[unreality]

if you want to participate, send me a message by 6 pm Eastern Standard Time (UTC -5) tomorrow (wednesday may 26).

Title your message something along the lines of "LPI contest" or whatever.

The body of the message can be no longer than 100 characters. A character if you don't know is a single instance of keyboard input, such as a number, letter, space, pound symbol, etc. These are the only characters you can use in your message:

0123456789.,( )+-*/^!%\

^ = exponent (raise the thing directly to the left to the power of the thing directly to the right; ie, 4*5^6*7 is equal to 28 * (5^6). If you wanted the 4*5 unit to be raised, you would need to surround it in parentheses, that's how the order of operations works).

! = factorial (0! = 1 and n! = n * (n-1)!, only valid for positive integers)

\ = integer division, ie, divide and truncate. The goal is for your number to be a positive integer; it will be invalid otherwise

% = modulus. The remainder function. Not sure why you would want to use this but there you go.

Anyway, remember, you only have 100 characters to express your number. You can't use pre established mathematical constants like Graham's number or whatever.

Good luck!

P.s. I may need help with the mathematics figuring out what is the biggest, if it comes to that, so also tell me in your PM if you're good at math haha

[peace*out]

what are you trying to say in the message? if we want to write a # we can just write that #. do we HAVE to use all those characters above?

[unreality]

what are you trying to say in the message? if we want to write a # we can just write that #. do we HAVE to use all those characters above?

the highest number you can get with pure numbers in 100 characters is 100 9's in a row (which is equal to 10^100 - 1). You can go higher using multiplication, exponentiation, etc

[peace*out]

so would it be 100 characters using ^*/...yah. or would it be 100 characters if the number was drawn out

[unreality]

so would it be 100 characters using ^*/...yah. or would it be 100 characters if the number was drawn out

no 100 characters including usage of binary operators like +,-,/,*,^,etc. The actual number it creates could be too large for an efficient representation as actual digits

[peace*out]

*hopefully* last question: is the goal to make the biggest number?

[unreality]

*hopefully* last question: is the goal to make the biggest number?

there is no objectively biggest number, but yes the goal is to make a number that's bigger than anyone else's

[Guest]

So, to clarify:

*What you send in is a mathematical statement that is less than or equal to 100 characters long; including all numbers, operators, and parentheses

*The goal is to have the answer to the mathematical equation be a higher number than anyone else's

I've sent mine in, I hope you can read through all the parentheses. And I hope you can figure out a way to do the math, I tried putting mine in my calculator and I got an overload error.

[Guest]

Apparently, most people aren't very confident in their ability to create large numbers. But that's okay, they're probably right.

[Glycereine]

Apparently, most people aren't very confident in their ability to create large numbers. But that's okay, they're probably right.

I'm just modest

[Framm 18]

Apparently, most people aren't very confident in their ability to create large numbers. But that's okay, they're probably right.

I am very confident that my number is very large, I also know my what my math skills are like.

[unreality]

okay I have them all in but wasn't able to check til tonight, I need to get to bed (only a couple days of school left ) but tomorrow I'll start the hardest part of this whole thing, which is figuring out which numbers are actually bigger haha.

[unreality]

also check this out http://www.scottaaronson.com/writings/bignumbers.html

[unreality]

thanks to everyone who submitted an entry! I received seven:

 Gmaster:

 99999999999999999999999999999999999999999999999999!^999999999999999999999999999999999999999999999999


 harvey45:

 999999999^(((99999!^(((9999!^(9999!^(9999!^(9999!^(9999!^(9999!^(9999!^(9999!^9999!))))))))!)!))!)!)


 MissKitten:

 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!


 Glycereine:

 ((((((((((((((((((((((((9^99)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9


 Framm 18:

 (99999999999999999999999999999999999999999999999!)^999999999999999999999999999999999999999999999999!


 LJayden:

 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!


 dawh:

 (9999999999999999999999^999999999999999999999999^999999999999999999999999^999999999999999999999999)!


mine:

 9!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

now it's time to figure out which one is the biggest. These can't exactly be plugged into a calculator, but I think we'll be able to analyze them side by side, eliminating smaller numbers, until we have a winner.

Also, Miss Kitten and LJayden both submitted the same thing so we can call that one "MissJayden" haha and they can win or lose together.

Anyway, here are some notes that could be useful:

* n! will always be less than n^n

* for large values of n! we might be able to make some approximations using the Gamma function

* smaller exponentials can be calculated, like 9^99 = 2.951 x 10^94

* framm's can be shortened to (10^47 - 1)! ^ (10^48 - 1)!

* gmaster's can be shortened to (10^50 - 1)! ^ (10^47 - 1)

I think we can ascertain that framm's is larger than gmaster's. Yes gmaster's exponential base is about 1000 times bigger, but framm's is raised to the power of something at the very least 10 times bigger and at the most (10^48)^(10^48) times bigger but somewhere in between.

Does anyone disagree that gmaster can be eliminated?

That doesn't mean we have to eliminate gmaster from using his to eliminate others that might be smaller than his (which would then be smaller than framm's), but so far at least we have established the inequality:

Framm > Gmaster

and yes this part will be the hardest part of the game I'm definitely going to need help doing this so if you want to pitch in be my guest, I have to go for a bit though

[Gmaster479]

I think I am gone, Framm's is bigger because it seems I can't to count to 100 digits .

I would think that either dawh or Glycerine has it. Both of them use powers on top of powers, which based on the article seems to make the biggest number. The question becomes whether more exponents or more numbers with fewer exponents wins it.

[Glycereine]

My reasoning for my route may or may not help you determine... What I did was see how many characters it took to raise to another power (it takes 4, ()^9).

Then I tried to determine if there was any other modification I could make that would increase the number more. I determined that raising a number to 99999 was less than having it raised to 9 then raised to 9 again. However without a program to calculate this I don't really know how to show it in the long run vs something like dawh's or harvey's.

Also I wouldn't count out the factorals yet... unreality's is going to be a bastard of a large number as well.

[Guest]

My reasoning for my route may or may not help you determine... What I did was see how many characters it took to raise to another power (it takes 4, ()^9).

Then I tried to determine if there was any other modification I could make that would increase the number more. I determined that raising a number to 99999 was less than having it raised to 9 then raised to 9 again. However without a program to calculate this I don't really know how to show it in the long run vs something like dawh's or harvey's.

Also I wouldn't count out the factorals yet... unreality's is going to be a bastard of a large number as well.

I think that based on the article, your number would be clearly larger than mine (since higher levels of exponentiation seem to increase faster), if I hadn't thrown in the factorial at the end. As the article doesn't address factorial growth, I'm not sure how it compares. I figured that with the three characters it took to do a group factorial ( ()! ), that would be larger than adding a couple '9's or an exponent somewhere else in the sequence. I think that yours would have been larger for certain if you hadn't forcibly inverted the tetration ( ) with those parentheses. If you had let the exponents do the work for you, I think it would be hard to beat.

Harvey's seems pretty large too.

[peace*out]

what does "!" mean?

[Glycereine]

what does "!" mean?

! is a factoral, meaning the number is multiplied by all numbers (integers) less than it down to 1.

so 3! is 3*2*1

10! is 10*9*8*7*6*5*4*3*2*1

[unreality]

using this as a reference: http://en.wikipedia.org/wiki/Factorial

"As n grows, the factorial n! becomes larger than all polynomials and exponential functions (but slower than double exponential functions) in n."

That's not that helpful for the crazy stuff we've got here but from some of the information following that I realized that we can use logarithms. It's true that for positive numbers, if a > b then log(a) > log(b)

for example, to confirm that Framm > Gmaster....

gmaster => 999999999999999999999999999999999999999999999999 * log(99999999999999999999999999999999999999999999999999!)

framm => 999999999999999999999999999999999999999999999999! * log (99999999999999999999999999999999999999999999999!)

now divide both sides by 10^48 - 1

gmaster => 1 * log(99999999999999999999999999999999999999999999999999!)

framm => 999999999999999999999999999999999999999999999998! * log (99999999999999999999999999999999999999999999999!)

Taking the log of gmaster's factorial, we can express the upper bound of his factorial as (10^50 - 1)^(10^50 - 1). The log of that makes this:

gmaster => 1 * (10^50 - 1) * log(10^50 - 1) = about 50*(10^50)

now if we follow through on the log for framm, we express framm's upper bound as (10^47 - 1)^(10^47 - 1).

framm => 999999999999999999999999999999999999999999999998! * (10^47 - 1) * 47

divide both gmaster and framm's by about 10^47 and we get

gmaster = 50*1000 = 50,000

framm = 999999999999999999999999999999999999999999999998! * 47

I think that confirms that Framm's is higher than Gmaster's.

Using logs (or maybe even repeated logs) we can probably solve a lot of these

[unreality]

I have just received a new entry, from plainglazed:

((((((((((((((((((((((((9!^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^9)^99!)

[Glycereine]

This one would have beat mine for certain (9! is better than 99) except for the way it ended.

because you need 4 characters for every ()^9 except for the first 3 characters to start 9^9. so a base of 9!^9 instead of 99^9 would have beaten mine.

However 2 characters were wasted on an opening and ending parenthesis that could have been another ()^9 instead of (9!)

[Guest]

Can't you just put 10 and 98 !'s?

Because 10! is about 3.2 million and the number would just get infinitely bigger

[unreality]

Can't you just put 10 and 98 !'s?

Because 10! is about 3.2 million and the number would just get infinitely bigger

yes but mine would be bigger because 9! is bigger than 10, after that it follows the same pattern.

But I realized that 9^9 > 9! (guaranteed) so repeated exponentation would trump repeated factorials if there were a same number

[Glycereine]

yes but mine would be bigger because 9! is bigger than 10, after that it follows the same pattern.

But I realized that 9^9 > 9! (guaranteed) so repeated exponentation would trump repeated factorials if there were a same number

The question is... is 9!! or 9^9 more.

And the answer is that 9!! is A LOT more.

so unreality's trumps mine (and I think mine was the largest of the exponent based approaches)

[Glycereine]

You can eliminate me based on above.

Also you can eliminate MissKitten and Jayden based on:

99 is less than 9! (again by a lot), so front-loading 9's is nowhere near as effective as back-loading !'s.