[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

[Guest]

nice I didn't know it was acceptable to put multiple carats next to each other for other hyper operators (for example google won't accept 3^^2 in its calculator ) But more seriously, nice job!

Here's a question though. If we did "proper notation" for 9!!!!!!...etc and wrapped it in parentheses:

9!)!)!)!)!)!)!)..

with an appropriate number in the beginning, do you think that still beats the other submissions (though not 9<98>9 i'm sure)

1 + x + 2x = 100

1 + 3x = 100

x = 33

If i did that right, it means the proper version of my original submission would be 9 factorialized 33 times (instead of 99).

Wait! We don't need outer parentheses!

So we can save two more digits on the 33rd factorial

9!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!

that's 9 followed by 32 "!)" units and a "!". Hence 1 + 32*2 + 1 = 66

plus the 32 more opening parentheses that need to go in front = 98

((((((((((((((((((((((((((((((((9!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!

the above is 98 characters and represents a 9 factorialized 33 times. But we still have 2 extra characterse

It would be a waste to package another set of parentheses because that would use up what we have left and not change anything. We can't get any more factorial signs out of this. So the only thing I can think to do is:

((((((((((((((((((((((((((((((((999!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!

of course 9 to 999 is no substitute for another factorial, but it's not possible with all the parentheses. So the largest number creatable with just factorials is 999 factorialized 33 times

edit: a better option (but it goes down the slippery slope of the exponents and might as well say "change it all to exponents") but it is to do 9^9 instead of 999

because 9^9 = 387 420 489

but since the next char is "!", does that mean 9^9!.. is that 9 raised to the power of 9! or 9^9 factorialized?

Operational precedence between unbracketed exponents and factorials would be the factorial as it is a unary operator. Unary operators take precendence over dyadic operators. Thus, 9^9! should be evaluated as 9 raised to the factorial of 9 and not the factorial of 9 raised to the power of 9.

In regards to whether your revised submission would be greater number than the other contest submissions, I suspect so. From what I read, in general, factorialization gets bigger quicker than standard exponentiation.

[Guest]

The following may be off (as may be my assumptions about it), but based upon the pattern of expansion of the factorials, exponentiation and tetration I examined...

The size of the number OF THE NUMBER OF DIGITS of the 100 character number of exponentiation [...9^9^9...]

is approximately 5.0 x E+1 digits.

The size of the number OF THE NUMBER OF DIGITS of the 100 character number of factorialization [...((999!)!...]

is approximately 2.5 x E+2 digits.

The size of the number of THE NUMBER of DIGITS of the 100 character number of tetration (hyper4) [...9^^9^^9...]

is approximately 1.0 x E+33 digits.

I am not sure I could use scientific notiation to express the size of the number OF THE NUMBER OF DIGITS

of the 100 character number of hecatontation (hyper100).

Note: The scientific notation does not describe the number of digits in the number --- but THE NUMBER OF DIGITS of the number that describes the number of digits in the number. All these numbers are huge!!!!