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World Champion Largest Number - Graham's Number (instant headache!)
The Penguin Dictionary of Curious and Interesting Numbers (book) ^ | 1986 | David Wells

Posted on 11/28/2022 1:43:52 PM PST by ProtectOurFreedom

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. David Wells, Dictionary of Curious and Interesting Numbers. 1986



TOPICS: Hobbies; Reference; Science; Weird Stuff
KEYWORDS: big; busybeavernumber; davidwells; donaldknuth; eliezersyudkowsky; geeks; grahamsnumber; greatbignumber; jeromebarkley; knuth; math; numbers; rlgraham; skewesnumber
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As long as we are discussing the Maricopa County vote tabulations here and here, I thought it would sensible to discuss IMPOSSIBLY BIG NUMBERS in the context of Dem voting crimes.
1 posted on 11/28/2022 1:43:53 PM PST by ProtectOurFreedom
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To: ProtectOurFreedom

(G+1)


2 posted on 11/28/2022 1:45:55 PM PST by Scrambler Bob (My /s is more true than your /science (or you might mean /seance))
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To: Scrambler Bob

Infinity - 1


3 posted on 11/28/2022 1:46:45 PM PST by Scrambler Bob (My /s is more true than your /science (or you might mean /seance))
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To: Scrambler Bob

It’s weird the author didn’t discuss that. “G+1” would appear to be the number of fraudulent manufactured “D” votes in Maricopa County. We could call it G + MC.


4 posted on 11/28/2022 1:47:59 PM PST by ProtectOurFreedom (If you're not part of the solution, you're just scumming up the bottom of the beaker!)
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To: Scrambler Bob

3^3^...^3 + 1


5 posted on 11/28/2022 1:50:45 PM PST by Seaplaner (Never give in. Never give in. Never, never, never...in nothing, great or small...Winston Churchill)
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To: ProtectOurFreedom

Talking about the federal budget?


6 posted on 11/28/2022 1:51:33 PM PST by Larry Lucido (Donate! Don't just post clickbait!)
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To: ProtectOurFreedom

Good. I couldn’t sleep last night worrying about how we’re going to represent the number if dollars needed to buy a loaf of bread after 4 years of biden.


7 posted on 11/28/2022 1:52:10 PM PST by I want the USA back (Our news media isn't worth camel spit. Neither is the democrat party. )
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To: ProtectOurFreedom

Isn’t this the number of votes Trump claims he was robbed of in 2020?


8 posted on 11/28/2022 1:54:37 PM PST by PatriotarchyQ
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To: ProtectOurFreedom
Donald E Knuth.

There are a lot of very smart people in this ole world, but Dr Knuth stands above them.

There may be some that are called "smarter" but in terms of applied math and science, he is way, way up there.

Yes, the same Dr Knuth that wrote the massive Art of Computer Programming way back in 1973.

9 posted on 11/28/2022 2:04:58 PM PST by texas booster (Join FreeRepublic's Folding@Home team (Team # 36120) Cure Alzheimer's!)
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To: ProtectOurFreedom
"Oh Deep Thought - Give us the ultimate answer to life the universe and Everything!"

> 42 <


10 posted on 11/28/2022 2:07:33 PM PST by GaltAdonis
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To: ProtectOurFreedom
Compared to Rayo's Number, Graham's number can be counted on your fingers.

For details see Prof. Tony Padilla's explanation in The Daddy of Big Numbers (Rayo's Number) on YouTube.

11 posted on 11/28/2022 2:07:44 PM PST by Carl Vehse (A proud member of the LGBFJB community)
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To: ProtectOurFreedom

So what’s the point? Not enough material in the universe to write the number. How is it relevant to anything if it can’t be used? Get a life.


12 posted on 11/28/2022 2:09:28 PM PST by Fungi
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To: PatriotarchyQ

“Claims”???

It’s a proven fact.


13 posted on 11/28/2022 2:18:29 PM PST by ProtectOurFreedom (If you're not part of the solution, you're just scumming up the bottom of the beaker!)
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To: Fungi

“Get a life”??

I’ve proven fraud in Maricopa County and you tell me to “get a life”?


14 posted on 11/28/2022 2:19:33 PM PST by ProtectOurFreedom (If you're not part of the solution, you're just scumming up the bottom of the beaker!)
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To: All

George Cantor territory!


15 posted on 11/28/2022 2:24:24 PM PST by Reily
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To: Seaplaner

3^3^...^3 + 1

Yes.

What is

4^4^...^4


16 posted on 11/28/2022 2:41:15 PM PST by Scrambler Bob (My /s is more true than your /science (or you might mean /seance))
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To: Fungi

Not enough material in the universe to write the number.
= = =

Start with those Chinese blank sheets of paper.


17 posted on 11/28/2022 2:42:46 PM PST by Scrambler Bob (My /s is more true than your /science (or you might mean /seance))
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To: Scrambler Bob

Thanks. My computer just caught fire.


18 posted on 11/28/2022 3:08:56 PM PST by Seaplaner (Never give in. Never give in. Never, never, never...in nothing, great or small...Winston Churchill)
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To: Seaplaner

Good Laugh.

Say, can we tweet that number to our adversaries’ computers?

Or send it in an e-mail to the DNC?

Or put it in my browser history for the FIB to find!


19 posted on 11/28/2022 3:15:29 PM PST by Scrambler Bob (My /s is more true than your /science (or you might mean /seance))
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To: ProtectOurFreedom

Tree (3) is larger than Graham’s Number.


20 posted on 11/28/2022 3:20:20 PM PST by Drew68 (Ron DeSantis for President 2024)
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