Big number game (less silly version)

[MichaelPoole]

So, I see KSP forum already had a "my number is bigger than yours" thread here http://forum.kerbalspaceprogram.com/index.php?/topic/53404-my-number-is-bigger-than-yours/ but it ended up being way too silly and locked. So here I present a more "serious" version of it. The rules I can think of are:

1. The number must be computable (by computable, I do not mean it has to actually be able to get calculated into a decimal form by a human being or a computer, your number can easily be not representable in exponents in the observable universe, I am saying it must be theoretically computable, unlike say Busy Beaver numbers).

2. The number must be well defined (so you cannot write something like "the largest number you can think of").

3. Do not use numbers of previous users with a trivial addition like "+1" or well known numbers like Graham's number without explaining the process how you get to them.

4. The number must be finite, so no transfinite numbers.

5. You should explain the process used to create the number so people less versed in large numbers are not immediately discouraged from the game by some genius who posts a complicated ordinal notation in the first 5 posts (you can use a notation like that if you explain it). You don't have to explain basic, well known functions like factorials or exponents through.

6. This is not really a rule, but rather than filling pages with exponents, try to find more compact, smart ways to make larger numbers. If you don't know to do that, go ahead and do it the way you know it, but please don't make page filling posts like this http://forum.kerbalspaceprogram.com/index.php?/topic/53404-my-number-is-bigger-than-yours/&do=findComment&comment=777536 .

Everybody can post multiple times and new numbers. I will start with a very big, but easy to make number.

100! = factorial of 100, it is also the amount of ways you can arrange 100 different objects in a row. It is 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000, or  9.3326× 10¹⁵⁷.

Edited February 6, 2016 by MichaelPoole

[quasarrgames]

Not sure if this counts, but... the number of digits in pi. It could have an end, maybe, maybe not. Will we ever know? Maybe, maybe not. It's a mystery. Infinitely definite, but not definitely infinite.

Heh.

 

 

 

Okay FINE if that doesn't count, try the number of cubic planck lengths in the observable universe (9.47x10¹⁹³ i believe) or the number of possible pages in the library of babel, 10³²⁰⁰

[MichaelPoole]

The Library of Babel number 10³²⁰⁰ is so far the largest here. Digits of Pi does not meet the criteria of being well defined and it might be infinite. It should be said the Library of Babel number is in fact much bigger, as even the number of books in it is at least 25^1312000.

 

Note - your number does not have to have any physical or other meaning. It is your number after all. So you do not need to be concerned with Planck volumes or whatever.

Edited February 7, 2016 by MichaelPoole