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Googolplex^Googolplex^Googolplex^Googolplex^Googol plex^Googolplex^Googolplex^Googolplex^Googolplex^G oogolplex^Googolplex^Googolplex^Googolplex^Googolp lex^Googolplex^Googolplex^Googolplex^Googolplex^Go ogolplex^Googolplex^Googolplex^Googolplex^Googolpl ex^Googolplex^Googolplex^Googolplex^Googolplex^Goo golplex^Googolplex^Googolplex^Googolplex^Googolple x^Googolplex^Googolplex^Googolplex^Googolplex^Goog olplex^Googolplex^Googolplex^Googolplex^Googolplex ^Googolplex^Googolplex^Googolplex^Googolplex^Googo lplex^Googolplex^Googolplex^Googolplex^Googolplex^ Googolplex^Googolplex^Googolplex^Googolplex^Googol plex^Googolplex^Googolplex^Googolplex^Googolplex^G oogolplex^Googolplex^Googolplex^Googolplex^Googolp lex^Googolplex^Googolplex^Googolplex^Googolplex^Go ogolplex^Googolplex^Googolplex^Googolplex^Googolpl ex^Googolplex^Googolplex^Googolplex^Googolplex^Goo golplex^Googolplex^Googolplex^Googolplex^Googolple x^Googolplex^Googolplex^Googolplex^Googolplex^Goog 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ogolplex^Googolplex^Googolplex^Googolplex^Googolpl ex^Googolplex^Googolplex^Googolplex^Googolplex^Goo golplex^Googolplex

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You could hold down Ctrl+V until the last stars in the Milky Way flicker out and die, until even the remnant white dwarfs have faded to black, and you still wouldn't even come close.

To illustrate:

A googolplex is 1010100, which is less than 10101010

So a "power tower" of x googolplexes, what you're doing, is less than a tower of 4x tens.

That tower of tens can be written much more concisely as 10↑↑4x.

Now consider that if I write 10↑↑↑10, that expands to 10↑↑(10↑↑10). The bit in the brackets in brackets is already bigger than a googolplex, which means 10↑↑↑10 is a tower of well over a googolplex of tens. And remember there's not even a googol, never mind a googolplex, of atoms in the observable universe.

Now remember that my h1 on the last page has not three arrows but ten, and that's just the beginning of the hn series.

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New rule:

A word that represents a number count as one number digit. (Hopefully we don't see plenty of Googolplexes around.)

So 3.5 is not bigger than 3?

Sorry. I mean the number has to be 0.-infinite-1 greater than the previous number.

Even the googolplex walls and the Graham's number abuses are emphatically finite.

/grumblegrumblegrumble

Sorry, but you have to grumble for this case. I'll let Googolplex (10^10^100) go for the sake of this, but the number of digits in Graham's number is far too numerous to contend with and thus is considered transfinite (even Graham doesn't know the first digit). There are other numbers besides Graham's number and Googolplex, such as Skewe’s numbers (10^10^10^963 at the largest) and Poincare Recurrence time (10^10^10^10^10^1.1).

Let's reset due to this rule change.

Googolplex.

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googolplexgoogolplexgoogolplexgoogolplexgoogolplexgoogolplexgoogolplexgoogolplexgoogolplexgoogolplex

edit: to be precise for people with better eyes (aka they still can't see it) thats exactly 10 googolplexes

Edited by Nemrav
googol not google
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1310. Equivalent to 1010..10 with 13 levels.

Demonstration of biggerness:

Googolplex = 1010100 < 10101010

Googolplexgoogolplex = 101010100 < 1010101010 (Hurray for Wolfram Alpha :) )

More generally ngoogolplex < n+310

Really illustrates how much MOAR LEVELS in power towers outdoes bigger numbers in those levels.

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New Notation: Op(x)

Utilization: a Op(x) b

Where Op(x) refers to a mathematical operator (ie addition, multiplication, etc)

So:

Op(1) -> addition

Op(2) -> multiplication

Op(3) -> exponents

Op(4) -> tetration

Etc.

So, I give you:

Googoplex Op(42) Googolplex

Or, Googolplex Op(43) 2.

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To be honest a definition of a number in a programming language won't be that different to the mathematical or English-language definition of the same number.

Oh, and 10^^10^^10.0001

EXCEPTION:


x = 1
def Double(x):
x = x*2
return x
while True:
x = Double(x)

Not 100% sure that that would actually work, but I hope I fulfilled my purpose.

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OK, looks like there's a mess here.

For rule #2a: Transfinite numbers are numbers that don't have known number of digits or can't be expressed via an expression. Graham's number has no known number of digits so it is transfinite. But Poincare Recurrence Time isn't because it can be expressed via an expression. Also the Java double rule has been removed, so you can go as high as you can, but you are still limited to 10 number digits and words that contains specific numbers.

Also... googolplexes are numbers.

The round is reset due to the Rule un-8 violated (the OP clearly said no computer codes).

So...

Poincare Recurrence Time (10^10^10^10^10^1.1) ^Poincare Recurrence Time.

BTW: Three new numbers: Googolplexian (10^Googolplex), Mersenne numbers, and perfect numbers.

Marsenne numbers: 2n - 1 where n is a prime number.

Perfect numbers: 2n-1(2n - 1) where n is a prime number.

For example: The Mersenne number with n = 3 is 7. The perfect counterpart is 28.

Perfect numbers are always larger than their corresponding prime Mersenne numbers.

Edited by Designer225
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Well, that's not the standard definition of "transfinite numbers". Anything that boils to 10x, where x is possibly stupidly large, has a trivially known number of digits - x. /grumblegrumblegrumble

Incidentally, SunJumper's was an alternative way of writing the hyperoperation sequence, or superscripted Knuth's up-arrows. Starwhip's code I grant isn't much like mathematical notation. It may or may not terminate, but in any case can never make x larger than the maximum value of a double, which is something around 10308. If arbitrary-precision arithmetic was used it would not terminate and instead be equivalent to writing infinity, and thus banned.

/wafflewafflewaffle

10PP, where P is that Poincare recurrence time. (Of the observable Universe, I assume.)

Edited by cantab
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Well, that's not the standard definition of "transfinite numbers". Anything that boils to 10x, where x is possibly stupidly large, has a trivially known number of digits - x. /grumblegrumblegrumble

Except, we really don't know how many digits Graham's number really has. (Although we do know how many digits Poincare Recurrence Time has.)

Anyway, Graham's number is no longer prohibited. Transfinite numbers (numbers that are larger than all finite numbers, even Graham's number, but isn't really infinite) are still prohibited.

To make things somewhat easier, I'll stretch more and actually allow codes. (Yup, Rule 8 is up again, as did Rule 3c and 3d.) Just don't make a mess, though.

P^P^P, where P is Poincare Recurrence Time (by the way, this is based on the assumption that history repeats itself).

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