# Googol

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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.

## History Edit

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.

## Properties Edit

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]

## Size Edit

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.[6]

A cube with edge length 35mm contains about a googol Planck volumes.[7]

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 notations Edit

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 impact Edit

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.[8]

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