Information About

Googolplex




It can also be written as {10}^{ m googol}, or
:10^{\scriptscriptstyle10\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000}, or as a 1 followed by a Googol (10100) Zeroes . Note that 10^{\,\!10^{100}} is the same as 10^{\,\!(10^{100})} because Exponentiation works from the top down. The term ''googol'' was coined by Milton Sirotta , nephew of Mathematician Edward Kasner . ''Googolplex'' was coined by Kasner to define an especially large number by extension from his nephew's idea.


HOW BIG IS A GOOGOLPLEX?


A googol is greater than the number of Elementary Particle s in the Known Universe , which has been variously estimated from 1072 up to 1087. Since a googolplex is ''one followed by a googol zeroes'', it would not be possible to write down or store a googolplex in Decimal Notation , even if all the matter in the known universe were converted into paper and ink or disk drives.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. to write down a googolplex.

Thus in the physical world it is difficult to give examples of numbers that compare closely to a googolplex. In analyzing in a black hole with a mass roughly equivalent to the Andromeda Galaxy is in the range of a googolplex.

In Pure Mathematics , the magnitude of a googolplex is not as large as some of the specially defined extraordinarily Large Number s, such as those written with Tetration , Knuth's Up-arrow Notation , Steinhaus-Moser Notation , or Conway Chained Arrow Notation . Even more simply, one can name numbers larger than a googolplex with fewer symbols, for example,
:9^{9^{9^{9^{9^9}}}},
is much larger. This last number can be expressed more concisely as {\ ^{6}9} using tetration, or 9\uparrow\uparrow6 using up-arrow notation.

Some , perhaps the largest Natural Number mathematicians actually have a use for.

A googolplex is a huge number that can be expressed compactly because of nested exponentiation. Other procedures (like tetration) can express large numbers even more compactly. The natural question is: what procedure uses the smallest number of symbols to express the biggest number? A shows that for n=6 the busy beaver can write down a number at least as big as 1.29 imes10^{865} {Link without Title} . It is an open question whether the seventh busy beaver can express a googolplex.


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SEE ALSO



EXTERNAL LINKS

  • Who Can Name the Bigger Number? http://www.scottaaronson.com/writings/bignumbers.html

  • Comparing googolplex to numbers similar in size: http://home.earthlink.net/~mrob/pub/math/numbers-15.html#l_p1_1000e100

  • The Biggest Numbers in the Universe: http://www.strangehorizons.com/2001/20010402/biggest_numbers.shtml

  • Known Prime Factor s of googolplex + n (0 <= n <= 999): http://www.alpertron.com.ar/GOOGOL.HTM

  • A googolplex as a compressed file: http://selenic.com/googolplex/

  • Another Googolplex page: http://www.procrastinators.org/googolplex.html

  • A humorous C Program to count to a googolplex: http://www.fpx.de/fp/Fun/Googolplex/

  • The Challenge of Large Numbers http://www.fortunecity.com/emachines/e11/86/largeno.html

  • Googolplex is "inconceivable" but still "describable": http://jimvb.home.mindspring.com/hamlet.htm