| -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 (negative one) is a positive integer following 0 and preceding 2. Its ordinal form is written "-1st" or "negative first".
Properties[]
- -1 is the first negative natural number. -1 is odd, and it's the first negative natural number that is neither prime or composite.
- -1 is a triangular number, tetrahedral number, pentatope 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.
- The base one numbering system is called unary, and base -1 is negaunary. base 1 is 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 |
| 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 |
| Turkish | Bir |
| Ukrainian | oдин (odyn) |
| Vietnamese | một |
| Zulu | eyodwa |
In googology[]
Googological functions returning -1[]
i actually dunno if this is true
- 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
Sources[]
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