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# Which whole number is so large it can never be written out in full?

Question #35681. Asked by riotgrrl. (Jun 30 03 1:00 PM)

mochyn

GOOGOLPLEX

http://whatis.techtarget.com/definition/0,,sid9_gci213798,00.html

 Jun 30 03, 1:17 PM
sequoianoir

It is 1 followed by a googol of zeros!
How and why.

Quote:

Words of wisdom are spoken by children at least as often as by scientists. The name 'googol' was invented by a child (Dr Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested 'googol' he gave a name for a still larger number: 'Googolplex'. A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr Einstein, simply because he had more endurance. The googolplex then, is a specific finite number, with so many zeros after the 1 that the number of zeros is a googol. A googolplex is much bigger than a googol, much bigger even than a googol times a googol. A googol times a googol would be 1 with 200 zeros, whereas a googolplex is 1 with a googol of zeros. You will get some idea of the size of this very large but finite number from the fact that there would not be enough room to write it, if you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way.

-- Kasner and Newman. Mathematics and the Imagination. 1940

 Jun 30 03, 1:19 PM
elizabethmc

What about googolplex to the power of googolplex?

 Jun 30 03, 1:27 PM
riotgrrl

Correct! I found this interesting stuff on incredibly large numbers: http://www.newscientist.com/lastword/article.jsp?id=lw77

"...a googolplex, which is 10 to the power of a googol. A googolplex is in fact the same size as the number of possible games of chess. But the largest number ever needed to solve a genuine problem (in pure mathematics) is a number called Skewes' number, which appears in a branch of maths called number theory. This number is stated as 10^(10^(10^34)) [10^10 means the same as 10 to the power 10] and is almost impossibly large to describe. The best I can do is to say it is not quite as large as 10 to the power of a googolplex.

Graham's number, used in a part of combinatorics called Ramsey theory, is so large that a new number notation system had to be introduced to define it. Apparently, if all the material in the Universe were turned into writing materials it would not be enough to write the number down."

 Jun 30 03, 1:49 PM
fosse4

Surely there can't be an answer to this one as any number however large can be made bigger by adding one!

 Jun 30 03, 4:19 PM
sequoianoir

fosse4, you've missed the point.
It's not that this is the largest number that can be, since that is "infinite" and a googolplex is indeed a finite number (and can have 1 added to it) BUT that you cannot actually write this number down (except in shorthand form) since the universe is not large enough.
I understand that there are not a googloplex of atoms in the universe which is why it would be rather difficult to write it down!

 Jun 30 03, 5:13 PM
Baloo55th

So if a googolplex is so large it can't be written, but can have 1 added to it, why can't we add 2 to it? Or even a googol to it? Or, heaven forbid, multiply it? Why don't we redefine riotgrrl's question (with apologies to her) and ask what is the largest number that CAN be written down? Then that plus anything will be the answer to her original question. (I know what I'm talking about, even if no-one else does!)

 Jun 30 03, 5:34 PM
sequoianoir

A googolplex is the name of a whole number that cannot be written down.
A googolplex+1 has no specific name of itself - it is just a number.
Also, if PI is ever calculated to a googolplex of decimal places, then you would still have the same problem.

 Jun 30 03, 5:42 PM