1

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 , and it's the only natural number that is neither prime nor composite.
*1 is a , , , etc. It's also a , 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 .
*1 is the only known odd .
*The base one numbering system is called , as demonstrated by the video below:
thumb|center|300 px1 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 ==
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". 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.
 coined post-nothingness for this number,https://sites.google.com/d/10rdtjem0y_0xH7Xenq5b0Ni2qIQPNXxE/p/13D2BhwKrg7f-UWOV6Zf-av2M9Th5Yt2X/edit Retrieved 2024-08-04. 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 and the , have banknotes with this number in the denomination. Likewise, some currencies, such as the , the and the , have coins with this number in the denomination.
==Sources==
==See also==
zh:一
cs:1
es:1
Category:Numbers
Category:Banknote denominations
Category:Class 0
Category:Coin denominations
Category:Factorial numbers
Category:Fibonacci numbers
Category:Numbers 0-99
Category:Odd numbers
Category:Prime powers
Category:Primorial numbers
Category:Gar-
Category:Fz-
Category:Fuga-
Category:Megafuga-
Category:Numbers with 1 to 2 digits
Category:Numbers named with the fuga- family of prefixes