Time for a Math Puzzle

[puffff]

Originally posted by: giantpinkbunnyhead
You need to come up with the number of greatest possible magnitude you possibly can, using ONLY ten characters. (or less, I suppose...) You can use any characters you want. You cannot use limits or infinity, or anything "conceptual". Just numbers and operators. Basically... find an expression that results in the number of greatest possible magnitude.

Fixed. C'mon, haven't you guys ever read the Phantom Tollbooth?

 

[chuckywang]

Originally posted by: sao123

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

No, they don't. Check out Stirling's formula.

 

[Syringer]

Originally posted by: chuckywang

Originally posted by: sao123

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

No, they don't. Check out Stirling's formula.

9^9 = 9*9*9...*9
9! = 9*8*7...*1

 

[sao123]

Originally posted by: Syringer

Originally posted by: chuckywang

Originally posted by: sao123

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

No, they don't. Check out Stirling's formula.

9^9 = 9*9*9...*9
9! = 9+8+7...+1

uh fixed that obvious error.

 

[Crescent13]

0/1^9^9^99


What do I win?

 

[Goosemaster]

999!^^^9

 

[JujuFish]

Originally posted by: sao123

Originally posted by: Syringer

Originally posted by: chuckywang

Originally posted by: sao123

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

No, they don't. Check out Stirling's formula.

9^9 = 9*9*9...*9
9! = 9+8+7...+1

uh fixed that obvious error.

Uh, no, you created an error.

 

[giantpinkbunnyhead]

?? that is zero! you win... a hundred BEEELION DOLLARS!!!

 

[blahblah99]

9^99999999

 

[linkgoron]

1/0

 

[Syringer]

Originally posted by: sao123

Originally posted by: Syringer

Originally posted by: chuckywang

Originally posted by: sao123

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

No, they don't. Check out Stirling's formula.

9^9 = 9*9*9...*9
9! = 9+8+7...+1

uh fixed that obvious error.

Did you drop out of high school?

 

[BlueFlamme]

Originally posted by: Syringer
9^9 = 9*9*9...*9
9! = 9*8*7...*1

Now take it to the next step:
9^9 = 3.8e7
3.8e7^9 = 3.8e7 * 3.8e7 * ... 3.8e7 9 times, which yields 1.96e77

However going with factorial
9! = 3.6e5
3.6e5! is too large for my calculator to compute
3.6e4! = 9.2e148,394
So take that number and multiply it by every number between 36,000 and 360,000.

Which one grows fastest again? If you want an official proof, go google it.

I grant you that an Ackermann seq. grows faster, but that is not the same as 9^9^...^9

 

[Syringer]

There's a difference between 9^(9^9) and (9^9)^9.

 

[sao123]

Originally posted by: Syringer

Originally posted by: sao123

Originally posted by: Syringer

Originally posted by: chuckywang

Originally posted by: sao123

Originally posted by: dullard

Originally posted by: DrPizza
9^^^^^^^^9

But how does that compare to my answer:

9!!!!!!!!!

I think factorials grow faster?

no. exponentials grow faster.

No, they don't. Check out Stirling's formula.

9^9 = 9*9*9...*9
9! = 9+8+7...+1

uh fixed that obvious error.

Did you drop out of high school?

no...but diff eq ruined my basic math skills...
I just saw what i did and i said WTFAMIDOING????

 

[Toastedlightly]

I vote for the factorial, but do they stack like that?

 

[BlueFlamme]

Originally posted by: Syringer
There's a difference between 9^(9^9) and (9^9)^9.

Well the OP specifically stated that parenthesis counted as your spaces, but come to think of it I cannot properly recall which way you are to interprist 9^9^9 if no parenth's are involved.

And yeah, going by your way is larger, I screwed up the math because I wasn't using a calculator where I could type in the full string. Laziness at home on a friday night FTL.

Re-reading my previous post I recall that I acknowledged that continuous exponentials will grow faster than factorials except for the fact that you get almost twice the number of factorials involved. 9^9^9 is not gonna keep up with 9!!!!

And I'm way too lazy to even try delving into any actual proofs :beer:

 

[habib89]

1/.0000001

 

[desteffy]

9!!!!!!!!!!

 

[reverend boltron]

?-naught

explanation

 

[JoeFahey]

42

 

[Howard]

Originally posted by: DrPizza
For what it's worth, even with the nested ^^^ notation, it can still be beaten by a long shot.
(Ironically, about 2 weeks ago, I read a short paper on the problem of writing the largest number possible - using notation a mathematician would understand - on the back of an index card about 2 weeks ago.)

I found something similar:
here
There's a section that deals with the halting problem and Turing machine...

But as Rado stressed, even if we can?t list the Busy Beaver numbers, they?re perfectly well-defined mathematically. If you ever challenge a friend to the biggest number contest, I suggest you write something like this:

BB(11111)?Busy Beaver shift #?1, 6, 21, etc

If your friend doesn?t know about Turing machines or anything similar, but only about, say, Ackermann numbers, then you?ll win the contest. You?ll still win even if you grant your friend a handicap, and allow him the entire lifetime of the universe to write his number. The key to the biggest number contest is a potent paradigm, and Turing?s theory of computation is potent indeed.

Embarassingly, that link made me very happy.

 

[BlueFlamme]

Originally posted by: habib89
1/.0000001

9/.0000001 is larger...

 

[DrPizza]

Originally posted by: Howard

Embarassingly, that link made me very happy.

Nothing to be embarassed about... it's a great article!