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I read something interesting about the so-called Graham's number.
The number is a well-defined finite integer which is used in a serious
proof of a mathematical problem, so it's not an artificially created one
(in other words, the number came up when estimating the upper bound of
that mathematical problem).
The number is so large that the entire observable universe would not be
large enough to write it down, even if each written digit has the size of
one Planck volume.
Moreover, the amount of digits in Graham's number is so large, that the
entire observable universe is not big enough to likewise write down this
amount.
Even the amount of digits in this amount is likewise too large.
The amount of such recursions you need to do before you get to a number
which would fit in the observable universe (which is obviously a finite
amount because the number is a finite integer) is so large that this amount
wouldn't fit inside the observable universe.
A somewhat large number indeed.
--
- Warp
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On 07/01/2011 12:15 PM, Warp wrote:
> I read something interesting about the so-called Graham's number.
>
> A somewhat large number indeed.
Required XKCD quote: http://xkcd.com/207/
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Warp <war### [at] tag povrayorg> wrote:
> I read something interesting about the so-called Graham's number.
>
> The number is a well-defined finite integer which is used in a serious
> proof of a mathematical problem, so it's not an artificially created one
> (in other words, the number came up when estimating the upper bound of
> that mathematical problem).
>
> The number is so large that the entire observable universe would not be
> large enough to write it down, even if each written digit has the size of
> one Planck volume.
>
> Moreover, the amount of digits in Graham's number is so large, that the
> entire observable universe is not big enough to likewise write down this
> amount.
>
> Even the amount of digits in this amount is likewise too large.
>
> The amount of such recursions you need to do before you get to a number
> which would fit in the observable universe (which is obviously a finite
> amount because the number is a finite integer) is so large that this amount
> wouldn't fit inside the observable universe.
>
> A somewhat large number indeed.
>
> --
> - Warp
"Graham's number bottles of beer on the wall, Graham's number bottles of beer,
take one down - pass it around..."
C'mon everyone sing now! ;-)
Best Regards,
Mike C.
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On 07/01/2011 2:14 PM, Mike the Elder wrote:
> "Graham's number bottles of beer on the wall, Graham's number bottles of beer,
> take one down - pass it around..."
>
> C'mon everyone sing now!;-)
>
:-P
--
Regards
Stephen
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On 07/01/2011 02:14 PM, Mike the Elder wrote:
> Graham's number bottles of beer on the wall
Not in /this/ universe. Perhaps you missed it; they wouldn't fit. Not
all of them, anyway. (And even if they did, think of the gravitational
pull...)
Not to mention that by the time you get to, say,
g64 - 516 056 140 516 705 656 487 915 031 530 479 870 231 501 654 987
409 651 068 406 540 684 065 408 940 687 651 301 597 504 664 298 400 295
740 804 918 510 587 096 738 160 941 406 849 849 702 980 417 923 159 405
940 456 478 941 054
you might get tired of singing it. :-P
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Warp wrote:
> I read something interesting about the so-called Graham's number.
I had known it was large, but I never really appreciated how large before. Wow.
--
Darren New, San Diego CA, USA (PST)
Serving Suggestion:
"Don't serve this any more. It's awful."
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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> > I read something interesting about the so-called Graham's number.
> I had known it was large, but I never really appreciated how large before. Wow.
Amusingly, the currently-known lower bound for that problem (for which
the Graham number is the upper bound) is 13.
Quite a range.
--
- Warp
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On 07/01/2011 06:58 PM, Warp wrote:
> Amusingly, the currently-known lower bound for that problem (for which
> the Graham number is the upper bound) is 13.
>
> Quite a range.
I'd ask what the error percentage is - but I'm guessing the answer won't
fit in the known universe...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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