A googolplex is the large number 10, or equivalently, 10 or . Written out in ordinary

decimal notation The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of the ...

, it is 1 followed by 10¹⁰⁰ zeroes; that is, a 1 followed by a

googol A googol is the large number 10100 or ten to the power of one hundred. In decimal notation, it is written as the digit 1 followed by one hundred zeros: 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, ...

of zeroes. Its prime factorization is 2 ×5.

History

In 1920, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term ''

'', which is 10, and then proposed the further term ''googolplex'' to be "one, followed by writing zeroes until you get tired". Kasner decided to adopt a more formal definition because "different people get tired at different times and it would never do to have Carnera ea better mathematician than Dr. Einstein, simply because he had more endurance and could write for longer". It thus became standardized to 10^(10¹⁰⁰) = 10^10¹⁰⁰, due to the right-associativity of

exponentiation In mathematics, exponentiation, denoted , is an operation (mathematics), operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication ...

Size

A typical book can be printed with 10 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10 such books to print all the zeros of a googolplex (that is, printing a googol zeros). If each book had a mass of 100 grams, all of them would have a total mass of 10 kilograms. In comparison,

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

's mass is 5.97 × 10 kilograms, the mass of the

Milky Way The Milky Way or Milky Way Galaxy is the galaxy that includes the Solar System, with the name describing the #Appearance, galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars in other arms of the galax ...

galaxy is estimated at 1.8 × 10 kilograms, and the total mass of all the stars in the

observable universe The observable universe is a Ball (mathematics), spherical region of the universe consisting of all matter that can be observation, observed from Earth; the electromagnetic radiation from these astronomical object, objects has had time to reach t ...

is estimated at 2 × 10⁵² kg. To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the mass of the observable universe by a factor of roughly 5 × 10⁴⁰.

In pure mathematics

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as

tetration In mathematics, tetration (or hyper-4) is an operation (mathematics), operation based on iterated, or repeated, exponentiation. There is no standard mathematical notation, notation for tetration, though Knuth's up arrow notation \uparrow \upa ...

, hyperoperation, Knuth's up-arrow notation, Steinhaus–Moser notation, or Conway chained arrow notation.

In the physical universe

In the PBS science program '' Cosmos: A Personal Voyage'', Episode 9: "The Lives of the Stars",

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

and television personality

Carl Sagan Carl Edward Sagan (; ; November 9, 1934December 20, 1996) was an American astronomer, planetary scientist and science communicator. His best known scientific contribution is his research on the possibility of extraterrestrial life, including e ...

estimated that writing a googolplex in full decimal form (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than is available in the known universe. Sagan gave an example that if the entire volume of the

is filled with fine dust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different

combinations In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are t ...

in which the particles could be arranged and numbered would be about one googolplex. is a high estimate of the elementary particles existing in the visible universe (not including

dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...

), mostly photons and other massless force carriers.

Mod ''n''

The residues (mod ''n'') of a googolplex, starting with mod 1, are: :0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 1, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 24, 10, 5, 0, 1, 18, 25, 28, 10, 28, 16, 0, 1, 4, 24, 12, 10, 36, 9, 16, 4, 0, ... This sequence is the same as the sequence of residues (mod ''n'') of a googol up until the 17th position.

References

External links

* * * * {{Large numbers Integers Large integers Units of amount Numbers Large numbers