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Googol is a very well-known large number, equal to 10100 or 1 followed by 100 zeroes.[1]

Coined before 1940, it has become very famous as a generic example of a large number, and is what the field of googology is named after.

## HistoryEdit

The term was coined by Edward Kasner's nine-year-old nephew, Milton Sirotta, some time before 1940. It was first published in a book co-written by Kasner Mathematics and the Imagination. The name was most likely influenced by name of the title character of the American comic strip Barney Google and Snuffy Smith, which was very popular at the time. Barney Google's name was in turn inspired by Vincent Vickers' 1939 children's book The Google Book.

## PropertiesEdit

The googol is equal to ten duotrigintillion in the short scale, or ten sexdecilliard in the long scale.[2] Googol can be expressed as {10,100} in BEAF, or as E100, E100#1, or E2#2 in Hyper-E notation.

Sbiis Saibian has given the alternative name guppyding.[3]

Aarex Tiaokhiao calls this number unoohol, 100-noogol, or booiolplex.[4]

Username5243 calls this number goodolplex, and it's equal to 10[1]10[1]2 in Username5243's Array Notation.[5]

SuperJedi224 calls this number Decigol.[6]

## SizeEdit

There are a mere $$10^{80}$$ elementary particles in the observable universe, so googol has little use when measuring real-world quantities. However. it is still much less than the number of Planck volumes in the observable universe (which is about 10183), so it still has some real-world meaning. Sbiis Saibian showed that a googol particles in a tightly packed sphere would still have a diameter of 5.6 quadrillion meters, or half a light-year.[7]

A cube with edge length 35mm contains about a googol Planck volumes.[8]

Googol is comparable to some numbers produced by combinatorics. For example, 70 factorial (the number of ways 70 distinct objects can be arranged in a row) is about 20% larger than $$10^{100}$$.

A googol seconds is about a sexvigintillion (1081) times the estimated age of the universe. A googol angstroms is approximately 100 trevigintillion light-years.

It takes approximately 317 novemvigintillion years to count to a googol one integer at a time. Counting by googols, half googols, or duotrigintillions, of course, one could count there faster but it is not considered kosher in hide-and-seek or googology.

## Approximations in other notationsEdit

Notation Approximation
Up-arrow notation $$10 \uparrow 100$$ (exact)
Chained arrow notation $$10 \rightarrow 100$$ (exact)
Hyper-E notation $$E100$$ (exact)
Hyperfactorial array notation $$70!$$
BEAF $$\{10,100\}$$ (exact)
Fast-growing hierarchy $$f_2(324)$$
Hardy hierarchy $$H_{\omega^2}(324)$$
Slow-growing hierarchy $$g_{\omega^{\omega^2}}(10)$$ (exact)

## Cultural impactEdit

The definition of googol, googolplex, and similar numbers eventually branched into the field of googology, the study of, nomenclature of, and creation of notations for large numbers.

Larry Page and Sergey Brin, the founders of the Google search engine, named their company after a pun on googol, as their goal is to cache the mass of data that makes up the World Wide Web.[9]

Googology Wiki has a tongue-in-cheek goal to reach 10100 articles.

## SourcesEdit

Googol and related numbers

Saibian's guppy regiment numbers
-minutia group
n-ary numbers with multipliers
Eyelash mite group: eyelash mite-speck · eyelash mite-crumb · eyelash mite-chunk · (binary/ternary/octal)eyelash mite · eyelash mite-bunch · eyelash mite-crowd · eyelash mite-swarm
Dust mite group: dust mite-speck · dust mite-crumb · dust mite-chunk · (binary/ternary/octal)dust mite · dust mite-bunch · dust mite-crowd · dust mite-swarm
Cheese mite group: cheese mite-speck · cheese mite-crumb · cheese mite-chunk · (binary/ternary/octal)cheese mite · cheese mite-bunch · cheese mite-crowd · cheese mite-swarm
Clover mite group: clover mite-speck · clover mite-crumb · clover mite-chunk · (binary/ternary/octal)clover mite · clover mite-bunch · clover mite-crowd · clover mite-swarm
Pipsqueak group: (binary/ternary/octal)pipsqueak
Little squeaker group: (binary/ternary/octal)little squeaker
Small fry group: (binary/ternary/octal)small fry
Guppy group: (binary/ternary/octal)guppyspeck · (binary/ternary/octal)guppycrumb · (binary/ternary/octal)guppychunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)guppy(bit/byte)
Minnow group: (binary/ternary/octal)minnowspeck · (binary/ternary/octal)minnowcrumb · (binary/ternary/octal)minnowchunk · (ternary)minnow(bit/byte)
Goby group: (binary/ternary/octal)gobyspeck · (binary/ternary/octal)gobycrumb · (binary/ternary/octal)gobychunk · (ternary)goby(bit/byte)
Jumbo shrimp group: (binary/ternary/octal)jumbo shrimp
Lightweight group: (binary/ternary/octal)lightweight
Ogol group: (binary/ternary/octal)ogolspeck · (binary/ternary/octal)ogolcrumb · (binary/ternary/octal)ogolchunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)ogol(bit/byte)
Tiny twerpuloid group: (binary/ternary/octal)tiny twerpuloid
Googol group: (binary/ternary/octal)googolspeck · (binary/ternary/octal)googolcrumb · (binary/ternary/octal)googolchunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)googol(bit/byte) · googolbunch · googolcrowd · googolswarm
Eceton group: ecetonspeck · ecetoncrumb · ecetonchunk · ecetonbunch · ecetoncrowd · ecetonswarm
Numbers with base-multipliers
Numbers with -plex