| 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Numbers 0 - 99 | |||||||||
| 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 |
Visualization of one
1 (one) is a positive integer following 0 and preceding 2. Its ordinal form is written "1st" or "first".
Properties[]
- 1 is the first natural number. 1 is odd, and it's the only natural number that is neither prime nor composite.
- 1 is a triangular number, tetrahedral number, pentatope number, dodecahedral number, etc. It's also a square number, cube number, etc.
- 1 is the multiplicative identity, meaning that \(a = a \times 1\) for all \(a\). In fact, \(a \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_n 1 = a\) (arrow notation) for all \(n,a \geq 0\), so 1 is a sort of identity for all the hyper operators beyond addition. Furthermore, for all \(n,a > 0\), \(a \underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_n 0 = 1\) and \(1 \uparrow\uparrow\ldots\uparrow\uparrow n\). 1 appears frequently as a "default" argument in googological notations, such as BEAF, chained arrow notation, and hyper-E notation.
- All natural numbers are just strings of 1's added together. For example, 1,000,000 is a string of 1 million 1's added together.
- 1 is the only odd practical number.
- 1 is the only known odd multiperfect number.
- The base one numbering system is called unary, as demonstrated by the video below:
1 has been callled "wau" by Vi Hart to highlight its more unusual properties.
In other languages[]
| Language | Name |
|---|---|
| Afrikaans | een |
| Albanian | një |
| Amharic | አንድ |
| Arabic | واحد |
| Armenian | մեկը |
| Azerbaijani | bir |
| Bangla | এক |
| Basque | bat |
| Belarusian | адзін |
| Bosnian, Croatian | jedan |
| Bulgarian | един (edin) |
| Burmese | တစ် |
| Catalan, French | un |
| Chinese | 一 (yī) |
| Czech, Slovak, Polish | jeden |
| Esperanto | unu |
| German | eins |
| Hungarian | egy |
| Italic, Spanish | uno |
| Japanese | いち (ichi) |
| Latvian | viens |
| Macedonian, | eден (eden) |
| Malay | Satu |
| Russian | один (odin) |
| Serbian | jедан (jedan) |
| Slovenian | ena |
| Toki Pona | Wan |
| Turkish | Bir |
| Ukrainian | oдин (odyn) |
| Vietnamese | một |
| Zulu | eyodwa |
In googology[]
Sbiis Saibian argued that all numbers larger than 1 should be called "large numbers," because the reciprocals of large numbers are small. He called them "superuniary numbers" or "superuniaries".[1] The large numbers and small numbers are "mirrored" about 1, so it makes sense to say that 1 is the threshold of largeness. A number like 1 + 1/googol could be called a "very small large number." The smallest large number is a logical impossibility, of course.
1 was also the first number by Adam Elga in the Big Number Duel.
1 can be named garone, fzone, fugaone, or megafugaone with the gar-, fz-, fuga-, or megafuga- prefixes respectively.
Nihilustheabsolutist coined post-nothingness for this number,[2] because 1 is the first non decimal number after 0 where 0 in this context is nothing.
Googological functions returning 1[]
- Rado's Sigma Function: \(\Sigma(1)=1\)
- Maximum shifts function: \(S(1)=1\)
- Xi function: \(\Xi(1)=1\)
- Goodstein function: \(G(1)=1\)
- Weak Goodstein function: \(g(1)=1\)
- Kirby-Paris hydra: \(\text{Hydra}(1)=1\)
- Buchholz hydra: \(\text{BH}(2)=1\)
- TREE function: \(\text{TREE}(1)=1\)
- Weak tree function: \(\text{tree}(0)=1\)
- Fusible numbers: \(m_1(0) = 1\)
- Exploding Tree function: \(E(1)=1\)
- Latin square: \(L(1)=1\)
- Gijswijt's sequence: \(c(1)=1\)
- Tetration: \(1 \uparrow\uparrow n = 1\)
- Hyper-E: E0
- Hayden's Array Notation: a()b = 1
As a cash denomination[]
Some currencies, such as the Ghanaian cedi and the United States dollar, have banknotes with this number in the denomination. Likewise, some currencies, such as the euro, the Israeli new shekel and the pound sterling, have coins with this number in the denomination.
Sources[]
- ↑ Saibian, Sbiis. Very Small Very Large Numbers. Retrieved January 2013.
- ↑ https://sites.google.com/d/10rdtjem0y_0xH7Xenq5b0Ni2qIQPNXxE/p/13D2BhwKrg7f-UWOV6Zf-av2M9Th5Yt2X/edit Retrieved 2024-08-04.
See also[]
Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · garmillion · gargoogol · gareceton · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzthirty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex · megafugagrangol
Extensions:
Booga-:: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag-:: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex