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 Prime Numbers in the Library.


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