very large finite numbers - another topic

[ixfd64]

http://en.wikipedia.org/wiki/Other_n..._large_numbers

This should be pretty interesting...

I don't think that we'll ever worry about numbers of this size, unless we go into the study of Catalan-Mersenne numbers, etc.

[mfgoode]

The World Champion largest number in the latest Guiness Book of Records is an upperbound by R.L. Graham from a problem part of combinatorics called Ramsey Theory.
http://www-users.cs.york.ac.uk/~susan/cyc/g/graham.htm
An excelent book called the Penguin Dictionary of Curious and interesting numbers 1986 by David Wells is worth reading.
It covers the entire range of imortant numbers from -1 to Grahams number.
Mally

[jinydu]

Yet it's so easy to come up with numbers far larger than Graham's Number... Certainly, their criteria is stricter than that, right?

[akruppa]

Maybe they require the number to have some significance in mathematics, i.e. be used in some proof or be the numerical result of some naturally occuring question (preferably with a stricter definition of "significance" than this one). The thing with Graham's number is that it is the best known upper bound for some constant (I forgot what it was for). Amusingly this upper limit isn't tight by any standards, afair the presumed value for the constant was somewhere in the low double digits.

Alex

[jinydu]

Here's the link:

http://mathworld.wolfram.com/GrahamsNumber.html

[mfgoode]

Originally Posted by akruppa

Maybe they require the number to have some significance in mathematics, i.e. be used in some proof or be the numerical result of some naturally occuring question (preferably with a stricter definition of "significance" than this one). The thing with Graham's number is that it is the best known upper bound for some constant (I forgot what it was for). Amusingly this upper limit isn't tight by any standards, afair the presumed value for the constant was somewhere in the low double digits.

Alex

Grahams number is of practical value as it stems from a problem of combinatiorics called Ramsey Theory.
[Quote:= David Wells]
There is A TWIST inthe tail of this true fairy story. Remember that Graham's number is an upper bound just like Skewe's number. What is likely to be the actual answer to Graham' problem? Gardner quotes the opinions of the experts in Ramsey theory, who suspect that the answer is 6 !! (1986) [Un Quote]
From jinydu's website
["Here, is Knuth's so-called arrow notation. is often cited as the largest number that has ever been put to practical use (Exoo 2003).

In chained arrow notation, satisfies the inequality

(4) {eqn. not come thru. Refer to original website of Mathworld }

Graham and Rothschild (1971) also provided a lower limit by showing that must be at least 6. More recently, Exoo (2003) has shown that must be at least 11 and provides experimental evidence suggesting that it is actually even larger. " ]
Mally

[ixfd64]

A while ago, someone created a thread discussing very large numbers in the real world, excluding mathematics concepts (prime numbers, Graham's number, etc).

http://mersenneforum.org/showthread.php?t=1493

Well, I was looking on the Wikipedia when I found this:

http://en.wikipedia.org/wiki/1_E19_s_and_more

Pretty cool if you ask me.

[mfgoode]

This reminds me of the time an old lady was in the front row listening intently to a world renowned astronomer lecturing on the age of planets.
"And now ladies and gentlemen our planet will last out for another billion years" he said
At that the lady fainted in the front row.
Well she was attended too and soon regained consciousness.
The astronomer went up to her and said "What happened to you? I said the this planet will last out for a billion years!
"Oh my God! replied the old lady. "I thought a million years!"
Mally

[Numbers]

And that reminds me of the time when Sir Thomas Beacham was conducting the London Philharmonic Orchestra at rehearsal of a piece that required a moving cello solo. The principal cellist was a world-renowned player and a very attractive lady. She was playing a Stradivarius cello, an exceptional instrument by any standards. However, Sir Thomas was not pleased with her playing and called the rehearsal to a halt. "Madam," he said, "you have between your legs one of the finest instruments known to man. And all you can do is sit there and scratch it".

[ixfd64]

This guy made up names for very large numbers, most of which are larger than Graham's number.

Most of these terms seem to be neologisms, but are still pretty interesting.

edit: forgot link!

http://hometown.aol.com/hedrondude/scrapers.html

[ixfd64]

http://www.sf.airnet.ne.jp/~ts/langu...rgenumber.html

For those who can read Japanese, could anyone please tell me if this is in wide use? Thanks.