Knowledge

Constant function

Source πŸ“

1455:
in the category of sets, where 1 is the one-point set. Because of this, and the adjunction between Cartesian products and hom in the category of sets (so there is a canonical isomorphism between functions of two variables and functions of one variable valued in functions of another (single) variable,
1540: 919: 1604: 729:
of a function is a measure of the rate of change of function values with respect to change in input values. Because a constant function does not change, its derivative is 0. This is often written:
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does not appear on the right side of the function expression and so its value is "vacuously substituted"; namely
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Carter, John A.; Cuevas, Gilbert J.; Holliday, Berchie; Marks, Daniel; McClure, Melissa S. (2005). "1".
1535:{\displaystyle \operatorname {hom} (X\times Y,Z)\cong \operatorname {hom} (X(\operatorname {hom} (Y,Z))} 2083: 1152: 991: 799: 246: 1934: 2036: 732: 334: 2228: 1543: 2167: 1030: 561: 429: 196: 121: 76: 1254: 2197: 2192: 2187: 2065: 1606: 1303: 719: 458: 29: 1889: 1222: 503:
As a real-valued function of a real-valued argument, a constant function has the general form
2177: 2157: 1910: 392: 1196: 1067: 2243: 2162: 2029: 1706: 1674: 1644: 1617: 1390: 973: 949: 549: 377: 339: 151: 62: 8: 2056: 1776: 557: 311: 301: 296: 2233: 2100: 2095: 2021: 1956: 1758: 1738: 1370: 1340: 1042: 676: 422: 306: 281: 1993: 1838: 1045:'s axiomatization of set theory, the Elementary Theory of the Category of Sets (ETCS). 1990: 1914: 1865: 1817: 1547: 1019: 382: 286: 276: 261: 20: 1550:
of sets as tensor product and the one-point set as tensor unit. In the isomorphisms
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Advanced Mathematical Concepts - Pre-calculus with Applications, Student Edition
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Leinster, Tom (27 Jun 2011). "An informal introduction to topos theory".
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is a constant function. For example, given the constant function
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because it is a polynomial of degree 0, and its general form is
1905:
Varberg, Dale E.; Purcell, Edwin J.; Rigdon, Steven E. (2007).
1599:{\displaystyle \lambda :1\times X\cong X\cong X\times 1:\rho } 709:
axis in the plane. Its graph is symmetric with respect to the
1864:(1 ed.). Glencoe/McGraw-Hill School Pub Co. p. 22. 1008: 666:
is nonzero. This function has no intersection point with the
541:
is the specific constant function where the output value is
183: 914:{\displaystyle y'(x)=\left(x\mapsto -{\sqrt {2}}\right)'=0} 1988: 1859: 948:
is both order-preserving and order-reversing, and if the
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whose (output) value is the same for every input value.
1761: 1741: 1709: 1677: 1647: 1620: 1556: 1462: 1423: 1393: 1373: 1343: 1306: 1257: 1225: 1199: 1155: 1114: 1070: 853: 802: 735: 1904: 1894:(3rd ed.). John Wiley & Sons. p. 122. 112: 1767: 1747: 1727: 1695: 1660: 1633: 1598: 1534: 1447: 1406: 1379: 1349: 1329: 1292: 1243: 1211: 1185: 1141: 1082: 913: 830: 764: 694:. It is the (trivial) constant function and every 1614:, the left and right unitors are the projections 108: 2266: 228: 2074:Zero polynomial (degree undefined or βˆ’1 or βˆ’βˆž) 1387:is canonically isomorphic to the function set 718:axis, and therefore a constant function is an 2037: 430: 84: 1935:"Zero Derivative implies Constant Function" 2044: 2030: 437: 423: 93: 1974:Herrlich, Horst and Strecker, George E., 1960: 1448:{\displaystyle \operatorname {hom} (1,X)} 1954: 1029:A constant function factors through the 772:. The converse is also true. Namely, if 725:In the context where it is defined, the 468: 1836: 1816:. Facts on File, New York. p. 94. 1360:As a corollary, the one-point set is a 1041:. This observation is instrumental for 213: 204: 2267: 1809: 1357:is by definition a constant function. 2025: 1989: 1884: 595:, and so on. No matter what value of 473:An example of a constant function is 232: 217: 198: 187: 172: 153: 142: 123: 97: 78: 1064:to the set of constant functions in 679:. On the other hand, the polynomial 168: 159: 1142:{\displaystyle {\tilde {y}}:X\to Y} 925: 608:The graph of the constant function 495:is 4 regardless of the input value 464: 13: 644:, the constant function is called 14: 2296: 1982: 1186:{\displaystyle {\tilde {y}}(x)=y} 846:is the identically zero function 831:{\displaystyle y(x)=-{\sqrt {2}}} 1018:Every constant function between 1000:, which implies that it is also 138: 129: 1841:. Lamar University. p. 224 1793:if and only if it is constant. 765:{\displaystyle (x\mapsto c)'=0} 55:History of the function concept 1948: 1927: 1898: 1878: 1853: 1830: 1803: 1722: 1710: 1690: 1678: 1529: 1526: 1514: 1505: 1499: 1487: 1469: 1442: 1430: 1287: 1276: 1267: 1261: 1235: 1174: 1168: 1162: 1133: 1121: 1074: 972:Every constant function whose 934:, constant functions are both 883: 868: 862: 812: 806: 749: 742: 736: 626:that passes through the point 1: 2234:Horner's method of evaluation 1796: 1108:, there is a unique function 16:Type of mathematical function 2280:Elementary special functions 1978:, Heldermann Verlag (2007). 1735:respectively to the element 1542:) the category of sets is a 1219:. Conversely, if a function 700:is a root. Its graph is the 7: 2239:Polynomial identity testing 1813:Encyclopedia of Mathematics 568:. The independent variable 10: 2301: 1293:{\displaystyle f(x)=f(x')} 992:full transformation monoid 646:non-zero constant function 530:For example, the function 413:List of specific functions 18: 2211: 2150: 2063: 1330:{\displaystyle x,x'\in X} 692:identically zero function 1544:closed monoidal category 1364:in the category of sets. 1244:{\displaystyle f:X\to Y} 675:axis, meaning it has no 601:is input, the output is 560:of this function is the 19:Not to be confused with 2224:Greatest common divisor 550:domain of this function 484:, because the value of 2275:Elementary mathematics 2096:Quadratic function (2) 1837:Dawkins, Paul (2007). 1810:Tanton, James (2005). 1769: 1749: 1729: 1697: 1662: 1635: 1600: 1536: 1449: 1408: 1381: 1351: 1331: 1294: 1245: 1213: 1212:{\displaystyle x\in X} 1187: 1143: 1084: 1083:{\displaystyle X\to Y} 930:For functions between 915: 832: 766: 634:. In the context of a 500: 2079:Constant function (0) 1911:Pearson Prentice Hall 1779:in the one-point set. 1770: 1750: 1730: 1728:{\displaystyle (x,*)} 1698: 1696:{\displaystyle (*,x)} 1663: 1661:{\displaystyle p_{2}} 1636: 1634:{\displaystyle p_{1}} 1601: 1537: 1450: 1409: 1407:{\displaystyle X^{1}} 1382: 1352: 1332: 1295: 1246: 1214: 1188: 1144: 1085: 916: 833: 783:for all real numbers 767: 472: 2285:Polynomial functions 2212:Tools and algorithms 2132:Quintic function (5) 2120:Quartic function (4) 2057:polynomial functions 1759: 1739: 1707: 1675: 1645: 1618: 1554: 1460: 1421: 1391: 1371: 1341: 1304: 1255: 1223: 1197: 1153: 1112: 1068: 851: 800: 733: 2142:Septic equation (7) 2137:Sextic equation (6) 2084:Linear function (1) 2009:"Constant function" 1994:"Constant Function" 2108:Cubic function (3) 2101:Quadratic equation 1991:Weisstein, Eric W. 1765: 1745: 1725: 1693: 1658: 1631: 1596: 1532: 1445: 1404: 1377: 1347: 1327: 1290: 1241: 1209: 1183: 1139: 1080: 1048:For any non-empty 1043:F. William Lawvere 1020:topological spaces 968:must be constant. 911: 840:The derivative of 828: 762: 552:is the set of all 501: 247:Classes/properties 2262: 2261: 2203:Quasi-homogeneous 1886:Young, Cynthia Y. 1839:"College Algebra" 1768:{\displaystyle *} 1748:{\displaystyle x} 1548:Cartesian product 1380:{\displaystyle X} 1350:{\displaystyle f} 1165: 1124: 1096:and each element 980:are the same set 942:; conversely, if 894: 826: 455:constant function 447: 446: 359:Generalizations 21:function constant 2292: 2125:Quartic equation 2046: 2039: 2032: 2023: 2022: 2018: 2004: 2003: 1967: 1966: 1964: 1952: 1946: 1945: 1943: 1941: 1931: 1925: 1924: 1909:(9th ed.). 1902: 1896: 1895: 1882: 1876: 1875: 1857: 1851: 1850: 1848: 1846: 1834: 1828: 1827: 1807: 1791:locally constant 1785:A function on a 1774: 1772: 1771: 1766: 1754: 1752: 1751: 1746: 1734: 1732: 1731: 1726: 1702: 1700: 1699: 1694: 1667: 1665: 1664: 1659: 1657: 1656: 1640: 1638: 1637: 1632: 1630: 1629: 1612: 1605: 1603: 1602: 1597: 1541: 1539: 1538: 1533: 1454: 1452: 1451: 1446: 1413: 1411: 1410: 1405: 1403: 1402: 1386: 1384: 1383: 1378: 1356: 1354: 1353: 1348: 1336: 1334: 1333: 1328: 1320: 1299: 1297: 1296: 1291: 1286: 1250: 1248: 1247: 1242: 1218: 1216: 1215: 1210: 1192: 1190: 1189: 1184: 1167: 1166: 1158: 1148: 1146: 1145: 1140: 1126: 1125: 1117: 1107: 1101: 1095: 1089: 1087: 1086: 1081: 1059: 1053: 1039:category of sets 999: 985: 967: 957: 947: 936:order-preserving 926:Other properties 922: 920: 918: 917: 912: 904: 900: 896: 895: 890: 861: 845: 839: 837: 835: 834: 829: 827: 822: 794: 788: 782: 771: 769: 768: 763: 755: 717: 715: 708: 706: 699: 689: 674: 672: 665: 661: 643: 638:in one variable 633: 617: 604: 600: 594: 587: 580: 573: 567: 547: 540: 529: 527: 516: 498: 494: 483: 465:Basic properties 439: 432: 425: 237: 236: 230: 222: 221: 215: 207: 206: 202: 192: 191: 185: 177: 176: 170: 162: 161: 157: 147: 146: 140: 132: 131: 127: 117: 116: 110: 102: 101: 95: 87: 86: 82: 49: 26: 25: 2300: 2299: 2295: 2294: 2293: 2291: 2290: 2289: 2265: 2264: 2263: 2258: 2207: 2146: 2089:Linear equation 2059: 2050: 2007: 1985: 1976:Category Theory 1971: 1970: 1953: 1949: 1939: 1937: 1933: 1932: 1928: 1921: 1913:. p. 107. 1903: 1899: 1883: 1879: 1872: 1858: 1854: 1844: 1842: 1835: 1831: 1824: 1808: 1804: 1799: 1760: 1757: 1756: 1740: 1737: 1736: 1708: 1705: 1704: 1676: 1673: 1672: 1652: 1648: 1646: 1643: 1642: 1625: 1621: 1619: 1616: 1615: 1608: 1555: 1552: 1551: 1461: 1458: 1457: 1422: 1419: 1418: 1398: 1394: 1392: 1389: 1388: 1372: 1369: 1368: 1342: 1339: 1338: 1313: 1305: 1302: 1301: 1279: 1256: 1253: 1252: 1224: 1221: 1220: 1198: 1195: 1194: 1157: 1156: 1154: 1151: 1150: 1116: 1115: 1113: 1110: 1109: 1103: 1097: 1091: 1069: 1066: 1065: 1055: 1049: 1035:terminal object 995: 981: 963: 953: 943: 940:order-reversing 932:preordered sets 928: 889: 879: 875: 874: 854: 852: 849: 848: 847: 841: 821: 801: 798: 797: 796: 790: 784: 773: 748: 734: 731: 730: 711: 710: 702: 701: 695: 680: 668: 667: 663: 649: 639: 627: 620:horizontal line 609: 602: 596: 589: 582: 575: 569: 565: 542: 531: 519: 518: 504: 496: 485: 474: 467: 443: 407: 368:Binary relation 354: 321: 241: 235: 227: 220: 212: 201: 197: 190: 182: 175: 167: 156: 152: 145: 137: 126: 122: 115: 107: 100: 92: 81: 77: 36: 24: 17: 12: 11: 5: 2298: 2288: 2287: 2282: 2277: 2260: 2259: 2257: 2256: 2251: 2246: 2241: 2236: 2231: 2226: 2221: 2215: 2213: 2209: 2208: 2206: 2205: 2200: 2195: 2190: 2185: 2180: 2175: 2170: 2165: 2160: 2154: 2152: 2148: 2147: 2145: 2144: 2139: 2134: 2129: 2128: 2127: 2117: 2116: 2115: 2113:Cubic equation 2105: 2104: 2103: 2093: 2092: 2091: 2081: 2076: 2070: 2068: 2061: 2060: 2049: 2048: 2041: 2034: 2026: 2020: 2019: 2005: 1984: 1983:External links 1981: 1980: 1979: 1969: 1968: 1947: 1926: 1920:978-0131469686 1919: 1897: 1877: 1871:978-0078682278 1870: 1852: 1829: 1822: 1801: 1800: 1798: 1795: 1783: 1782: 1781: 1780: 1775:is the unique 1764: 1744: 1724: 1721: 1718: 1715: 1712: 1692: 1689: 1686: 1683: 1680: 1655: 1651: 1628: 1624: 1595: 1592: 1589: 1586: 1583: 1580: 1577: 1574: 1571: 1568: 1565: 1562: 1559: 1531: 1528: 1525: 1522: 1519: 1516: 1513: 1510: 1507: 1504: 1501: 1498: 1495: 1492: 1489: 1486: 1483: 1480: 1477: 1474: 1471: 1468: 1465: 1444: 1441: 1438: 1435: 1432: 1429: 1426: 1401: 1397: 1376: 1365: 1346: 1326: 1323: 1319: 1316: 1312: 1309: 1289: 1285: 1282: 1278: 1275: 1272: 1269: 1266: 1263: 1260: 1240: 1237: 1234: 1231: 1228: 1208: 1205: 1202: 1182: 1179: 1176: 1173: 1170: 1164: 1161: 1138: 1135: 1132: 1129: 1123: 1120: 1079: 1076: 1073: 1046: 1027: 1016: 1005: 927: 924: 910: 907: 903: 899: 893: 888: 885: 882: 878: 873: 870: 867: 864: 860: 857: 825: 820: 817: 814: 811: 808: 805: 761: 758: 754: 751: 747: 744: 741: 738: 466: 463: 445: 444: 442: 441: 434: 427: 419: 416: 415: 409: 408: 406: 405: 400: 395: 390: 385: 380: 375: 370: 364: 361: 360: 356: 355: 353: 352: 347: 342: 337: 331: 328: 327: 323: 322: 320: 319: 314: 309: 304: 299: 294: 289: 284: 279: 274: 269: 264: 259: 253: 250: 249: 243: 242: 240: 239: 233: 224: 218: 209: 199: 194: 188: 179: 173: 164: 154: 149: 143: 134: 124: 119: 113: 104: 98: 89: 79: 73: 70: 69: 58: 57: 51: 50: 33: 32: 15: 9: 6: 4: 3: 2: 2297: 2286: 2283: 2281: 2278: 2276: 2273: 2272: 2270: 2255: 2254:GrΓΆbner basis 2252: 2250: 2247: 2245: 2242: 2240: 2237: 2235: 2232: 2230: 2227: 2225: 2222: 2220: 2219:Factorization 2217: 2216: 2214: 2210: 2204: 2201: 2199: 2196: 2194: 2191: 2189: 2186: 2184: 2181: 2179: 2176: 2174: 2171: 2169: 2166: 2164: 2161: 2159: 2156: 2155: 2153: 2151:By properties 2149: 2143: 2140: 2138: 2135: 2133: 2130: 2126: 2123: 2122: 2121: 2118: 2114: 2111: 2110: 2109: 2106: 2102: 2099: 2098: 2097: 2094: 2090: 2087: 2086: 2085: 2082: 2080: 2077: 2075: 2072: 2071: 2069: 2067: 2062: 2058: 2054: 2047: 2042: 2040: 2035: 2033: 2028: 2027: 2024: 2016: 2015: 2010: 2006: 2001: 2000: 1995: 1992: 1987: 1986: 1977: 1973: 1972: 1963: 1958: 1951: 1936: 1930: 1922: 1916: 1912: 1908: 1901: 1893: 1892: 1887: 1881: 1873: 1867: 1863: 1856: 1840: 1833: 1825: 1823:0-8160-5124-0 1819: 1815: 1814: 1806: 1802: 1794: 1792: 1788: 1787:connected set 1778: 1762: 1742: 1719: 1716: 1713: 1687: 1684: 1681: 1671: 1670:ordered pairs 1653: 1649: 1626: 1622: 1613: 1611: 1593: 1590: 1587: 1584: 1581: 1578: 1575: 1572: 1569: 1566: 1563: 1560: 1557: 1549: 1545: 1523: 1520: 1517: 1511: 1508: 1502: 1496: 1493: 1490: 1484: 1481: 1478: 1475: 1472: 1466: 1463: 1439: 1436: 1433: 1427: 1424: 1417: 1399: 1395: 1374: 1366: 1363: 1359: 1358: 1344: 1324: 1321: 1317: 1314: 1310: 1307: 1283: 1280: 1273: 1270: 1264: 1258: 1238: 1232: 1229: 1226: 1206: 1203: 1200: 1180: 1177: 1171: 1159: 1136: 1130: 1127: 1118: 1106: 1100: 1094: 1077: 1071: 1063: 1058: 1052: 1047: 1044: 1040: 1036: 1032: 1031:one-point set 1028: 1025: 1021: 1017: 1014: 1010: 1006: 1003: 998: 993: 989: 984: 979: 975: 971: 970: 969: 966: 961: 956: 951: 946: 941: 937: 933: 923: 908: 905: 901: 897: 891: 886: 880: 876: 871: 865: 858: 855: 844: 823: 818: 815: 809: 803: 793: 787: 780: 776: 759: 756: 752: 745: 739: 728: 723: 721: 720:even function 714: 705: 698: 693: 687: 683: 678: 671: 660: 656: 652: 647: 642: 637: 631: 625: 621: 616: 612: 606: 599: 592: 585: 578: 572: 563: 559: 555: 551: 545: 538: 534: 526: 522: 515: 511: 507: 492: 488: 481: 477: 471: 462: 460: 456: 452: 440: 435: 433: 428: 426: 421: 420: 418: 417: 414: 411: 410: 404: 401: 399: 396: 394: 391: 389: 386: 384: 381: 379: 376: 374: 371: 369: 366: 365: 363: 362: 358: 357: 351: 348: 346: 343: 341: 338: 336: 333: 332: 330: 329: 326:Constructions 325: 324: 318: 315: 313: 310: 308: 305: 303: 300: 298: 295: 293: 290: 288: 285: 283: 280: 278: 275: 273: 270: 268: 265: 263: 260: 258: 255: 254: 252: 251: 248: 245: 244: 238: 225: 223: 210: 208: 195: 193: 180: 178: 165: 163: 150: 148: 135: 133: 120: 118: 105: 103: 90: 88: 75: 74: 72: 71: 68: 64: 60: 59: 56: 53: 52: 47: 43: 39: 35: 34: 31: 28: 27: 22: 2249:Discriminant 2168:Multivariate 2078: 2012: 1997: 1975: 1950: 1938:. Retrieved 1929: 1906: 1900: 1890: 1880: 1861: 1855: 1843:. Retrieved 1832: 1812: 1805: 1784: 1609: 1104: 1098: 1092: 1056: 1054:, every set 1050: 1007:It has zero 996: 982: 964: 954: 944: 929: 842: 791: 785: 778: 774: 724: 712: 703: 696: 691: 685: 681: 669: 658: 654: 650: 645: 640: 629: 619: 614: 610: 607: 597: 590: 583: 576: 570: 554:real numbers 543: 536: 532: 524: 520: 513: 509: 505: 502: 490: 486: 479: 475: 454: 448: 393:Higher-order 256: 45: 41: 37: 2198:Homogeneous 2193:Square-free 2188:Irreducible 2053:Polynomials 1940:January 12, 1891:Precalculus 1845:January 12, 1607:natural in 677:root (zero) 451:mathematics 378:Multivalued 340:Composition 335:Restriction 2269:Categories 2158:Univariate 2014:PlanetMath 1797:References 1367:Every set 1251:satisfies 1149:such that 1090:. For any 1062:isomorphic 1024:continuous 1002:idempotent 727:derivative 636:polynomial 586:(βˆ’2.7) = 4 312:Surjective 302:Measurable 297:Continuous 272:Polynomial 2244:Resultant 2183:Trinomial 2163:Bivariate 1999:MathWorld 1962:1012.5647 1763:∗ 1720:∗ 1682:∗ 1594:ρ 1585:× 1579:≅ 1573:≅ 1567:× 1558:λ 1546:with the 1512:⁡ 1497:⁡ 1491:≅ 1476:× 1467:⁡ 1428:⁡ 1362:generator 1322:∈ 1236:→ 1204:∈ 1163:~ 1134:→ 1122:~ 1075:→ 988:left zero 887:− 884:↦ 819:− 743:↦ 562:singleton 317:Bijective 307:Injective 282:Algebraic 61:Types by 2229:Division 2178:Binomial 2173:Monomial 1907:Calculus 1888:(2021). 1755:, where 1318:′ 1300:for all 1284:′ 1193:for all 1013:gradient 978:codomain 902:′ 859:′ 753:′ 662:, where 517:or just 459:function 398:Morphism 383:Implicit 287:Analytic 277:Rational 262:Identity 257:Constant 67:codomain 44: ( 30:Function 1416:hom set 1037:in the 990:of the 962:, then 960:lattice 789:, then 690:is the 622:in the 593:(Ο€) = 4 579:(0) = 4 403:Functor 373:Partial 350:Inverse 2066:degree 1917:  1868:  1820:  1033:, the 974:domain 950:domain 556:. The 548:. The 292:Smooth 267:Linear 63:domain 1957:arXiv 1777:point 1414:, or 1009:slope 986:is a 958:is a 781:) = 0 688:) = 0 624:plane 618:is a 558:image 539:) = 4 482:) = 4 457:is a 388:Space 2055:and 1942:2014 1915:ISBN 1866:ISBN 1847:2014 1818:ISBN 1703:and 1668:the 1641:and 976:and 938:and 657:) = 628:(0, 564:set 512:) = 453:, a 65:and 2064:By 1789:is 1509:hom 1494:hom 1464:hom 1425:hom 1102:in 1060:is 1022:is 1011:or 994:on 952:of 566:{4} 546:= 4 449:In 2271:: 2011:. 1996:. 1337:, 777:β€²( 722:. 613:= 605:. 588:, 581:, 523:= 231:β†’ 216:β†’ 203:β†’ 186:β†’ 171:β†’ 158:β†’ 141:β†’ 128:β†’ 111:β†’ 109:𝔹 96:β†’ 94:𝔹 85:𝔹 83:β†’ 40:↦ 2045:e 2038:t 2031:v 2017:. 2002:. 1965:. 1959:: 1944:. 1923:. 1874:. 1849:. 1826:. 1743:x 1723:) 1717:, 1714:x 1711:( 1691:) 1688:x 1685:, 1679:( 1654:2 1650:p 1627:1 1623:p 1610:X 1591:: 1588:1 1582:X 1576:X 1570:X 1564:1 1561:: 1530:) 1527:) 1524:Z 1521:, 1518:Y 1515:( 1506:( 1503:X 1500:( 1488:) 1485:Z 1482:, 1479:Y 1473:X 1470:( 1443:) 1440:X 1437:, 1434:1 1431:( 1400:1 1396:X 1375:X 1345:f 1325:X 1315:x 1311:, 1308:x 1288:) 1281:x 1277:( 1274:f 1271:= 1268:) 1265:x 1262:( 1259:f 1239:Y 1233:X 1230:: 1227:f 1207:X 1201:x 1181:y 1178:= 1175:) 1172:x 1169:( 1160:y 1137:Y 1131:X 1128:: 1119:y 1105:Y 1099:y 1093:X 1078:Y 1072:X 1057:Y 1051:X 1026:. 1015:. 1004:. 997:X 983:X 965:f 955:f 945:f 921:. 909:0 906:= 898:) 892:2 881:x 877:( 872:= 869:) 866:x 863:( 856:y 843:y 838:. 824:2 816:= 813:) 810:x 807:( 804:y 792:y 786:x 779:x 775:y 760:0 757:= 750:) 746:c 740:x 737:( 716:- 713:y 707:- 704:x 697:x 686:x 684:( 682:f 673:- 670:x 664:c 659:c 655:x 653:( 651:f 641:x 632:) 630:c 615:c 611:y 603:4 598:x 591:y 584:y 577:y 571:x 544:c 537:x 535:( 533:y 528:. 525:c 521:y 514:c 510:x 508:( 506:y 499:. 497:x 493:) 491:x 489:( 487:y 480:x 478:( 476:y 438:e 431:t 424:v 345:Ξ» 234:X 229:β„‚ 219:X 214:β„‚ 205:β„‚ 200:X 189:X 184:ℝ 174:X 169:ℝ 160:ℝ 155:X 144:X 139:β„€ 130:β„€ 125:X 114:X 99:X 80:X 48:) 46:x 42:f 38:x 23:.

Index

function constant
Function
History of the function concept
domain
codomain
X β†’ 𝔹
𝔹 β†’ X
𝔹 β†’ X
X β†’ β„€
β„€ β†’ X
X β†’ ℝ
ℝ β†’ X
ℝ β†’ X
X β†’ β„‚
β„‚ β†’ X
β„‚ β†’ X
Classes/properties
Constant
Identity
Linear
Polynomial
Rational
Algebraic
Analytic
Smooth
Continuous
Measurable
Injective
Surjective
Bijective

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