What is the largest number....

[ChrisK]

...that can be represented by three decimal (0-9) digits alone?

[UnklMickey]

(approximately)

196,627,050,475,552,913,618,075,908,526,910,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

[ChrisK]

No,

Exponentiation/powers are hierarchical, the answer is MUCH bigger.

[UnklMickey]

of course.

what i posted was the equivalent of:

(9⁹)⁹

or (9 raised to the 9th ) raised to the ninth.



what would be much larger, would be:

9 raised to the (9 raised to the 9th)


and NO, i'm not gonna multiply that out!

[ChrisK]

Yeppers!

The answer is 369,693,099.631,570,358,743,543,095,095,.......

[ChrisK]

Digits

[ChrisK]

Long.


It's 10^{369,693,099.631,570,358,743,543,095,095,.......}

[UnklMickey]

i have 3 U.S. coins, that add up to $0.35

and one of them is not a nickel.................................

[quarry]

unklmickey said:

i have 3 U.S. coins, that add up to $0.35

and one of them is not a nickel.................................

Cuz "one of them" is a quarter. The other two are nickels!

[wolf]

Chris K
Wouldn't it be better to express the number with the power of 10 being an integer?
Your answer (though correct) doesn't state the actual value of the number. It's analagous to saying that a Stratocaster has 10^.477121255 pickups.
Accurate sure but not very comprehensible to humans.

Okay to evaluate the actual value of the number (or an approximation thereof), we must raise the decimal portion of the number to the power of 10. For simplicity's sake let's just take the first 6 decimal places:
10^.631570 = 4.28124
and so the actual number is approximately:
4.28124 x 10^369693099

[ChrisK]

Indeed.

I kept it at the power of 10 simply to show the significant magnitude of the result. The actual calculation means in full integer form is unavailable for most folk a'planet. I'm not even gonna try to calculate this even in Mathematica.

I got this one from David Wells book "The Dictionary of Curious and Interesting Numbers" from Penguin Books. I've had mine for so long the pages are shedding about.

It's a must have.

[mlrpa]

I collect shiny things!

[JohnH]

If one may be permitted a further non-numeric symbol, then the following is WAY bigger than any of them.

(9^(9^9)!

or (9 raised to the (9 raised to the ninth) factorial

John

[UnklMickey]

johnh said:

...factorial...

okay, you have my interest.

what's that mean? / how does that work?


EDIT: never mind, i looked it up on wikipedia:

en.wikipedia.org/wiki/Factorial


if i understand correctly, then:

(2^(2^2)! = 20922789888000


just to be certain i have this right, could you please post the decimal equivalent for:

(9^(9^9)! =

LSH...


BTW, with a bit of nesting, you can get a number that will make your expression look puny, by comparison.



unk

[JohnH]

Unk yes you have interpreted what I meant. Sorry I had to go to the computer/spreadsheet version of raising to a power (^), since I dont know how to do super-superscripts.

As to the decimal value of my expression, lets just say that it is larger than the number of switched options on a triple-humbucker axe with a six-position varitone, as wired by a demented GuitarNut on a full moon.

cheers

John

[UnklMickey]

okay, so how about this:

(9!^[(9!^9!)!]

but i guess if we go down that path, we could just as easily just use only one nine, and go here:



9!!!!!!!!!!!!!!!!!!!!!!!...

[vonFrenchie]

Here is the REAL question.... would we ever use this number?

[fobits]

Here is the REAL question.... would we ever use this number?

Certainly.

That's the number of years it would take me to play like Jerry Garcia.

[vonFrenchie]

OOOOH! Now it all makes sense!