2249],{"className":2236},[605],[571,2238],{"className":2239,"style":610},[609],[571,2241,592],{"className":2242},[614,615],[571,2244],{"className":2245,"style":717},[695],[571,2247,2212],{"className":2248},[721],[571,2250],{"className":2251,"style":717},[695],[571,2253,2255,2258,2261,2264,2267,2270],{"className":2254},[605],[571,2256],{"className":2257,"style":1067},[609],[571,2259,1878],{"className":2260},[926],[571,2262,592],{"className":2263},[614,615],[571,2265],{"className":2266,"style":696},[695],[571,2268,888],{"className":2269},[700],[571,2271],{"className":2272,"style":696},[695],[571,2274,2276,2279,2282,2285,2288,2291],{"className":2275},[605],[571,2277],{"className":2278,"style":1067},[609],[571,2280,631],{"className":2281,"style":647},[614,615],[571,2283,1895],{"className":2284},[1017],[571,2286],{"className":2287,"style":696},[695],[571,2289,812],{"className":2290},[700],[571,2292],{"className":2293,"style":696},[695],[571,2295,2297,2300],{"className":2296},[605],[571,2298],{"className":2299,"style":643},[609],[571,2301,631],{"className":2302,"style":647},[614,615]," anwendet: ",[571,2305,2307,2345],{"className":2306},[574],[571,2308,2310],{"className":2309},[578],[580,2311,2312],{"xmlns":582},[584,2313,2314,2342],{},[587,2315,2316,2318,2320,2322,2324,2326,2328,2330,2332,2334,2336,2338,2340],{},[590,2317,878],{"mathvariant":881},[590,2319,592],{},[590,2321,878],{"mathvariant":881},[664,2323,899],{},[590,2325,878],{"mathvariant":881},[590,2327,592],{},[664,2329,888],{},[590,2331,631],{},[590,2333,878],{"mathvariant":881},[664,2335,812],{},[590,2337,878],{"mathvariant":881},[590,2339,631],{},[590,2341,878],{"mathvariant":881},[594,2343,2344],{"encoding":596},"|x| \\leq |x - y| + |y|",[571,2346,2348,2372,2393,2414],{"className":2347,"ariaHidden":601},[600],[571,2349,2351,2354,2357,2360,2363,2366,2369],{"className":2350},[605],[571,2352],{"className":2353,"style":1067},[609],[571,2355,878],{"className":2356},[614],[571,2358,592],{"className":2359},[614,615],[571,2361,878],{"className":2362},[614],[571,2364],{"className":2365,"style":717},[695],[571,2367,899],{"className":2368},[721],[571,2370],{"className":2371,"style":717},[695],[571,2373,2375,2378,2381,2384,2387,2390],{"className":2374},[605],[571,2376],{"className":2377,"style":1067},[609],[571,2379,878],{"className":2380},[614],[571,2382,592],{"className":2383},[614,615],[571,2385],{"className":2386,"style":696},[695],[571,2388,888],{"className":2389},[700],[571,2391],{"className":2392,"style":696},[695],[571,2394,2396,2399,2402,2405,2408,2411],{"className":2395},[605],[571,2397],{"className":2398,"style":1067},[609],[571,2400,631],{"className":2401,"style":647},[614,615],[571,2403,878],{"className":2404},[614],[571,2406],{"className":2407,"style":696},[695],[571,2409,812],{"className":2410},[700],[571,2412],{"className":2413,"style":696},[695],[571,2415,2417,2420,2423,2426],{"className":2416},[605],[571,2418],{"className":2419,"style":1067},[609],[571,2421,878],{"className":2422},[614],[571,2424,631],{"className":2425,"style":647},[614,615],[571,2427,878],{"className":2428},[614],", also ",[571,2431,2433,2471],{"className":2432},[574],[571,2434,2436],{"className":2435},[578],[580,2437,2438],{"xmlns":582},[584,2439,2440,2468],{},[587,2441,2442,2444,2446,2448,2450,2452,2454,2456,2458,2460,2462,2464,2466],{},[590,2443,878],{"mathvariant":881},[590,2445,592],{},[590,2447,878],{"mathvariant":881},[664,2449,888],{},[590,2451,878],{"mathvariant":881},[590,2453,631],{},[590,2455,878],{"mathvariant":881},[664,2457,899],{},[590,2459,878],{"mathvariant":881},[590,2461,592],{},[664,2463,888],{},[590,2465,631],{},[590,2467,878],{"mathvariant":881},[594,2469,2470],{"encoding":596},"|x| - |y| \\leq |x - y|",[571,2472,2474,2498,2522,2543],{"className":2473,"ariaHidden":601},[600],[571,2475,2477,2480,2483,2486,2489,2492,2495],{"className":2476},[605],[571,2478],{"className":2479,"style":1067},[609],[571,2481,878],{"className":2482},[614],[571,2484,592],{"className":2485},[614,615],[571,2487,878],{"className":2488},[614],[571,2490],{"className":2491,"style":696},[695],[571,2493,888],{"className":2494},[700],[571,2496],{"className":2497,"style":696},[695],[571,2499,2501,2504,2507,2510,2513,2516,2519],{"className":2500},[605],[571,2502],{"className":2503,"style":1067},[609],[571,2505,878],{"className":2506},[614],[571,2508,631],{"className":2509,"style":647},[614,615],[571,2511,878],{"className":2512},[614],[571,2514],{"className":2515,"style":717},[695],[571,2517,899],{"className":2518},[721],[571,2520],{"className":2521,"style":717},[695],[571,2523,2525,2528,2531,2534,2537,2540],{"className":2524},[605],[571,2526],{"className":2527,"style":1067},[609],[571,2529,878],{"className":2530},[614],[571,2532,592],{"className":2533},[614,615],[571,2535],{"className":2536,"style":696},[695],[571,2538,888],{"className":2539},[700],[571,2541],{"className":2542,"style":696},[695],[571,2544,2546,2549,2552],{"className":2545},[605],[571,2547],{"className":2548,"style":1067},[609],[571,2550,631],{"className":2551,"style":647},[614,615],[571,2553,878],{"className":2554},[614],", und ebenso mit vertauschten Rollen.",[558,2557,2559],{"id":2558},"beispiele","Beispiele",[563,2561,2562,2563,767,2615,2673],{},"Verschiedene Vorzeichen, ",[571,2564,2566,2585],{"className":2565},[574],[571,2567,2569],{"className":2568},[578],[580,2570,2571],{"xmlns":582},[584,2572,2573,2582],{},[587,2574,2575,2577,2579],{},[590,2576,592],{},[664,2578,2212],{},[673,2580,2581],{},"3",[594,2583,2584],{"encoding":596},"x = 3",[571,2586,2588,2606],{"className":2587,"ariaHidden":601},[600],[571,2589,2591,2594,2597,2600,2603],{"className":2590},[605],[571,2592],{"className":2593,"style":610},[609],[571,2595,592],{"className":2596},[614,615],[571,2598],{"className":2599,"style":717},[695],[571,2601,2212],{"className":2602},[721],[571,2604],{"className":2605,"style":717},[695],[571,2607,2609,2612],{"className":2608},[605],[571,2610],{"className":2611,"style":731},[609],[571,2613,2581],{"className":2614},[614],[571,2616,2618,2639],{"className":2617},[574],[571,2619,2621],{"className":2620},[578],[580,2622,2623],{"xmlns":582},[584,2624,2625,2636],{},[587,2626,2627,2629,2631,2633],{},[590,2628,631],{},[664,2630,2212],{},[664,2632,888],{},[673,2634,2635],{},"5",[594,2637,2638],{"encoding":596},"y = -5",[571,2640,2642,2660],{"className":2641,"ariaHidden":601},[600],[571,2643,2645,2648,2651,2654,2657],{"className":2644},[605],[571,2646],{"className":2647,"style":643},[609],[571,2649,631],{"className":2650,"style":647},[614,615],[571,2652],{"className":2653,"style":717},[695],[571,2655,2212],{"className":2656},[721],[571,2658],{"className":2659,"style":717},[695],[571,2661,2663,2667,2670],{"className":2662},[605],[571,2664],{"className":2665,"style":2666},[609],"height:0.7278em;vertical-align:-0.0833em;",[571,2668,888],{"className":2669},[614],[571,2671,2635],{"className":2672},[614],":",[571,2675,2677],{"className":2676},[1860],[571,2678,2680,2742],{"className":2679},[574],[571,2681,2683],{"className":2682},[578],[580,2684,2685],{"xmlns":582,"display":1869},[584,2686,2687,2739],{},[587,2688,2689,2691,2693,2695,2697,2699,2701,2703,2705,2707,2710,2714,2716,2718,2720,2722,2724,2726,2728,2730,2732,2734,2736],{},[590,2690,878],{"mathvariant":881},[673,2692,2581],{},[664,2694,812],{},[664,2696,1878],{"stretchy":2215},[664,2698,888],{},[673,2700,2635],{},[664,2702,1895],{"stretchy":2215},[590,2704,878],{"mathvariant":881},[664,2706,2212],{},[673,2708,2709],{},"2",[2711,2712,2713],"mtext",{},"  ",[664,2715,899],{},[2711,2717,2713],{},[590,2719,878],{"mathvariant":881},[673,2721,2581],{},[590,2723,878],{"mathvariant":881},[664,2725,812],{},[590,2727,878],{"mathvariant":881},[664,2729,888],{},[673,2731,2635],{},[590,2733,878],{"mathvariant":881},[664,2735,2212],{},[673,2737,2738],{},"8",[594,2740,2741],{"encoding":596},"|3 + (-5)| = 2 \\;\\leq\\; |3| + |-5| = 8",[571,2743,2745,2764,2794,2819,2838,2856,2875],{"className":2744,"ariaHidden":601},[600],[571,2746,2748,2751,2755,2758,2761],{"className":2747},[605],[571,2749],{"className":2750,"style":1067},[609],[571,2752,2754],{"className":2753},[614],"∣3",[571,2756],{"className":2757,"style":696},[695],[571,2759,812],{"className":2760},[700],[571,2762],{"className":2763,"style":696},[695],[571,2765,2767,2770,2773,2776,2779,2782,2785,2788,2791],{"className":2766},[605],[571,2768],{"className":2769,"style":1067},[609],[571,2771,1878],{"className":2772},[926],[571,2774,888],{"className":2775},[614],[571,2777,2635],{"className":2778},[614],[571,2780,1895],{"className":2781},[1017],[571,2783,878],{"className":2784},[614],[571,2786],{"className":2787,"style":717},[695],[571,2789,2212],{"className":2790},[721],[571,2792],{"className":2793,"style":717},[695],[571,2795,2797,2801,2804,2807,2810,2813,2816],{"className":2796},[605],[571,2798],{"className":2799,"style":2800},[609],"height:0.7804em;vertical-align:-0.136em;",[571,2802,2709],{"className":2803},[614],[571,2805],{"className":2806,"style":717},[695],[571,2808],{"className":2809,"style":717},[695],[571,2811,899],{"className":2812},[721],[571,2814],{"className":2815,"style":717},[695],[571,2817],{"className":2818,"style":717},[695],[571,2820,2822,2825,2829,2832,2835],{"className":2821},[605],[571,2823],{"className":2824,"style":1067},[609],[571,2826,2828],{"className":2827},[614],"∣3∣",[571,2830],{"className":2831,"style":696},[695],[571,2833,812],{"className":2834},[700],[571,2836],{"className":2837,"style":696},[695],[571,2839,2841,2844,2847,2850,2853],{"className":2840},[605],[571,2842],{"className":2843,"style":1067},[609],[571,2845,878],{"className":2846},[614],[571,2848],{"className":2849,"style":696},[695],[571,2851,888],{"className":2852},[700],[571,2854],{"className":2855,"style":696},[695],[571,2857,2859,2862,2866,2869,2872],{"className":2858},[605],[571,2860],{"className":2861,"style":1067},[609],[571,2863,2865],{"className":2864},[614],"5∣",[571,2867],{"className":2868,"style":717},[695],[571,2870,2212],{"className":2871},[721],[571,2873],{"className":2874,"style":717},[695],[571,2876,2878,2881],{"className":2877},[605],[571,2879],{"className":2880,"style":731},[609],[571,2882,2738],{"className":2883},[614],[563,2885,2886,2887,767,2938,862,2990,3124],{},"Gleiches Vorzeichen, ",[571,2888,2890,2908],{"className":2889},[574],[571,2891,2893],{"className":2892},[578],[580,2894,2895],{"xmlns":582},[584,2896,2897,2905],{},[587,2898,2899,2901,2903],{},[590,2900,592],{},[664,2902,2212],{},[673,2904,2709],{},[594,2906,2907],{"encoding":596},"x = 2",[571,2909,2911,2929],{"className":2910,"ariaHidden":601},[600],[571,2912,2914,2917,2920,2923,2926],{"className":2913},[605],[571,2915],{"className":2916,"style":610},[609],[571,2918,592],{"className":2919},[614,615],[571,2921],{"className":2922,"style":717},[695],[571,2924,2212],{"className":2925},[721],[571,2927],{"className":2928,"style":717},[695],[571,2930,2932,2935],{"className":2931},[605],[571,2933],{"className":2934,"style":731},[609],[571,2936,2709],{"className":2937},[614],[571,2939,2941,2960],{"className":2940},[574],[571,2942,2944],{"className":2943},[578],[580,2945,2946],{"xmlns":582},[584,2947,2948,2957],{},[587,2949,2950,2952,2954],{},[590,2951,631],{},[664,2953,2212],{},[673,2955,2956],{},"4",[594,2958,2959],{"encoding":596},"y = 4",[571,2961,2963,2981],{"className":2962,"ariaHidden":601},[600],[571,2964,2966,2969,2972,2975,2978],{"className":2965},[605],[571,2967],{"className":2968,"style":643},[609],[571,2970,631],{"className":2971,"style":647},[614,615],[571,2973],{"className":2974,"style":717},[695],[571,2976,2212],{"className":2977},[721],[571,2979],{"className":2980,"style":717},[695],[571,2982,2984,2987],{"className":2983},[605],[571,2985],{"className":2986,"style":731},[609],[571,2988,2956],{"className":2989},[614],[571,2991,2993,3036],{"className":2992},[574],[571,2994,2996],{"className":2995},[578],[580,2997,2998],{"xmlns":582},[584,2999,3000,3033],{},[587,3001,3002,3004,3006,3008,3010,3012,3014,3017,3019,3021,3023,3025,3027,3029,3031],{},[590,3003,878],{"mathvariant":881},[673,3005,2709],{},[664,3007,812],{},[673,3009,2956],{},[590,3011,878],{"mathvariant":881},[664,3013,2212],{},[673,3015,3016],{},"6",[664,3018,2212],{},[590,3020,878],{"mathvariant":881},[673,3022,2709],{},[590,3024,878],{"mathvariant":881},[664,3026,812],{},[590,3028,878],{"mathvariant":881},[673,3030,2956],{},[590,3032,878],{"mathvariant":881},[594,3034,3035],{"encoding":596},"|2 + 4| = 6 = |2| + |4|",[571,3037,3039,3058,3077,3095,3114],{"className":3038,"ariaHidden":601},[600],[571,3040,3042,3045,3049,3052,3055],{"className":3041},[605],[571,3043],{"className":3044,"style":1067},[609],[571,3046,3048],{"className":3047},[614],"∣2",[571,3050],{"className":3051,"style":696},[695],[571,3053,812],{"className":3054},[700],[571,3056],{"className":3057,"style":696},[695],[571,3059,3061,3064,3068,3071,3074],{"className":3060},[605],[571,3062],{"className":3063,"style":1067},[609],[571,3065,3067],{"className":3066},[614],"4∣",[571,3069],{"className":3070,"style":717},[695],[571,3072,2212],{"className":3073},[721],[571,3075],{"className":3076,"style":717},[695],[571,3078,3080,3083,3086,3089,3092],{"className":3079},[605],[571,3081],{"className":3082,"style":731},[609],[571,3084,3016],{"className":3085},[614],[571,3087],{"className":3088,"style":717},[695],[571,3090,2212],{"className":3091},[721],[571,3093],{"className":3094,"style":717},[695],[571,3096,3098,3101,3105,3108,3111],{"className":3097},[605],[571,3099],{"className":3100,"style":1067},[609],[571,3102,3104],{"className":3103},[614],"∣2∣",[571,3106],{"className":3107,"style":696},[695],[571,3109,812],{"className":3110},[700],[571,3112],{"className":3113,"style":696},[695],[571,3115,3117,3120],{"className":3116},[605],[571,3118],{"className":3119,"style":1067},[609],[571,3121,3123],{"className":3122},[614],"∣4∣",", es gilt Gleichheit.",[563,3126,3127,3128,767,3178,2673],{},"Umgekehrte Dreiecksungleichung mit ",[571,3129,3131,3148],{"className":3130},[574],[571,3132,3134],{"className":3133},[578],[580,3135,3136],{"xmlns":582},[584,3137,3138,3146],{},[587,3139,3140,3142,3144],{},[590,3141,592],{},[664,3143,2212],{},[673,3145,2581],{},[594,3147,2584],{"encoding":596},[571,3149,3151,3169],{"className":3150,"ariaHidden":601},[600],[571,3152,3154,3157,3160,3163,3166],{"className":3153},[605],[571,3155],{"className":3156,"style":610},[609],[571,3158,592],{"className":3159},[614,615],[571,3161],{"className":3162,"style":717},[695],[571,3164,2212],{"className":3165},[721],[571,3167],{"className":3168,"style":717},[695],[571,3170,3172,3175],{"className":3171},[605],[571,3173],{"className":3174,"style":731},[609],[571,3176,2581],{"className":3177},[614],[571,3179,3181,3200],{"className":3180},[574],[571,3182,3184],{"className":3183},[578],[580,3185,3186],{"xmlns":582},[584,3187,3188,3198],{},[587,3189,3190,3192,3194,3196],{},[590,3191,631],{},[664,3193,2212],{},[664,3195,888],{},[673,3197,2635],{},[594,3199,2638],{"encoding":596},[571,3201,3203,3221],{"className":3202,"ariaHidden":601},[600],[571,3204,3206,3209,3212,3215,3218],{"className":3205},[605],[571,3207],{"className":3208,"style":643},[609],[571,3210,631],{"className":3211,"style":647},[614,615],[571,3213],{"className":3214,"style":717},[695],[571,3216,2212],{"className":3217},[721],[571,3219],{"className":3220,"style":717},[695],[571,3222,3224,3227,3230],{"className":3223},[605],[571,3225],{"className":3226,"style":2666},[609],[571,3228,888],{"className":3229},[614],[571,3231,2635],{"className":3232},[614],[571,3234,3236],{"className":3235},[1860],[571,3237,3239,3301],{"className":3238},[574],[571,3240,3242],{"className":3241},[578],[580,3243,3244],{"xmlns":582,"display":1869},[584,3245,3246,3298],{},[587,3247,3248,3250,3252,3254,3256,3258,3260,3262,3264,3266,3268,3270,3272,3274,3276,3278,3280,3282,3284,3286,3288,3290,3292,3294,3296],{},[664,3249,878],{"fence":601,"stretchy":601,"minsize":877,"maxsize":877},[590,3251,878],{"mathvariant":881},[673,3253,2581],{},[590,3255,878],{"mathvariant":881},[664,3257,888],{},[590,3259,878],{"mathvariant":881},[664,3261,888],{},[673,3263,2635],{},[590,3265,878],{"mathvariant":881},[664,3267,878],{"fence":601,"stretchy":601,"minsize":877,"maxsize":877},[664,3269,2212],{},[673,3271,2709],{},[2711,3273,2713],{},[664,3275,899],{},[2711,3277,2713],{},[590,3279,878],{"mathvariant":881},[673,3281,2581],{},[664,3283,888],{},[664,3285,1878],{"stretchy":2215},[664,3287,888],{},[673,3289,2635],{},[664,3291,1895],{"stretchy":2215},[590,3293,878],{"mathvariant":881},[664,3295,2212],{},[673,3297,2738],{},[594,3299,3300],{"encoding":596},"\\bigl||3| - |-5|\\bigr| = 2 \\;\\leq\\; |3 - (-5)| = 8",[571,3302,3304,3359,3377,3432,3456,3474,3504],{"className":3303,"ariaHidden":601},[600],[571,3305,3307,3310,3347,3350,3353,3356],{"className":3306},[605],[571,3308],{"className":3309,"style":922},[609],[571,3311,3313],{"className":3312},[926],[571,3314,3316],{"className":3315},[930,931],[571,3317,3319,3339],{"className":3318},[935,936],[571,3320,3322,3336],{"className":3321},[940],[571,3323,3325],{"className":3324,"style":945},[944],[571,3326,3327,3330],{"style":948},[571,3328],{"className":3329,"style":953},[952],[571,3331,3332],{"style":956},[958,3333,3334],{"xmlns":960,"width":961,"height":877,"viewBox":962},[964,3335],{"d":966},[571,3337,971],{"className":3338},[970],[571,3340,3342],{"className":3341},[940],[571,3343,3345],{"className":3344,"style":978},[944],[571,3346],{},[571,3348,2828],{"className":3349},[614],[571,3351],{"className":3352,"style":696},[695],[571,3354,888],{"className":3355},[700],[571,3357],{"className":3358,"style":696},[695],[571,3360,3362,3365,3368,3371,3374],{"className":3361},[605],[571,3363],{"className":3364,"style":1067},[609],[571,3366,878],{"className":3367},[614],[571,3369],{"className":3370,"style":696},[695],[571,3372,888],{"className":3373},[700],[571,3375],{"className":3376,"style":696},[695],[571,3378,3380,3383,3386,3423,3426,3429],{"className":3379},[605],[571,3381],{"className":3382,"style":922},[609],[571,3384,2865],{"className":3385},[614],[571,3387,3389],{"className":3388},[1017],[571,3390,3392],{"className":3391},[930,931],[571,3393,3395,3415],{"className":3394},[935,936],[571,3396,3398,3412],{"className":3397},[940],[571,3399,3401],{"className":3400,"style":945},[944],[571,3402,3403,3406],{"style":948},[571,3404],{"className":3405,"style":953},[952],[571,3407,3408],{"style":956},[958,3409,3410],{"xmlns":960,"width":961,"height":877,"viewBox":962},[964,3411],{"d":966},[571,3413,971],{"className":3414},[970],[571,3416,3418],{"className":3417},[940],[571,3419,3421],{"className":3420,"style":978},[944],[571,3422],{},[571,3424],{"className":3425,"style":717},[695],[571,3427,2212],{"className":3428},[721],[571,3430],{"className":3431,"style":717},[695],[571,3433,3435,3438,3441,3444,3447,3450,3453],{"className":3434},[605],[571,3436],{"className":3437,"style":2800},[609],[571,3439,2709],{"className":3440},[614],[571,3442],{"className":3443,"style":717},[695],[571,3445],{"className":3446,"style":717},[695],[571,3448,899],{"className":3449},[721],[571,3451],{"className":3452,"style":717},[695],[571,3454],{"className":3455,"style":717},[695],[571,3457,3459,3462,3465,3468,3471],{"className":3458},[605],[571,3460],{"className":3461,"style":1067},[609],[571,3463,2754],{"className":3464},[614],[571,3466],{"className":3467,"style":696},[695],[571,3469,888],{"className":3470},[700],[571,3472],{"className":3473,"style":696},[695],[571,3475,3477,3480,3483,3486,3489,3492,3495,3498,3501],{"className":3476},[605],[571,3478],{"className":3479,"style":1067},[609],[571,3481,1878],{"className":3482},[926],[571,3484,888],{"className":3485},[614],[571,3487,2635],{"className":3488},[614],[571,3490,1895],{"className":3491},[1017],[571,3493,878],{"className":3494},[614],[571,3496],{"className":3497,"style":717},[695],[571,3499,2212],{"className":3500},[721],[571,3502],{"className":3503,"style":717},[695],[571,3505,3507,3510],{"className":3506},[605],[571,3508],{"className":3509,"style":731},[609],[571,3511,2738],{"className":3512},[614],[563,3514,3515,3516,616,3598,3683,3684,2673],{},"Komplexe Zahlen ",[571,3517,3519,3545],{"className":3518},[574],[571,3520,3522],{"className":3521},[578],[580,3523,3524],{"xmlns":582},[584,3525,3526,3542],{},[587,3527,3528,3531,3533,3535,3537,3539],{},[590,3529,3530],{},"z",[664,3532,2212],{},[673,3534,2581],{},[664,3536,812],{},[673,3538,2956],{},[590,3540,3541],{},"i",[594,3543,3544],{"encoding":596},"z = 3 + 4i",[571,3546,3548,3567,3585],{"className":3547,"ariaHidden":601},[600],[571,3549,3551,3554,3558,3561,3564],{"className":3550},[605],[571,3552],{"className":3553,"style":610},[609],[571,3555,3530],{"className":3556,"style":3557},[614,615],"margin-right:0.044em;",[571,3559],{"className":3560,"style":717},[695],[571,3562,2212],{"className":3563},[721],[571,3565],{"className":3566,"style":717},[695],[571,3568,3570,3573,3576,3579,3582],{"className":3569},[605],[571,3571],{"className":3572,"style":2666},[609],[571,3574,2581],{"className":3575},[614],[571,3577],{"className":3578,"style":696},[695],[571,3580,812],{"className":3581},[700],[571,3583],{"className":3584,"style":696},[695],[571,3586,3588,3592,3595],{"className":3587},[605],[571,3589],{"className":3590,"style":3591},[609],"height:0.6595em;",[571,3593,2956],{"className":3594},[614],[571,3596,3541],{"className":3597},[614,615],[571,3599,3601,3628],{"className":3600},[574],[571,3602,3604],{"className":3603},[578],[580,3605,3606],{"xmlns":582},[584,3607,3608,3625],{},[587,3609,3610,3613,3615,3617,3619,3621,3623],{},[590,3611,3612],{},"w",[664,3614,2212],{},[664,3616,888],{},[673,3618,2956],{},[664,3620,812],{},[673,3622,2581],{},[590,3624,3541],{},[594,3626,3627],{"encoding":596},"w = -4 + 3i",[571,3629,3631,3650,3671],{"className":3630,"ariaHidden":601},[600],[571,3632,3634,3637,3641,3644,3647],{"className":3633},[605],[571,3635],{"className":3636,"style":610},[609],[571,3638,3612],{"className":3639,"style":3640},[614,615],"margin-right:0.0269em;",[571,3642],{"className":3643,"style":717},[695],[571,3645,2212],{"className":3646},[721],[571,3648],{"className":3649,"style":717},[695],[571,3651,3653,3656,3659,3662,3665,3668],{"className":3652},[605],[571,3654],{"className":3655,"style":2666},[609],[571,3657,888],{"className":3658},[614],[571,3660,2956],{"className":3661},[614],[571,3663],{"className":3664,"style":696},[695],[571,3666,812],{"className":3667},[700],[571,3669],{"className":3670,"style":696},[695],[571,3672,3674,3677,3680],{"className":3673},[605],[571,3675],{"className":3676,"style":3591},[609],[571,3678,2581],{"className":3679},[614],[571,3681,3541],{"className":3682},[614,615]," mit 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5",[571,3718,3720,3744,3768],{"className":3719,"ariaHidden":601},[600],[571,3721,3723,3726,3729,3732,3735,3738,3741],{"className":3722},[605],[571,3724],{"className":3725,"style":1067},[609],[571,3727,878],{"className":3728},[614],[571,3730,3530],{"className":3731,"style":3557},[614,615],[571,3733,878],{"className":3734},[614],[571,3736],{"className":3737,"style":717},[695],[571,3739,2212],{"className":3740},[721],[571,3742],{"className":3743,"style":717},[695],[571,3745,3747,3750,3753,3756,3759,3762,3765],{"className":3746},[605],[571,3748],{"className":3749,"style":1067},[609],[571,3751,878],{"className":3752},[614],[571,3754,3612],{"className":3755,"style":3640},[614,615],[571,3757,878],{"className":3758},[614],[571,3760],{"className":3761,"style":717},[695],[571,3763,2212],{"className":3764},[721],[571,3766],{"className":3767,"style":717},[695],[571,3769,3771,3774],{"className":3770},[605],[571,3772],{"className":3773,"style":731},[609],[571,3775,2635],{"className":3776},[614],[571,3778,3780],{"className":3779},[1860],[571,3781,3783,3845],{"className":3782},[574],[571,3784,3786],{"className":3785},[578],[580,3787,3788],{"xmlns":582,"display":1869},[584,3789,3790,3842],{},[587,3791,3792,3794,3796,3798,3800,3802,3804,3806,3808,3810,3812,3815,3817,3819,3821,3827,3830,3833,3835,3837,3839],{},[590,3793,878],{"mathvariant":881},[590,3795,3530],{},[664,3797,812],{},[590,3799,3612],{},[590,3801,878],{"mathvariant":881},[664,3803,2212],{},[590,3805,878],{"mathvariant":881},[664,3807,888],{},[673,3809,1150],{},[664,3811,812],{},[673,3813,3814],{},"7",[590,3816,3541],{},[590,3818,878],{"mathvariant":881},[664,3820,2212],{},[3822,3823,3824],"msqrt",{},[673,3825,3826],{},"50",[664,3828,3829],{},"≈",[673,3831,3832],{},"7,0711",[2711,3834,2713],{},[664,3836,899],{},[2711,3838,2713],{},[673,3840,3841],{},"10",[594,3843,3844],{"encoding":596},"|z 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10",[571,3846,3848,3869,3890,3908,3926,3950,4028,4065],{"className":3847,"ariaHidden":601},[600],[571,3849,3851,3854,3857,3860,3863,3866],{"className":3850},[605],[571,3852],{"className":3853,"style":1067},[609],[571,3855,878],{"className":3856},[614],[571,3858,3530],{"className":3859,"style":3557},[614,615],[571,3861],{"className":3862,"style":696},[695],[571,3864,812],{"className":3865},[700],[571,3867],{"className":3868,"style":696},[695],[571,3870,3872,3875,3878,3881,3884,3887],{"className":3871},[605],[571,3873],{"className":3874,"style":1067},[609],[571,3876,3612],{"className":3877,"style":3640},[614,615],[571,3879,878],{"className":3880},[614],[571,3882],{"className":3883,"style":717},[695],[571,3885,2212],{"className":3886},[721],[571,3888],{"className":3889,"style":717},[695],[571,3891,3893,3896,3899,3902,3905],{"className":3892},[605],[571,3894],{"className":3895,"style":1067},[609],[571,3897,878],{"className":3898},[614],[571,3900],{"className":3901,"style":696},[695],[571,3903,888],{"className":3904},[700],[571,3906],{"className":3907,"style":696},[695],[571,3909,3911,3914,3917,3920,3923],{"className":3910},[605],[571,3912],{"className":3913,"style":2666},[609],[571,3915,1150],{"className":3916},[614],[571,3918],{"className":3919,"style":696},[695],[571,3921,812],{"className":3922},[700],[571,3924],{"className":3925,"style":696},[695],[571,3927,3929,3932,3935,3938,3941,3944,3947],{"className":3928},[605],[571,3930],{"className":3931,"style":1067},[609],[571,3933,3814],{"className":3934},[614],[571,3936,3541],{"className":3937},[614,615],[571,3939,878],{"className":3940},[614],[571,3942],{"className":3943,"style":717},[695],[571,3945,2212],{"className":3946},[721],[571,3948],{"className":3949,"style":717},[695],[571,3951,3953,3957,4019,4022,4025],{"className":3952},[605],[571,3954],{"className":3955,"style":3956},[609],"height:1.04em;vertical-align:-0.0839em;",[571,3958,3961],{"className":3959},[614,3960],"sqrt",[571,3962,3964,4010],{"className":3963},[935,936],[571,3965,3967,4007],{"className":3966},[940],[571,3968,3971,3987],{"className":3969,"style":3970},[944],"height:0.9561em;",[571,3972,3976,3980],{"className":3973,"style":3975},[3974],"svg-align","top:-3em;",[571,3977],{"className":3978,"style":3979},[952],"height:3em;",[571,3981,3984],{"className":3982,"style":3983},[614],"padding-left:0.833em;",[571,3985,3826],{"className":3986},[614],[571,3988,3990,3993],{"style":3989},"top:-2.9161em;",[571,3991],{"className":3992,"style":3979},[952],[571,3994,3998],{"className":3995,"style":3997},[3996],"hide-tail","min-width:0.853em;height:1.08em;",[958,3999,4004],{"xmlns":960,"width":4000,"height":4001,"viewBox":4002,"preserveAspectRatio":4003},"400em","1.08em","0 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80h400000v40h-400000z",[571,4008,971],{"className":4009},[970],[571,4011,4013],{"className":4012},[940],[571,4014,4017],{"className":4015,"style":4016},[944],"height:0.0839em;",[571,4018],{},[571,4020],{"className":4021,"style":717},[695],[571,4023,3829],{"className":4024},[721],[571,4026],{"className":4027,"style":717},[695],[571,4029,4031,4035,4038,4046,4050,4053,4056,4059,4062],{"className":4030},[605],[571,4032],{"className":4033,"style":4034},[609],"height:0.8389em;vertical-align:-0.1944em;",[571,4036,3814],{"className":4037},[614],[571,4039,4041],{"className":4040},[614],[571,4042,4045],{"className":4043},[4044],"mpunct",",",[571,4047,4049],{"className":4048},[614],"0711",[571,4051],{"className":4052,"style":717},[695],[571,4054],{"className":4055,"style":717},[695],[571,4057,899],{"className":4058},[721],[571,4060],{"className":4061,"style":717},[695],[571,4063],{"className":4064,"style":717},[695],[571,4066,4068,4071],{"className":4067},[605],[571,4069],{"className":4070,"style":731},[609],[571,4072,3841],{"className":4073},[614],[558,4075,4077],{"id":4076},"typische-fehler","Typische Fehler",[854,4079,4080,4266,4560],{},[857,4081,4082,4083,4208,4209,616,4237,4265],{},"Immer Gleichheit annehmen: ",[571,4084,4086,4124],{"className":4085},[574],[571,4087,4089],{"className":4088},[578],[580,4090,4091],{"xmlns":582},[584,4092,4093,4121],{},[587,4094,4095,4097,4099,4101,4103,4105,4107,4109,4111,4113,4115,4117,4119],{},[590,4096,878],{"mathvariant":881},[590,4098,592],{},[664,4100,812],{},[590,4102,631],{},[590,4104,878],{"mathvariant":881},[664,4106,2212],{},[590,4108,878],{"mathvariant":881},[590,4110,592],{},[590,4112,878],{"mathvariant":881},[664,4114,812],{},[590,4116,878],{"mathvariant":881},[590,4118,631],{},[590,4120,878],{"mathvariant":881},[594,4122,4123],{"encoding":596},"|x + y| = |x| + |y|",[571,4125,4127,4148,4169,4193],{"className":4126,"ariaHidden":601},[600],[571,4128,4130,4133,4136,4139,4142,4145],{"className":4129},[605],[571,4131],{"className":4132,"style":1067},[609],[571,4134,878],{"className":4135},[614],[571,4137,592],{"className":4138},[614,615],[571,4140],{"className":4141,"style":696},[695],[571,4143,812],{"className":4144},[700],[571,4146],{"className":4147,"style":696},[695],[571,4149,4151,4154,4157,4160,4163,4166],{"className":4150},[605],[571,4152],{"className":4153,"style":1067},[609],[571,4155,631],{"className":4156,"style":647},[614,615],[571,4158,878],{"className":4159},[614],[571,4161],{"className":4162,"style":717},[695],[571,4164,2212],{"className":4165},[721],[571,4167],{"className":4168,"style":717},[695],[571,4170,4172,4175,4178,4181,4184,4187,4190],{"className":4171},[605],[571,4173],{"className":4174,"style":1067},[609],[571,4176,878],{"className":4177},[614],[571,4179,592],{"className":4180},[614,615],[571,4182,878],{"className":4183},[614],[571,4185],{"className":4186,"style":696},[695],[571,4188,812],{"className":4189},[700],[571,4191],{"className":4192,"style":696},[695],[571,4194,4196,4199,4202,4205],{"className":4195},[605],[571,4197],{"className":4198,"style":1067},[609],[571,4200,878],{"className":4201},[614],[571,4203,631],{"className":4204,"style":647},[614,615],[571,4206,878],{"className":4207},[614]," gilt nur, wenn ",[571,4210,4212,4225],{"className":4211},[574],[571,4213,4215],{"className":4214},[578],[580,4216,4217],{"xmlns":582},[584,4218,4219,4223],{},[587,4220,4221],{},[590,4222,592],{},[594,4224,592],{"encoding":596},[571,4226,4228],{"className":4227,"ariaHidden":601},[600],[571,4229,4231,4234],{"className":4230},[605],[571,4232],{"className":4233,"style":610},[609],[571,4235,592],{"className":4236},[614,615],[571,4238,4240,4253],{"className":4239},[574],[571,4241,4243],{"className":4242},[578],[580,4244,4245],{"xmlns":582},[584,4246,4247,4251],{},[587,4248,4249],{},[590,4250,631],{},[594,4252,631],{"encoding":596},[571,4254,4256],{"className":4255,"ariaHidden":601},[600],[571,4257,4259,4262],{"className":4258},[605],[571,4260],{"className":4261,"style":643},[609],[571,4263,631],{"className":4264,"style":647},[614,615]," nicht verschiedene Vorzeichen haben.",[857,4267,4268,4269,4394,4395,767,4446,4502,4503,4531,4532,1095],{},"Die umgekehrte Ungleichung falsch herum aufschreiben: ",[571,4270,4272,4310],{"className":4271},[574],[571,4273,4275],{"className":4274},[578],[580,4276,4277],{"xmlns":582},[584,4278,4279,4307],{},[587,4280,4281,4283,4285,4287,4289,4291,4293,4295,4297,4299,4301,4303,4305],{},[590,4282,878],{"mathvariant":881},[590,4284,592],{},[664,4286,888],{},[590,4288,631],{},[590,4290,878],{"mathvariant":881},[664,4292,899],{},[590,4294,878],{"mathvariant":881},[590,4296,592],{},[590,4298,878],{"mathvariant":881},[664,4300,888],{},[590,4302,878],{"mathvariant":881},[590,4304,631],{},[590,4306,878],{"mathvariant":881},[594,4308,4309],{"encoding":596},"|x - y| \\leq |x| - |y|",[571,4311,4313,4334,4355,4379],{"className":4312,"ariaHidden":601},[600],[571,4314,4316,4319,4322,4325,4328,4331],{"className":4315},[605],[571,4317],{"className":4318,"style":1067},[609],[571,4320,878],{"className":4321},[614],[571,4323,592],{"className":4324},[614,615],[571,4326],{"className":4327,"style":696},[695],[571,4329,888],{"className":4330},[700],[571,4332],{"className":4333,"style":696},[695],[571,4335,4337,4340,4343,4346,4349,4352],{"className":4336},[605],[571,4338],{"className":4339,"style":1067},[609],[571,4341,631],{"className":4342,"style":647},[614,615],[571,4344,878],{"className":4345},[614],[571,4347],{"className":4348,"style":717},[695],[571,4350,899],{"className":4351},[721],[571,4353],{"className":4354,"style":717},[695],[571,4356,4358,4361,4364,4367,4370,4373,4376],{"className":4357},[605],[571,4359],{"className":4360,"style":1067},[609],[571,4362,878],{"className":4363},[614],[571,4365,592],{"className":4366},[614,615],[571,4368,878],{"className":4369},[614],[571,4371],{"className":4372,"style":696},[695],[571,4374,888],{"className":4375},[700],[571,4377],{"className":4378,"style":696},[695],[571,4380,4382,4385,4388,4391],{"className":4381},[605],[571,4383],{"className":4384,"style":1067},[609],[571,4386,878],{"className":4387},[614],[571,4389,631],{"className":4390,"style":647},[614,615],[571,4392,878],{"className":4393},[614]," ist falsch, z.B. ist für ",[571,4396,4398,4416],{"className":4397},[574],[571,4399,4401],{"className":4400},[578],[580,4402,4403],{"xmlns":582},[584,4404,4405,4413],{},[587,4406,4407,4409,4411],{},[590,4408,592],{},[664,4410,2212],{},[673,4412,1150],{},[594,4414,4415],{"encoding":596},"x = 1",[571,4417,4419,4437],{"className":4418,"ariaHidden":601},[600],[571,4420,4422,4425,4428,4431,4434],{"className":4421},[605],[571,4423],{"className":4424,"style":610},[609],[571,4426,592],{"className":4427},[614,615],[571,4429],{"className":4430,"style":717},[695],[571,4432,2212],{"className":4433},[721],[571,4435],{"className":4436,"style":717},[695],[571,4438,4440,4443],{"className":4439},[605],[571,4441],{"className":4442,"style":731},[609],[571,4444,1150],{"className":4445},[614],[571,4447,4449,4469],{"className":4448},[574],[571,4450,4452],{"className":4451},[578],[580,4453,4454],{"xmlns":582},[584,4455,4456,4466],{},[587,4457,4458,4460,4462,4464],{},[590,4459,631],{},[664,4461,2212],{},[664,4463,888],{},[673,4465,1150],{},[594,4467,4468],{"encoding":596},"y = -1",[571,4470,4472,4490],{"className":4471,"ariaHidden":601},[600],[571,4473,4475,4478,4481,4484,4487],{"className":4474},[605],[571,4476],{"className":4477,"style":643},[609],[571,4479,631],{"className":4480,"style":647},[614,615],[571,4482],{"className":4483,"style":717},[695],[571,4485,2212],{"className":4486},[721],[571,4488],{"className":4489,"style":717},[695],[571,4491,4493,4496,4499],{"className":4492},[605],[571,4494],{"className":4495,"style":2666},[609],[571,4497,888],{"className":4498},[614],[571,4500,1150],{"className":4501},[614]," die linke Seite ",[571,4504,4506,4519],{"className":4505},[574],[571,4507,4509],{"className":4508},[578],[580,4510,4511],{"xmlns":582},[584,4512,4513,4517],{},[587,4514,4515],{},[673,4516,2709],{},[594,4518,2709],{"encoding":596},[571,4520,4522],{"className":4521,"ariaHidden":601},[600],[571,4523,4525,4528],{"className":4524},[605],[571,4526],{"className":4527,"style":731},[609],[571,4529,2709],{"className":4530},[614],", die rechte ",[571,4533,4535,4548],{"className":4534},[574],[571,4536,4538],{"className":4537},[578],[580,4539,4540],{"xmlns":582},[584,4541,4542,4546],{},[587,4543,4544],{},[673,4545,675],{},[594,4547,675],{"encoding":596},[571,4549,4551],{"className":4550,"ariaHidden":601},[600],[571,4552,4554,4557],{"className":4553},[605],[571,4555],{"className":4556,"style":731},[609],[571,4558,675],{"className":4559},[614],[857,4561,4562,4563,4566,4567,4692,4693,1095],{},"Die Ungleichung zum Abschätzen ",[567,4564,4565],{},"nach unten"," verwenden: ",[571,4568,4570,4608],{"className":4569},[574],[571,4571,4573],{"className":4572},[578],[580,4574,4575],{"xmlns":582},[584,4576,4577,4605],{},[587,4578,4579,4581,4583,4585,4587,4589,4591,4593,4595,4597,4599,4601,4603],{},[590,4580,878],{"mathvariant":881},[590,4582,592],{},[664,4584,812],{},[590,4586,631],{},[590,4588,878],{"mathvariant":881},[664,4590,671],{},[590,4592,878],{"mathvariant":881},[590,4594,592],{},[590,4596,878],{"mathvariant":881},[664,4598,812],{},[590,4600,878],{"mathvariant":881},[590,4602,631],{},[590,4604,878],{"mathvariant":881},[594,4606,4607],{"encoding":596},"|x + y| \\geq |x| + |y|",[571,4609,4611,4632,4653,4677],{"className":4610,"ariaHidden":601},[600],[571,4612,4614,4617,4620,4623,4626,4629],{"className":4613},[605],[571,4615],{"className":4616,"style":1067},[609],[571,4618,878],{"className":4619},[614],[571,4621,592],{"className":4622},[614,615],[571,4624],{"className":4625,"style":696},[695],[571,4627,812],{"className":4628},[700],[571,4630],{"className":4631,"style":696},[695],[571,4633,4635,4638,4641,4644,4647,4650],{"className":4634},[605],[571,4636],{"className":4637,"style":1067},[609],[571,4639,631],{"className":4640,"style":647},[614,615],[571,4642,878],{"className":4643},[614],[571,4645],{"className":4646,"style":717},[695],[571,4648,671],{"className":4649},[721],[571,4651],{"className":4652,"style":717},[695],[571,4654,4656,4659,4662,4665,4668,4671,4674],{"className":4655},[605],[571,4657],{"className":4658,"style":1067},[609],[571,4660,878],{"className":4661},[614],[571,4663,592],{"className":4664},[614,615],[571,4666,878],{"className":4667},[614],[571,4669],{"className":4670,"style":696},[695],[571,4672,812],{"className":4673},[700],[571,4675],{"className":4676,"style":696},[695],[571,4678,4680,4683,4686,4689],{"className":4679},[605],[571,4681],{"className":4682,"style":1067},[609],[571,4684,878],{"className":4685},[614],[571,4687,631],{"className":4688,"style":647},[614,615],[571,4690,878],{"className":4691},[614]," ist falsch. Nach unten schätzt man mit der umgekehrten Form ab: ",[571,4694,4696,4734],{"className":4695},[574],[571,4697,4699],{"className":4698},[578],[580,4700,4701],{"xmlns":582},[584,4702,4703,4731],{},[587,4704,4705,4707,4709,4711,4713,4715,4717,4719,4721,4723,4725,4727,4729],{},[590,4706,878],{"mathvariant":881},[590,4708,592],{},[664,4710,812],{},[590,4712,631],{},[590,4714,878],{"mathvariant":881},[664,4716,671],{},[590,4718,878],{"mathvariant":881},[590,4720,592],{},[590,4722,878],{"mathvariant":881},[664,4724,888],{},[590,4726,878],{"mathvariant":881},[590,4728,631],{},[590,4730,878],{"mathvariant":881},[594,4732,4733],{"encoding":596},"|x + y| \\geq |x| - |y|",[571,4735,4737,4758,4779,4803],{"className":4736,"ariaHidden":601},[600],[571,4738,4740,4743,4746,4749,4752,4755],{"className":4739},[605],[571,4741],{"className":4742,"style":1067},[609],[571,4744,878],{"className":4745},[614],[571,4747,592],{"className":4748},[614,615],[571,4750],{"className":4751,"style":696},[695],[571,4753,812],{"className":4754},[700],[571,4756],{"className":4757,"style":696},[695],[571,4759,4761,4764,4767,4770,4773,4776],{"className":4760},[605],[571,4762],{"className":4763,"style":1067},[609],[571,4765,631],{"className":4766,"style":647},[614,615],[571,4768,878],{"className":4769},[614],[571,4771],{"className":4772,"style":717},[695],[571,4774,671],{"className":4775},[721],[571,4777],{"className":4778,"style":717},[695],[571,4780,4782,4785,4788,4791,4794,4797,4800],{"className":4781},[605],[571,4783],{"className":4784,"style":1067},[609],[571,4786,878],{"className":4787},[614],[571,4789,592],{"className":4790},[614,615],[571,4792,878],{"className":4793},[614],[571,4795],{"className":4796,"style":696},[695],[571,4798,888],{"className":4799},[700],[571,4801],{"className":4802,"style":696},[695],[571,4804,4806,4809,4812,4815],{"className":4805},[605],[571,4807],{"className":4808,"style":1067},[609],[571,4810,878],{"className":4811},[614],[571,4813,631],{"className":4814,"style":647},[614,615],[571,4816,878],{"className":4817},[614],{"title":4819,"searchDepth":4820,"depth":4820,"links":4821},"",2,[4822,4823,4824,4825],{"id":560,"depth":4820,"text":561},{"id":1654,"depth":4820,"text":1655},{"id":2558,"depth":4820,"text":2559},{"id":4076,"depth":4820,"text":4077},[4827,4829,4831,4834,4838,4841,4843,4845,4847,4849,4852,4855],{"lhs":4828,"rhs":2709},"abs(3 + (-5))",{"lhs":4830,"rhs":2738},"abs(3) + abs(-5)",{"lhs":4832,"rhs":4833},"abs(x + y)","abs(x) + abs(y)",{"lhs":4832,"rhs":4833,"where":4835},{"x":4836,"y":4837},-1.5,-2.5,{"lhs":4839,"rhs":4840},"abs(2 + 4)","abs(2) + abs(4)",{"lhs":4842,"rhs":2709},"abs(abs(3) - abs(-5))",{"lhs":4844,"rhs":2738},"abs(3 - (-5))",{"lhs":4846,"rhs":2635},"abs(3 + 4*i)",{"lhs":4848,"rhs":2635},"abs(-4 + 3*i)",{"lhs":4850,"rhs":4851},"abs((3 + 4*i) + (-4 + 3*i))","sqrt(50)",{"lhs":4853,"rhs":4854},"round(sqrt(50), 4)","7.0711",{"lhs":4856,"rhs":2709},"abs(1 - (-1))","x, y \\in \\mathbb{R} \\text{ oder } x, y \\in \\mathbb{C}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x, y \\in \\mathbb{R}\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 mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord 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