000006 Concept of Numbers
Numbers can be classified based on different Criteria:
01. Natural and Non-Natural Numbers:
01.01. Natural Numbers.
Natural Numbers are positive integers not including zero.
01.02. Non-Natural Numbers.
Non-Natural Numbers are numbers that do not fall under the definition of Natural Numbers.
02. Whole Numbers and Non-Whole: Numbers.
02.01. Whole Numbers.
Whole Numbers include Natural Numbers and the zero. In other words Whole Numbers include zero and positive integers.
02.02. Non-Whole Numbers.
Non-Whole Numbers are numbers that do not fall under the definition of Whole Numbers.
03. Integer Numbers and Float Numbers (Fractional Numbers):
03.01. Integer Numbers.
Integer Numbers include zero and positive integers and negative integers.
03.02. Float Numbers.
Float Numbers are numbers that do not fall under the definition of Integer Numbers.
04. Rational Numbers and Irrational Numbers.
04.01. Rational Numbers.
Rational Numbers are numbers that can be represented in the form of a ratio of two integers.
04.02. Irrational Numbers.
Irrational Numbers are numbers that cannot be represented in the form of a ratio of two integers.
Examples of irrational numbers are: the square root of 2 and PI.
05. Positive Numbers and Negative Numbers:
05.01. Positive Numbers.
05.02. Negative Numbers.
06. Even Numbers and Odd Numbers:
06.01. Even Numbers.
06.02. Odd Numbers.
07. Terminating Numbers and Non-Terminating Numbers:
07.01. Terminating Numbers.
07.02. Non-Terminating Numbers.
One type of Non-Terminating Numbers are Non-Terminating Decimals (Repeating Decimals / Recurring Decimals).
Examples of Non-Terminating Decimals in Numerator & Denominator Ascending Order:
0001 1 / 3
0002 1 / 6
0003 1 / 7
0004 1 / 9
0005 1 / 11
0006 1 / 12
0007 1 / 13
0008 1 / 14
0009 1 / 15
0010 1 / 17
0011 1 / 18
0012 1 / 19
0013 1 / 21
0014 1 / 22
0015 1 / 23
0016 1 / 24
0017 1 / 26
0018 1 / 27
0019 1 / 28
0020 1 / 29
0021 1 / 30
0022 1 / 31
0023 1 / 33
0024 1 / 34
0025 1 / 35
0026 1 / 36
0027 1 / 37
0028 1 / 38
0029 1 / 39
0030 1 / 41
0031 1 / 42
0032 1 / 43
0033 1 / 44
0034 1 / 45
0035 1 / 46
0036 1 / 47
0036 1 / 47
0037 1 / 59
0038 1 / 61
0038 1 / 67
0039 1 / 81
0040 1 / 97
0041 2 / 3
08. Composite Numbers and Prime Numbers:
08.01. Composite Numbers.
Composite Numbers are numbers that can be factored into numbers other than 1 and the number itself. In other words, a composite number is a number that when divided by one or more natural number other than 1 and itself, would result in a natural number.
08.02. Prime Numbers.
Prime Numbers are Integer Numbers that are:
A. Equal to or larger than 2.
B. Only divisible by 1 and the number itself.
In other words, a prime number is a number that when divided by any natural number other than 1 and itself, would NOT result in a natural number.
The first 1,000 Prime Numbers are (in ascending order):
For more and extensive discussion of Prime Numbers, see 000007 Prime Numbers.
00001: 2
00002: 3
00003: 5
00004: 7
00005: 11
00006: 13
00007: 17
00008: 19
00009: 23
00010: 29
00011: 31
00012: 37
00013: 41
00014: 43
00015: 47
00016: 53
00017: 59
00018: 61
00019: 67
00020: 71
00021: 73
00022: 79
00023: 83
00024: 89
00025: 97
00026: 101
00027: 103
00028: 107
00029: 109
00030: 113
00031: 127
00032: 131
00033: 137
00034: 139
00035: 149
00036: 151
00037: 157
00038: 163
00039: 167
00040: 173
00041: 179
00042: 181
00043: 191
00044: 193
00045: 197
00046: 199
00047: 211
00048: 223
00049: 227
00050: 229
00051: 233
00052: 239
00053: 241
00054: 251
00055: 257
00056: 263
00057: 269
00058: 271
00059: 277
00060: 281
00061: 283
00062: 293
00063: 307
00064: 311
00065: 313
00066: 317
00067: 331
00068: 337
00069: 347
00070: 349
00071: 353
00072: 359
00073: 367
00074: 373
00075: 379
00076: 383
00077: 389
00078: 397
00079: 401
00080: 409
00081: 419
00082: 421
00083: 431
00084: 433
00085: 439
00086: 443
00087: 449
00088: 457
00089: 461
00090: 463
00091: 467
00092: 479
00093: 487
00094: 491
00095: 499
00096: 503
00097: 509
00098: 521
00099: 523
00100: 541
00101: 547
00102: 557
00103: 563
00104: 569
00105: 571
00106: 577
00107: 587
00108: 593
00109: 599
00110: 601
00111: 607
00112: 613
00113: 617
00114: 619
00115: 631
00116: 641
00117: 643
00118: 647
00119: 653
00120: 659
00121: 661
00122: 673
00123: 677
00124: 683
00125: 691
00126: 701
00127: 709
00128: 719
00129: 727
00130: 733
00131: 739
00132: 743
00133: 751
00134: 757
00135: 761
00136: 769
00137: 773
00138: 787
00139: 797
00140: 809
00141: 811
00142: 821
00143: 823
00144: 827
00145: 829
00146: 839
00147: 853
00148: 857
00149: 859
00150: 863
00151: 877
00152: 881
00153: 883
00154: 887
00155: 907
00156: 911
00157: 919
00158: 929
00159: 937
00160: 941
00161: 947
00162: 953
00163: 967
00164: 971
00165: 977
00166: 983
00167: 991
00168: 997
00169: 1009
00170: 1013
00171: 1019
00172: 1021
00173: 1031
00174: 1033
00175: 1039
00176: 1049
00177: 1051
00178: 1061
00179: 1063
00180: 1069
00181: 1087
00182: 1091
00183: 1093
00184: 1097
00185: 1103
00186: 1109
00187: 1117
00188: 1123
00189: 1129
00190: 1151
00191: 1153
00192: 1163
00193: 1171
00194: 1181
00195: 1187
00196: 1193
00197: 1201
00198: 1213
00199: 1217
00200: 1223
00201: 1229
00202: 1231
00203: 1237
00204: 1249
00205: 1259
00206: 1277
00207: 1279
00208: 1283
00209: 1289
00210: 1291
00211: 1297
00212: 1301
00213: 1303
00214: 1307
00215: 1319
00216: 1321
00217: 1327
00218: 1361
00219: 1367
00220: 1373
00221: 1381
00222: 1399
00223: 1409
00224: 1423
00225: 1427
00226: 1429
00227: 1433
00228: 1439
00229: 1447
00230: 1451
00231: 1453
00232: 1459
00233: 1471
00234: 1481
00235: 1483
00236: 1487
00237: 1489
00238: 1493
00239: 1499
00240: 1511
00241: 1523
00242: 1531
00243: 1543
00244: 1549
00245: 1553
00246: 1559
00247: 1567
00248: 1571
00249: 1579
00250: 1583
00251: 1597
00252: 1601
00253: 1607
00254: 1609
00255: 1613
00256: 1619
00257: 1621
00258: 1627
00259: 1637
00260: 1657
00261: 1663
00262: 1667
00263: 1669
00264: 1693
00265: 1697
00266: 1699
00267: 1709
00268: 1721
00269: 1723
00270: 1733
00271: 1741
00272: 1747
00273: 1753
00274: 1759
00275: 1777
00276: 1783
00277: 1787
00278: 1789
00279: 1801
00280: 1811
00281: 1823
00282: 1831
00283: 1847
00284: 1861
00285: 1867
00286: 1871
00287: 1873
00288: 1877
00289: 1879
00290: 1889
00291: 1901
00292: 1907
00293: 1913
00294: 1931
00295: 1933
00296: 1949
00297: 1951
00298: 1973
00299: 1979
00300: 1987
00301: 1993
00302: 1997
00303: 1999
00304: 2003
00305: 2011
00306: 2017
00307: 2027
00308: 2029
00309: 2039
00310: 2053
00311: 2063
00312: 2069
00313: 2081
00314: 2083
00315: 2087
00316: 2089
00317: 2099
00318: 2111
00319: 2113
00320: 2129
00321: 2131
00322: 2137
00323: 2141
00324: 2143
00325: 2153
00326: 2161
00327: 2179
00328: 2203
00329: 2207
00330: 2213
00331: 2221
00332: 2237
00333: 2239
00334: 2243
00335: 2251
00336: 2267
00337: 2269
00338: 2273
00339: 2281
00340: 2287
00341: 2293
00342: 2297
00343: 2309
00344: 2311
00345: 2333
00346: 2339
00347: 2341
00348: 2347
00349: 2351
00350: 2357
00351: 2371
00352: 2377
00353: 2381
00354: 2383
00355: 2389
00356: 2393
00357: 2399
00358: 2411
00359: 2417
00360: 2423
00361: 2437
00362: 2441
00363: 2447
00364: 2459
00365: 2467
00366: 2473
00367: 2477
00368: 2503
00369: 2521
00370: 2531
00371: 2539
00372: 2543
00373: 2549
00374: 2551
00375: 2557
00376: 2579
00377: 2591
00378: 2593
00379: 2609
00380: 2617
00381: 2621
00382: 2633
00383: 2647
00384: 2657
00385: 2659
00386: 2663
00387: 2671
00388: 2677
00389: 2683
00390: 2687
00391: 2689
00392: 2693
00393: 2699
00394: 2707
00395: 2711
00396: 2713
00397: 2719
00398: 2729
00399: 2731
00400: 2741
00401: 2749
00402: 2753
00403: 2767
00404: 2777
00405: 2789
00406: 2791
00407: 2797
00408: 2801
00409: 2803
00410: 2819
00411: 2833
00412: 2837
00413: 2843
00414: 2851
00415: 2857
00416: 2861
00417: 2879
00418: 2887
00419: 2897
00420: 2903
00421: 2909
00422: 2917
00423: 2927
00424: 2939
00425: 2953
00426: 2957
00427: 2963
00428: 2969
00429: 2971
00430: 2999
00431: 3001
00432: 3011
00433: 3019
00434: 3023
00435: 3037
00436: 3041
00437: 3049
00438: 3061
00439: 3067
00440: 3079
00441: 3083
00442: 3089
00443: 3109
00444: 3119
00445: 3121
00446: 3137
00447: 3163
00448: 3167
00449: 3169
00450: 3181
00451: 3187
00452: 3191
00453: 3203
00454: 3209
00455: 3217
00456: 3221
00457: 3229
00458: 3251
00459: 3253
00460: 3257
00461: 3259
00462: 3271
00463: 3299
00464: 3301
00465: 3307
00466: 3313
00467: 3319
00468: 3323
00469: 3329
00470: 3331
00471: 3343
00472: 3347
00473: 3359
00474: 3361
00475: 3371
00476: 3373
00477: 3389
00478: 3391
00479: 3407
00480: 3413
00481: 3433
00482: 3449
00483: 3457
00484: 3461
00485: 3463
00486: 3467
00487: 3469
00488: 3491
00489: 3499
00490: 3511
00491: 3517
00492: 3527
00493: 3529
00494: 3533
00495: 3539
00496: 3541
00497: 3547
00498: 3557
00499: 3559
00500: 3571
00501: 3581
00502: 3583
00503: 3593
00504: 3607
00505: 3613
00506: 3617
00507: 3623
00508: 3631
00509: 3637
00510: 3643
00511: 3659
00512: 3671
00513: 3673
00514: 3677
00515: 3691
00516: 3697
00517: 3701
00518: 3709
00519: 3719
00520: 3727
00521: 3733
00522: 3739
00523: 3761
00524: 3767
00525: 3769
00526: 3779
00527: 3793
00528: 3797
00529: 3803
00530: 3821
00531: 3823
00532: 3833
00533: 3847
00534: 3851
00535: 3853
00536: 3863
00537: 3877
00538: 3881
00539: 3889
00540: 3907
00541: 3911
00542: 3917
00543: 3919
00544: 3923
00545: 3929
00546: 3931
00547: 3943
00548: 3947
00549: 3967
00550: 3989
00551: 4001
00552: 4003
00553: 4007
00554: 4013
00555: 4019
00556: 4021
00557: 4027
00558: 4049
00559: 4051
00560: 4057
00561: 4073
00562: 4079
00563: 4091
00564: 4093
00565: 4099
00566: 4111
00567: 4127
00568: 4129
00569: 4133
00570: 4139
00571: 4153
00572: 4157
00573: 4159
00574: 4177
00575: 4201
00576: 4211
00577: 4217
00578: 4219
00579: 4229
00580: 4231
00581: 4241
00582: 4243
00583: 4253
00584: 4259
00585: 4261
00586: 4271
00587: 4273
00588: 4283
00589: 4289
00590: 4297
00591: 4327
00592: 4337
00593: 4339
00594: 4349
00595: 4357
00596: 4363
00597: 4373
00598: 4391
00599: 4397
00600: 4409
00601: 4421
00602: 4423
00603: 4441
00604: 4447
00605: 4451
00606: 4457
00607: 4463
00608: 4481
00609: 4483
00610: 4493
00611: 4507
00612: 4513
00613: 4517
00614: 4519
00615: 4523
00616: 4547
00617: 4549
00618: 4561
00619: 4567
00620: 4583
00621: 4591
00622: 4597
00623: 4603
00624: 4621
00625: 4637
00626: 4639
00627: 4643
00628: 4649
00629: 4651
00630: 4657
00631: 4663
00632: 4673
00633: 4679
00634: 4691
00635: 4703
00636: 4721
00637: 4723
00638: 4729
00639: 4733
00640: 4751
00641: 4759
00642: 4783
00643: 4787
00644: 4789
00645: 4793
00646: 4799
00647: 4801
00648: 4813
00649: 4817
00650: 4831
00651: 4861
00652: 4871
00653: 4877
00654: 4889
00655: 4903
00656: 4909
00657: 4919
00658: 4931
00659: 4933
00660: 4937
00661: 4943
00662: 4951
00663: 4957
00664: 4967
00665: 4969
00666: 4973
00667: 4987
00668: 4993
00669: 4999
00670: 5003
00671: 5009
00672: 5011
00673: 5021
00674: 5023
00675: 5039
00676: 5051
00677: 5059
00678: 5077
00679: 5081
00680: 5087
00681: 5099
00682: 5101
00683: 5107
00684: 5113
00685: 5119
00686: 5147
00687: 5153
00688: 5167
00689: 5171
00690: 5179
00691: 5189
00692: 5197
00693: 5209
00694: 5227
00695: 5231
00696: 5233
00697: 5237
00698: 5261
00699: 5273
00700: 5279
00701: 5281
00702: 5297
00703: 5303
00704: 5309
00705: 5323
00706: 5333
00707: 5347
00708: 5351
00709: 5381
00710: 5387
00711: 5393
00712: 5399
00713: 5407
00714: 5413
00715: 5417
00716: 5419
00717: 5431
00718: 5437
00719: 5441
00720: 5443
00721: 5449
00722: 5471
00723: 5477
00724: 5479
00725: 5483
00726: 5501
00727: 5503
00728: 5507
00729: 5519
00730: 5521
00731: 5527
00732: 5531
00733: 5557
00734: 5563
00735: 5569
00736: 5573
00737: 5581
00738: 5591
00739: 5623
00740: 5639
00741: 5641
00742: 5647
00743: 5651
00744: 5653
00745: 5657
00746: 5659
00747: 5669
00748: 5683
00749: 5689
00750: 5693
00751: 5701
00752: 5711
00753: 5717
00754: 5737
00755: 5741
00756: 5743
00757: 5749
00758: 5779
00759: 5783
00760: 5791
00761: 5801
00762: 5807
00763: 5813
00764: 5821
00765: 5827
00766: 5839
00767: 5843
00768: 5849
00769: 5851
00770: 5857
00771: 5861
00772: 5867
00773: 5869
00774: 5879
00775: 5881
00776: 5897
00777: 5903
00778: 5923
00779: 5927
00780: 5939
00781: 5953
00782: 5981
00783: 5987
00784: 6007
00785: 6011
00786: 6029
00787: 6037
00788: 6043
00789: 6047
00790: 6053
00791: 6067
00792: 6073
00793: 6079
00794: 6089
00795: 6091
00796: 6101
00797: 6113
00798: 6121
00799: 6131
00800: 6133
00801: 6143
00802: 6151
00803: 6163
00804: 6173
00805: 6197
00806: 6199
00807: 6203
00808: 6211
00809: 6217
00810: 6221
00811: 6229
00812: 6247
00813: 6257
00814: 6263
00815: 6269
00816: 6271
00817: 6277
00818: 6287
00819: 6299
00820: 6301
00821: 6311
00822: 6317
00823: 6323
00824: 6329
00825: 6337
00826: 6343
00827: 6353
00828: 6359
00829: 6361
00830: 6367
00831: 6373
00832: 6379
00833: 6389
00834: 6397
00835: 6421
00836: 6427
00837: 6449
00838: 6451
00839: 6469
00840: 6473
00841: 6481
00842: 6491
00843: 6521
00844: 6529
00845: 6547
00846: 6551
00847: 6553
00848: 6563
00849: 6569
00850: 6571
00851: 6577
00852: 6581
00853: 6599
00854: 6607
00855: 6619
00856: 6637
00857: 6653
00858: 6659
00859: 6661
00860: 6673
00861: 6679
00862: 6689
00863: 6691
00864: 6701
00865: 6703
00866: 6709
00867: 6719
00868: 6733
00869: 6737
00870: 6761
00871: 6763
00872: 6779
00873: 6781
00874: 6791
00875: 6793
00876: 6803
00877: 6823
00878: 6827
00879: 6829
00880: 6833
00881: 6841
00882: 6857
00883: 6863
00884: 6869
00885: 6871
00886: 6883
00887: 6899
00888: 6907
00889: 6911
00890: 6917
00891: 6947
00892: 6949
00893: 6959
00894: 6961
00895: 6967
00896: 6971
00897: 6977
00898: 6983
00899: 6991
00900: 6997
00901: 7001
00902: 7013
00903: 7019
00904: 7027
00905: 7039
00906: 7043
00907: 7057
00908: 7069
00909: 7079
00910: 7103
00911: 7109
00912: 7121
00913: 7127
00914: 7129
00915: 7151
00916: 7159
00917: 7177
00918: 7187
00919: 7193
00920: 7207
00921: 7211
00922: 7213
00923: 7219
00924: 7229
00925: 7237
00926: 7243
00927: 7247
00928: 7253
00929: 7283
00930: 7297
00931: 7307
00932: 7309
00933: 7321
00934: 7331
00935: 7333
00936: 7349
00937: 7351
00938: 7369
00939: 7393
00940: 7411
00941: 7417
00942: 7433
00943: 7451
00944: 7457
00945: 7459
00946: 7477
00947: 7481
00948: 7487
00949: 7489
00950: 7499
00951: 7507
00952: 7517
00953: 7523
00954: 7529
00955: 7537
00956: 7541
00957: 7547
00958: 7549
00959: 7559
00960: 7561
00961: 7573
00962: 7577
00963: 7583
00964: 7589
00965: 7591
00966: 7603
00967: 7607
00968: 7621
00969: 7639
00970: 7643
00971: 7649
00972: 7669
00973: 7673
00974: 7681
00975: 7687
00976: 7691
00977: 7699
00978: 7703
00979: 7717
00980: 7723
00981: 7727
00982: 7741
00983: 7753
00984: 7757
00985: 7759
00986: 7789
00987: 7793
00988: 7817
00989: 7823
00990: 7829
00991: 7841
00992: 7853
00993: 7867
00994: 7873
00995: 7877
00996: 7879
00997: 7883
00998: 7901
00999: 7907
01000: 7919
Prime Numbers can be further divided into:
08.02.01. Co-Prime Numbers.
08.02.02. Triplet Prime Numbers.
08.02.03. Mersenne Numbers.
08.02.04. Regular Prime Numbers.
08.02.05. Pseudoprime Numbers.
09. Set Numbers and Non-Set Numbers.
09.01. Set Numbers.
Set Numbers can be sub-classified in different ways:
09.01.01. Classification A
09.01.01.01. Empty Set.
09.01.01.02. Singleton Set.
09.01.01.03. Finite Set.
09.01.01.04. Infinite Set.
09.01.01.05. Equal Sets.
09.01.01.06. Equivalent Sets.
09.01.01.07. Universal Set.
09.01.01.08. Proper Subet.
09.01.01.09. Superset.
09.01.01.10. Proper Superset.
09.01.01.11. Power Set.
09.01.02. Non-Random Numbers and Random Numbers.
09.01.02.01. Non-Random Numbers.
09.01.02.01.01. Arithmetic Sequences ( Arithmetic Progression/ Arithmetic Series)
09.01.02.01.02. Geometric Sequences ( Geometric Progression/ Geometric Series)
09.01.02.01.03. Triangular Sequences ( Triangular Progression/ Triangular Series)
09.01.02.01.04. Mersenne Sequences ( Mersenne Progression/ Mersenne Series)
09.01.02.02. Random Numbers.
09.01.02. Set Numbers Classified by Dimensions
09.01.02.01. One-Dimensional Sets.
09.01.02.02. Multi-Dimensional Sets.
09.01.02.02.01. Determinates
09.01.02.02.02. Matrices
09.01.03. Set Numbers Classified by Number of Items in the Set:
09.01.03.02. Two Numbers.
09.01.03.03. Three Numbers.
09.01.03.03.01. Set of 3 Integer Numbers / Pythagorean Triples
09.01.03.03.01.01. Sides of Right Angle Triangles.
Examples:
3 4 5
4 3 5
5 12 13
6 8 10
7 24 25
8 15 17
9 40 41
11 60 61
12 5 13
12 35 37
13 84 85
15 8 17
15 112 113
16 63 65
17 144 145
19 180 181
20 21 29
20 99 101
21 220 221
24 7 25
24 143 145
28 45 53
28 195 197
32 56 65
33 255 257
36 77 85
39 80 89
44 117 125
48 55 73
51 140 149
52 165 173
57 176 185
60 91 109
60 221 229
63 16 65
65 72 97
77 36 85
84 13 85
84 187 205
85 132 157
88 105 137
95 168 193
96 247 265
99 20 101
104 153 185
105 208 233
115 252 277
117 44 125
119 120 169
120 209 241
132 85 157
133 156 205
140 171 221
153 104 185
156 133 205
160 231 281
161 240 289
168 95 193
171 140 221
187 84 205
204 253 325
207 224 305
208 105 233
209 120 241
231 160 281
240 161 289
247 96 265
252 115 277
253 240 325
696 697 985
4059 4060 5741
23660 23661 33461
137903 137904 195025
803760 803761 1136689
4684659 4684660 6625109
10. Radical Numbers and Non-Radical Numbers.
10.01. Radical Numbers.
Radical Numbers are numbers with an absolute exponent less than 1.
10.02. Non-Radical Numbers.
Non-Radical Numbers are numbers with an absolute exponent equal to or greater than 1.
11. Harshad Numbers and Non-Harshad Numbers.
11.01. Harshad Numbers
11.02. Non-Harshad Numbers
12. Graham Numbers and Non-Graham Numbers.
12.01. Graham Number
12.02. Non-Graham Number
13. Ten-Based Numbers (Decimal Numbers); Two-Based Numbers (Binary Numbers); Eight-Based Numbers (Octal Numbers); Sixteen-Based Numbers (Hexadecimal Numbers).
The Ten-Based Numbers (Decimal Numbers); Two-Based Numbers (Binary Numbers); Eight-Based Numbers (Octal Numbers); and Sixteen-Based Numbers (Hexadecimal Numbers) use the concept of positional rotation. Positional Rotation means that each item in a number acquires its value based on its position.
An example of that is the number 111 in the Ten-Based Numbers (Decimal Numbers). Starting from the right to the left:
The 1 that is to the far right represents 1 multiplied by 1 equaling 1.
The 1 that is the second from the right represents 1 multiplied by 10 equaling 10.
The 1 that is the third from the right represents 1 multiplied by 100 equaling 100.
Thus 111 means 1 plus 10 plus 100 equaling 111.
The number 111 in Binary Numbers is written as 1101111.
The 1 that is to the far right represents 1 multiplied by 1 equaling 1.
The 1 that is the second from the right represents 1 multiplied by 2 equaling 2.
The 1 that is the third from the right represents 1 multiplied by 4 equaling 4.
The 1 that is the fourth from the right represents 1 multiplied by 8 equaling 8.
The 0 that is the fifth from the right represents 0 multiplied by 16 equaling 0.
The 1 that is the six from the right represents 1 multiplied by 32 equaling 32.
The 1 that is the seventh from the right represents 1 multiplied by 64 equaling 64.
Thus 1101111 means 1 plus 2 plus 4 plus 8 plus 0 plus 32 plus 64 equaling 111.
13.01. Ten-Based Numbers (Decimal Numbers)
The Ten-Based Numbers (Decimal Numbers) usually use the ten Arabic Numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
In the Ten-Based Numbers (Decimal Numbers) can include Integral Part and Fractional Part.
13.01.01. Integral Part
The terms that are used to describe the integral part of a number left to the decimal point include:
13.01.01.01. Tens: 01 Zero
13.01.01.02. Hundreds: 02 Zeros
13.01.01.03. Thousands: 03 Zeros
13.01.01.04. Millions: 06 Zeros
13.01.01.05. Billions: 09 Zeros
13.01.01.06. Trillions: 12 Zeros
13.01.01.07. Quadrillions: 15 Zeros
13.01.01.08. Quintillion: 18 Zeros
13.01.01.09. Sextillion: 21 Zeros
13.01.01.10. Septillion: 24 Zeros
13.01.11. Octillion: 27 Zeros
13.01.01.12. Nonillion: 30 Zeros
13.01.01.13. Decillion: 33 Zeros
13.01.01.14. Undecillion: 36 Zeros
13.01.01.15. Duodecillion: 39 Zeros
13.01.01.16. Tredecillion: 42 Zeros
13.01.01.17. Quattuordecillion: 45 Zeros
13.01.01.18. Quindecillion: 48 Zeros
13.01.01.19. Sexdecillion: 51 Zeros
13.01.01.20. Septendecillion: 54 Zeros
13.01.01.21. Octodecillion: 57 Zeros
13.01.01.22. Novemdecillion: 60 Zeros
13.01.01.23. Vigintillion: 63 Zeros
13.01.01.24. Duotrigintillion: 99 Zeros
13.01.01.25. Googol: 100 Zeros
13.01.01.26. Centillion: 303 Zeros
13.01.01.27. Googolplex: 10^(10^100) Zero or 10^Googol Zeros
The term Zillion refer to a number that is so massive with endless number of zeros.
13.01.02. Fractional Part
The terms that are used to describe the fractional part of a number right to the decimal point include. The fractional part of a number right to the decimal point sometimes is referred to as mantissa.
13.01.02.01. Deci: 1 / 01 Zero
13.01.02.02. Centi: 1 / 02 Zeros
13.01.02.03. Milli: 1 / 03 Zeros
13.01.02.04. Micro: 1 / 06 Zeros
13.01.02.05. Nano: 1 / 09 Zeros
13.01.02.06. Pico: 1 / 12 Zeros
13.01.02.07. Femto: 1 / 15 Zeros
13.01.02.08. Atto: 1 / 18 Zeros
13.01.02.09. Zepto: 1 / 21 Zeros
13.01.02.10. Zocto: 1 / 24 Zeros
13.02. Two-Based Numbers (Binary Numbers).
The Two-Based Numbers (Binary Numbers) usually use the two Arabic Numbers (0, 1).
13.03. Eight-Based Numbers (Octal Numbers).
The Eight-Based Numbers (Octal Numbers) usually use the eight Arabic Numbers (0, 1, 2, 3, 4, 5, 6, 7).
13.04. Sixteen-Based Numbers (Hexadecimal Numbers).
The Sixteen-Based Numbers (Hexadecimal Numbers) usually use the ten Arabic Numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the six Latin letters (A, B, C, D, E, F)
Epsilon is used in mathematics to represent a positive infinitesimal quantity
EPSILON is used in programming languages as a name of a constant of infinitesimal quantity. This helps overcome the shortcomings of the binary system in some calculations. And thus we avoid logical errors resulting from these shortcomings of the binary system. One of the shortcomings of the binary system is its inexact representation of some of the fractions in the decimal system.
Epsilon is the fifth letter of the 24 letters of the Greek Alphabet:
01 Alpha
02 Beta
03 Chi
04 Delta
05 Epsilon
06 Eta
07 Gamma
08 Iota
09 Kappa
10 Lambda
11 Mu
12 Nu
13 Omega
14 Omicron
15 Phi
16 Pi
17 Psi
18 Rho
19 Sigma
20 Tau
21 Theta
22 Upsilon
23 Xi
24 Zeta
14. Real Numbers and Imaginary Numbers and Complex Numbers.
14.01. Real Numbers
14.02. Imaginar Numbers
14.03. Complex Numbers
15. Special Numbers and Non-Special Numbers.
15.01. Special Numbers
Examples of Special Numbers are:
15.01.01. Zero.
The origin of the word "zero" is from the Hindu "Sunya" meaning void or emptiness, then the Arabic "Sifr" then the Latin "Cephirum", then the Italian "zevero", then the English word "zero"
The English word "cipher" is driven from the Arabic word.
15.01.02. PI
As of Thursday, May 6, 2021, the largest discovered number of digits right of the decimal point (mantissa) in PI was 31 trillion digits.
15.01.03. e
15.01.04. Infinity
Infinity + Infinity = Infinity
Infinity * Infinity = Infinity
15.01.05. Fibonacci Numbers
15.01.06. Graham's Number
15.01.07. Apery Constant
Apery Constant was found by Roger Apery. Apery Constant is defined as (1/1^3) + (1/2^3) + (1/3^3) + (1/4^3) + .....
15.01.08. Square Root of 2
As of Tuesday, June 28, 2016, Ron Watkin discovered the largest number of digits after the decimal point in the square root of Two as 10 trillion digits.
The Square Root of 2 is used in designing paper sizes. This includes international paper sizes and U.S. paper sizes.
Examples:
The paper international size A0 is 841 * 1189 mm = 33.1 * 46.8 inch
The paper international size A4 is 297*210 mm. 297: 210 = 2^0.5 : 1
The following is the discovered 1045 digits right of the decimal point (mantissa) in the square root of 2:
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008344491148185876555542864551233142199263113325
15.02. Non-Special Numbers
16. Carmichael Numbers and Non-Carmichael Numbers.
16.01. Carmichael Numbers
16.02. Non-Carmichael Numbers
17. Transcendental Numbers and Non-Transcendental Numbers.
17.01. Transcendental Numbers
17.02. Non-Transcendental Numbers
18. Perfect Numbers and Non-Perfect Numbers.
18.01. Perfect Numbers
18.02. Non-Perfect Numbers