maths question

[joshd]

why do stacked powers, as in 9 to the power of 9^9^9^9^9^9 give such crazily big numbers?

http://www.scottaaronson.com/writings/bignumbers.html

what is happening to make them soooo big?

"Take 9 to the power of 9^9, for example. This behemoth, equal to 9387,420,489, has 369,693,100 digits."

surely 9^9^9 is the same as 9^81?

what am i not understanding?

EDIT: sorry, i did not realise that it explained this further down the page...

EDIT EDIT: nope it doesnt, i still dont get it.

 

[The General]

9^9 = 9x9x9x9x9x9x9x9x9

9^9^9 = (9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)

9^9^9^9 = [(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]x[(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)x(9x9x9x9x9x9x9x9x9)]


Hope that helps.


9 to the power of 9 to the power of 9 is NOT 9 to the power of 81.

This is because 9 to the power of 9 is 3486784401 so...

9^9^9 = 9 to the power of 3486784401.

It's not 9 to the power of 9x9, its 9

It'd be a lot easier if I knew how to use superscript ... if you need, I'll write it on a piece of paper and scan it lol.

But I'm pretty sure that if you don't understand it by now, chankama will help you.

 

[joshd]

Hope that helps.


9 to the power of 9 to the power of 9 is NOT 9 to the power of 81.

This is because 9 to the power of 9 is 3486784401 so...

9^9^9 = 9 to the power of 3486784401.

It's not 9 to the power of 9x9, its 9 to the power of 9x9x9x9x9x9x9x9x9

darn, yes. 9^9 is 81... hmmm wtf? i am glad i have already taken my maths exams... i cant do it anymore. lol.

i see! no wonder they make such crazily big numbers. lol.

so 9^9^9^9^9^9^9^9^9^9^9^9^9 is just incomprehensible! i think superPI should be replaced for this stuff for stress testing lol.

i dont think you can use superscript on VB. yes, i get it now. although chankama will probably add more to your explanation, and confuse me with his maths genius-ness.

 

[The General]

No no, 9^9 is NOT 81, 9x9 = 81, 9^9 is 9 times itself 9 times, which is 3486784401.

 

[joshd]

i know! i said that! i put a and said i was glad i already did my maths if i am now making mistakes like that.

there, i edited in a "wtf?" after it to make it wasier to understand.

 

[MrZucchiniHead]

wow imagine what 99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^
would equal.

i think this would put way more stress on a computer than super PI.

 

[The General]

 

[Waphlez]

wow imagine what 99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^99999^
would equal.

i think this would put way more stress on a computer than super PI.

Why not make it (99999!)^(99999!)^(99999!)^(99999!)^(99999!)^
(99999!)^(99999!)^(99999!)^(99999!)^ (99999!)^(99999!)^(99999!)^(99999!)^(99999!)^(99999!)^(99999!)^(99999!)^(99999!)?

Remember 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

so 99999! = 99999 x 99998 x 99997 x 99996 x 99995 etc. = ???

 

[joshd]

so the "!" means "the number, multiplied by all the numbers below it all the way down do 0"??

if so, this number is getting so large it isnt even worth thinking about it!

my PI output i think was 40MB .txt file for 32M, well this would be 100s of GB!!

:O the linux calculator is so much better! i cant even work out how to square root on the windows one, even on scientific mode.


EDIT: mini competition time! biggest number you can make with only 5 digits

9^9^9^9^9 thats my go.

i dont think you can make a bigger one than that, but i expect you guys will find a way.

EDIT EDIT can you go 9^(9^9)^(9^9) does that make an even bigger number? i suppose that it is stacking them up twice... so i dont know.

 

[joshshift]

check this out.

here