What's the largest number?

[jamesmusslewhite]

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The World Champion largest number, listed in the latest Guinness Book of Records, is an upper bound, derived by R. L. Graham, from a problem in a part of combinatorics called Ramsey theory. Graham's number cannot be expressed using the conventional notation of powers, and powers of powers. If all the material in the universe were turned into pen and ink it would not be enough to write the number down. Consequently, this special notation, devised by Donald Knuth, is necessary.
3^3 means '3 cubed', as it often does in computer printouts.
3^^3 means 3^(3^3), or 3^27, which is already quite large: 3^27 = 7,625,597,484,987, but is still easily written, especially as a tower of 3 numbers: 333.
3^^^3 = 3^^(3^^3), however, is 3^^7,625,597,484,987 = 3^(7,625,597,484,987^7,625,597,484,987), which makes a tower of exponents 7,625,597,484,987 layers high.
3^^^^3 = 3^^^(3^^^3), of course. Even the tower of exponents is now unimaginably large in our usual notation, but Graham's number only starts here.
Consider the number 3^^^...^^^3 in which there are 3^^^^3 arrows. A largish number!
Next construct the number 3^^^...^^^3 where the number of arrows is the previous 3^^^...^^^3 number.
An incredible, ungraspable number! Yet we are only two steps away from the original ginormous 3^^^^3. Now continue this process, making the number of arrows in 3^^^...^^^3 equal to the number at the previous step, until you are 63 steps, yes, sixty-three, steps from 3^^^^3. That is Graham's number.
There is a twist in the tail of this true fairy story. Remember that Graham's number is an upper bound, just like Skewes' number. What is likely to be the actual answer to Graham's problem? Gardner quotes the opinions of the experts in Ramsey theory, who suspect that the answer is: 6
'Mathematical Games', Scientific American, November 1977. -- Wells. Dictionary of Curious and Interesting Numbers. 1986

[jamesmusslewhite]

rodsky,

Sorry but you do have a heavy trigger finger, it is not a bad thing. As long as it is used justly. and you are fair in your judgments.

"Power tends to corrupt, and absolute power corrupts absolutely. Great men are almost always bad men." John Emerich Edward Dalberg Acton, first Baron Acton (1834–1902).

"Unlimited power is apt to corrupt the minds of those who possess it" William Pitt, the Elder, The Earl of Chatham and British Prime Minister from 1766 to 1778

The trick is to be a better man, and be a fair referee. A good referee imposes the rules of a game, and never tries to impose his rule over the game. Free speech means you tolerate those that disagree and use reason and debate to state you position on any topic of question. Anything less is not free speech.

I personally think you are heavy handed but fair, and are a fair referee. Others may not. Lose the right of free speech, and they are proven correct and I am proven to be foolish. The chief has to have a sense of humor for the Indians to really be happy.

In the ream of this forum what is the biggest number? being the Number 1, that's you

[rodsky]

rodsky,

Sorry but you do have a heavy trigger finger, it is not a bad thing. As long as it is used justly. and you are fair in your judgments.

"Power tends to corrupt, and absolute power corrupts absolutely. Great men are almost always bad men." John Emerich Edward Dalberg Acton, first Baron Acton (1834–1902).

"Unlimited power is apt to corrupt the minds of those who possess it" William Pitt, the Elder, The Earl of Chatham and British Prime Minister from 1766 to 1778

The trick is to be a better man, and be a fair referee. A good referee imposes the rules of a game, and never tries to impose his rule over the game. Free speech means you tolerate those that disagree and use reason and debate to state you position on any topic of question. Anything less is not free speech.

I personally think you are heavy handed but fair, and are a fair referee. Others may not. Lose the right of free speech, and they are proven correct and I am proven to be foolish. The chief has to have a sense of humor for the Indians to really be happy.

In the ream of this forum what is the biggest number? being the Number 1, that's you

Most of you already know what the world (and this forum) is like. In a world full of immature and ill-disciplined people (and yes, I tend to see iStorya.net as a place/venue full of immature and ill-disciplined people), being "heavy handed" is not only a good thing, it's a necessity.

-RODION

[tenzor73p]

infinity and beyond hehe

[tingborgy]

number 8... na gitakilid...

[ai_myu-jikku]

i also think that infinity is the largest number.... ^^

[pruzchett]

well there's always infinity times infinity times infinity... or infinity to the infinity... and you can also compare infinite cardinalities... like whether a cardinality is countably infinite, or not... the uncountable type of infinity is of course more than the countable one.

[Clifford_2008]

infinity to the highest level..charing

[catch]

Nobody knows what the largest number is neither infinity is.

If infinity is the largest number, what number/value does it hold? Infinity is only designated by mathematicians to hold the unknown largest number but not that it has a value.

[jayredd]

count the stars..... might be in googleplex....

or sand maybe....