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1 (one) is a positive integer following 0 and preceding 2. Its ordinal form is written "1st" or "first."
Black-dot-1

Visualization of 1

Properties Edit

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, etc. A square number, cubic 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.

By definition 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.

In other languages Edit

Language Name
Afrikaans een
Bosnian, Croatian jedan
Bulgarian един (edin
Catalan, French un
Chinese 一 (yī)
Czech, Slovak, Polish jeden
German eins
Italic, Spanish uno
Japanese いち (ichi)
Latvian viens
Macedonian, eден (eden)
Russian один (odin)
Serbian jедан (jedan)
Slovenian ena
Ukrainian oдин (odyn)
Zulu eyodwa

In googology Edit

Sbiis Saibian argued that all numbers larger than 1 should be called "large numbers," because the reciprocals of large numbers are small.[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, obviously, also cannot exist.

1 was also the first number by Adam Elga in the Big Number Duel.

1 can be named garone, fzone, fugaone, megafugaone, or boogaone with the gar-, fz-, fuga-, megafuga-, and booga- prefixes respectively.

Googological functions returning 1 Edit

As a cash denomination Edit

OneDollarBill

U.S. one dollar bill.

Some currencies, such as the Ghanaian cedi and the United States dollar, have banknotes with this number in the denomination.

Some currencies, such as the euro and the pound sterling, have coins with this number in the denomination.

Sources Edit

  1. Saibian, SbiisVery Small Very Large Numbers. Retrieved January 2013.

See also Edit

Numbers named with the fuga- family of prefixes

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gargoogolplex
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fzeleven · fztwenty · fzhundred · fzgoogol · fzmillion · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaseven · boogaeight · booganine · boogaten · boogahundred · boogagoogol · boogagoogolplex