1

[[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]] [[{{#expr: (floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}} (number)|{{#switch:{{{1}}}|-1={{#ifexpr:(floor({{{number}}} div 10)) = 0|-1|←}}|10=→|#default={{#expr:(floor({{{number}}} div {{{factor}}})) * {{{factor}}}+({{{1}}}*{{{factor}}} div 10)}}}}]]

List of numbers — Integers

← 0 10 20 30 40 50 60 70 80 90 →

Cardinal

one

1st
(first)

∅

Roman numeral (unicode)

Ⅰ, ⅰ

mono- /haplo-

1₂

1₃

1₄

1₅

1₆

1₈

1₁₂

1₁₆

1₂₀

1₃₆

α'

১

一，弌，壹

१ (ek)

፩

Ⴁ/ⴁ/ბ(Bani)

೧

១

일, 하나

൧

๑

1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. It is also the first of the infinite sequence of natural numbers, followed by 2.

Etymology

The word one can be used as a noun, an adjective and a pronoun.^[1]

It comes from the English word an,^[1] which comes from the Proto-Germanic root *ainaz.^[1] The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-.^[1]

Compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish een, Dutch een, German eins and Old Norse einn.

Compare the Proto-Indo-European root *oi-no- (which means one, single^[1]) to Greek oinos (which means "ace" on dice^[1]), Latin unus (one^[1]), Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin and Breton un (one^[1]).

As a number

One, sometimes referred to as unity,^[2] is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number.

Any number multiplied by one remains that number, as one is the identity for multiplication. As a result, 1 is its own factorial, its own square, its own cube, and so on. One is also the result of the empty product, as any number multiplied by one is itself. It is also the only natural number that is neither composite nor prime with respect to division, but instead considered a unit.

As a digit

The glyph used today in the Western world to represent the number 1, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom, traces its roots back to the Indians, who wrote 1 as a horizontal line, much like the Chinese character 一. The Gupta wrote it as a curved line, and the Nagari sometimes added a small circle on the left (rotated a quarter turn to the right, this 9-look-alike became the present day numeral 1 in the Gujarati and Punjabi scripts). The Nepali also rotated it to the right but kept the circle small.^[3] This eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral $I$ . In some countries, the little serif at the top is sometimes extended into a long upstroke, sometimes as long as the vertical line, which can lead to confusion with the glyph for seven in other countries. Where the 1 is written with a long upstroke, the number 7 has a horizontal stroke through the vertical line.

While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, the character usually is of x-height, as, for example, in .

Decorative clay/stone circular off-white sundial with bright gold stylized sunburst in center of 24 hour clock face, one through twelve clockwise on right, and one through twelve again clockwise on left, with J shapes where ones' digits would be expected when numbering the clock hours. Shadow suggests 3 PM toward lower left.

The 24-hour tower clock in Venice, using J as a symbol for 1.

Many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used, while it may be for decorative purposes.

Mathematics

Mathematically, 1 is:

in arithmetic (algebra) and calculus, the natural number that follows 0 and precedes 2 and the multiplicative identity element of the integers, real numbers and complex numbers;
more generally, in algebra, the multiplicative identity (also called unity), usually of a group or a ring.

Tallying is often referred to as "base 1", since only one mark — the tally itself — is needed. This is more formally referred to as a unary numeral system. Unlike base 2 or base 10, this is not a positional notation.

Since the base 1 exponential function (1^x) always equals 1, its inverse does not exist (which would be called the logarithm base 1 if it did exist).

There are two ways to write the real number 1 as a recurring decimal: as 1.000..., and as 0.999....

Formalizations of the natural numbers have their own representations of 1:

in the Peano axioms, 1 is the successor of 0;
in Principia Mathematica, 1 is defined as the set of all singletons (sets with one element);
in the Von Neumann cardinal assignment of natural numbers, 1 is defined as the set {0}.

In a multiplicative group or monoid, the identity element is sometimes denoted 1, but e (from the German Einheit, "unity") is also traditional. However, 1 is especially common for the multiplicative identity of a ring, i.e., when an addition and 0 are also present. When such a ring has characteristic n not equal to 0, the element called 1 has the property that n1 = 1n = 0 (where this 0 is the additive identity of the ring). Important examples are finite fields.

1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few.

In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. Likewise, vectors are often normalized to give unit vectors, that is vectors of magnitude one, because these often have more desirable properties. Functions, too, are often normalized by the condition that they have integral one, maximum value one, or square integral one, depending on the application.

Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must equal 1.

It is also the first and second number in the Fibonacci sequence (0 is the zeroth) and is the first number in many other mathematical sequences.

1 is neither a prime number nor a composite number, but a unit, like −1 and, in the Gaussian integers, i and −i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units. (For example, 4 = 2², but if units are included, is also equal to, say, (−1)⁶ × 1²³ × 2², among infinitely many similar "factorizations".)

The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of characteristic 1. Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all.

1 is the only positive integer divisible by exactly one positive integer (whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers). 1 was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by 1 and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units.

By definition, 1 is the magnitude, absolute value, or norm of a unit complex number, unit vector, and a unit matrix (more usually called an identity matrix). Note that the term unit matrix is sometimes used to mean something quite different.

By definition, 1 is the probability of an event that is almost certain to occur.

1 is the most common leading digit in many sets of data, a consequence of Benford's law.

1 is the only known Tamagawa number for a simply connected algebraic group over a number field.

The generating function that has all coefficients 1 is given by

1/1 − x = 1 + x + x² + x³ + …

This power series converges and has finite value if and only if, |x| < 1.

In category theory, 1 is sometimes used to denote the terminal object of a category.

Table of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000
1 × x	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000

Division	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15
1 ÷ x	1	0.5	0.3	0.25	0.2	0.16	0.142857	0.125	0.1	0.1		0.09	0.083	0.076923	0.0714285	0.06
x ÷ 1	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20
1^x	1	1	1	1	1	1	1	1	1	1		1	1	1	1	1	1	1	1	1	1
x¹	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20

In technology

The resin identification code used in recycling to identify polyethylene terephthalate.^[4]
The ITU country code for the North American Numbering Plan area, which includes the United States, Canada, and parts of the Caribbean
A binary code is a sequence of 1 and 0 that is used in computers for representing any kind of data.
In many physical devices, 1 represents the value for "on", which means that electricity is flowing.^[5]^[6]
The numerical value of true in many programming languages.

1 is the ASCII code of "Start of Header".

In science

1 is the atomic number of hydrogen, and the atomic mass of its most common isotope.
+1 is the electric charge of positrons and protons.
Group 1 of the periodic table consists of the alkali metals.
Period 1 of the periodic table consists of just two elements, hydrogen and helium.
The dwarf planet Ceres has the minor-planet designation 1 Ceres because it was the first asteroid to be discovered.
The Roman numeral I often stands for the first-discovered satellite of a planet or minor planet (such as Neptune I, a.k.a. Triton). For some earlier discoveries, the Roman numerals originally reflected the increasing distance from the primary instead.

In philosophy

In the philosophy of Plotinus and a number of other neoplatonists, The One is the ultimate reality and source of all existence. Philo of Alexandria (20 BC – AD 50) regarded the number one as God's number, and the basis for all numbers ("De Allegoriis Legum," ii.12 [i.66]).

In literature

Number One is a character in the book series Lorien Legacies by Pittacus Lore.
Number 1 is also a character in the series "Artemis Fowl" by Eoin Colfer.
In a 1968 song by Three Dog's Night, the number one is identified as "the loneliest number".

In comics

A character in the Italian comic book Alan Ford (authors Max Bunker and Magnus), very old disabled man, the supreme leader of the group TNT.

In sports

In baseball scoring, the number 1 is assigned to the pitcher.
In association football (soccer) the number 1 is often given to the goalkeeper.
In most competitions of rugby league (though not the European Super League, which uses static squad numbering), the starting fullback wears jersey number 1.
In rugby union, the starting loosehead prop wears the jersey number 1.
1 is the lowest number permitted for use by players of the National Hockey League (NHL), as the league has banned 00 and 0. (The highest number permitted is 98.
In Formula One, the previous year's world champion is allowed to use the number 1.

In other fields

1 is the value of an ace in many playing card games, such as cribbage.
List of highways numbered 1
List of public transport routes numbered 1
1 is often used to denote the Gregorian calendar month of January.
1 CE, the first year of the Common Era
01, the former dialing code for Greater London
PRS One, a German paraglider design
+1 is the code for international telephone calls to countries in the North American Numbering Plan

References

Wikimedia Commons has media related to:

1 (number) (category)

1 2 3 4 5 6 7 8 "Online Etymology Dictionary". etymonline.com. Douglas Harper.
↑ Skoog, Douglas. Principles of Instrumental Analysis. Brooks/Cole, 2007, p. 758.
↑ Ifrah, Georges; et al. (1998). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by Bellos, David. yes. London: The Harvill Press. p. 392, Fig. 24.61.
↑ "Plastic Packaging Resins" (PDF). American Chemistry Council. Archived from the original (PDF) on 2011-07-21.
↑ Woodford, Chris (2006), Digital Technology, Evans Brothers, p. 9, ISBN 978-0-237-52725-9
↑ Godbole, Achyut S. (1 September 2002), Data Comms & Networks, Tata McGraw-Hill Education, p. 34, ISBN 978-1-259-08223-8

External links

Wikiquote has quotations related to: 1

Integers

0s
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99

100s
100 101 102 103 104 105 106 107 108 109
110 111 112 113 114 115 116 117 118 119
120 121 122 123 124 125 126 127 128 129
130 131 132 133 134 135 136 137 138 139
140 141 142 143 144 145 146 147 148 149
150 151 152 153 154 155 156 157 158 159
160 161 162 163 164 165 166 167 168 169
170 171 172 173 174 175 176 177 178 179
180 181 182 183 184 185 186 187 188 189
190 191 192 193 194 195 196 197 198 199

200s
200 201 202 203 204 205 206 207 208 209
210 211 212 213 214 215 216 217 218 219
220 221 222 223 224 225 226 227 228 229
230 231 232 233 234 235 236 237 238 239
240 241 242 243 244 245 246 247 248 249
250 251 252 253 254 255 256 257 258 259
260 261 262 263 264 265 266 267 268 269
270 271 272 273 274 275 276 277 278 279
280 281 282 283 284 285 286 287 288 289
290 291 292 293 294 295 296 297 298 299

300s
300 301 302 303 304 305 306 307 308 309
310 311 312 313 314 315 316 317 318 319
320 321 322 323 324 325 326 327 328 329
330 331 332 333 334 335 336 337 338 339
340 341 342 343 344 345 346 347 348 349
350 351 352 353 354 355 356 357 358 359
360 361 362 363 364 365 366 367 368 369
370 371 372 373 374 375 376 377 378 379
380 381 382 383 384 385 386 387 388 389
390 391 392 393 394 395 396 397 398 399

400s
400 401 402 403 404 405 406 407 408 409
410 411 412 413 414 415 416 417 418 419
420 421 422 423 424 425 426 427 428 429
430 431 432 433 434 435 436 437 438 439
440 441 442 443 444 445 446 447 448 449
450 451 452 453 454 455 456 457 458 459
460 461 462 463 464 465 466 467 468 469
470 471 472 473 474 475 476 477 478 479
480 481 482 483 484 485 486 487 488 489
490 491 492 493 494 495 496 497 498 499

500s
500 501 502 503 504 505 506 507 508 509
510 511 512 513 514 515 516 517 518 519
520 521 522 523 524 525 526 527 528 529
530 531 532 533 534 535 536 537 538 539
540 541 542 543 544 545 546 547 548 549
550 551 552 553 554 555 556 557 558 559
560 561 562 563 564 565 566 567 568 569
570 571 572 573 574 575 576 577 578 579
580 581 582 583 584 585 586 587 588 589
590 591 592 593 594 595 596 597 598 599

600s
600 601 602 603 604 605 606 607 608 609
610 611 612 613 614 615 616 617 618 619
620 621 622 623 624 625 626 627 628 629
630 631 632 633 634 635 636 637 638 639
640 641 642 643 644 645 646 647 648 649
650 651 652 653 654 655 656 657 658 659
660 661 662 663 664 665 666 667 668 669
670 671 672 673 674 675 676 677 678 679
680 681 682 683 684 685 686 687 688 689
690 691 692 693 694 695 696 697 698 699

700s
700 701 702 703 704 705 706 707 708 709
710 711 712 713 714 715 716 717 718 719
720 721 722 723 724 725 726 727 728 729
730 731 732 733 734 735 736 737 738 739
740 741 742 743 744 745 746 747 748 749
750 751 752 753 754 755 756 757 758 759
760 761 762 763 764 765 766 767 768 769
770 771 772 773 774 775 776 777 778 779
780 781 782 783 784 785 786 787 788 789
790 791 792 793 794 795 796 797 798 799

800s
800 801 802 803 804 805 806 807 808 809
810 811 812 813 814 815 816 817 818 819
820 821 822 823 824 825 826 827 828 829
830 831 832 833 834 835 836 837 838 839
840 841 842 843 844 845 846 847 848 849
850 851 852 853 854 855 856 857 858 859
860 861 862 863 864 865 866 867 868 869
870 871 872 873 874 875 876 877 878 879
880 881 882 883 884 885 886 887 888 889
890 891 892 893 894 895 896 897 898 899

900s
900 901 902 903 904 905 906 907 908 909
910 911 912 913 914 915 916 917 918 919
920 921 922 923 924 925 926 927 928 929
930 931 932 933 934 935 936 937 938 939
940 941 942 943 944 945 946 947 948 949
950 951 952 953 954 955 956 957 958 959
960 961 962 963 964 965 966 967 968 969
970 971 972 973 974 975 976 977 978 979
980 981 982 983 984 985 986 987 988 989
990 991 992 993 994 995 996 997 998 999

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