The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: BIG NUMBERS #1
Replies: 19   Last Post: Feb 11, 2003 9:59 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
C. Stevens

Posts: 25
Registered: 12/13/04
Re: BIG NUMBERS #1
Posted: Feb 4, 2003 1:09 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


Dave:I read with great interest your post on BIG NUMBERS.I made a (curious) construction based on a similiar construction I saw concerning Graham's #.My little construction is based on Conway's chained arrows notation and the colossi 3->3->2->2->2

>>>>>>>>>>>>>>>>>>>>>>>>=3->3->2->2->2!
^
^
^ 1)27 { {1)27 {1)27 } }
^ 2)3^..1)..^3 { {2)3^..1)..^3 {2)3^..1)..^3 } }
^ . {.. { . { . } }
^ . { . { . { . }27 }
^ . { . { . { . } levels}
<<<........... { ..< .....levels < .....levels } }
\________________________________________________/ }
| }
. }
. }
. }
>>>>>>>>>>>>>>>>>>>>>>>>. }
^ }
^ }
^ 1)27 { {1)27 {1)27 } }
^ 2)3^..1)..^3 { {2)3^..1)..^3 {2)3^..1)..^3 } }
^ 3)3^..2)..^3 {.. {3)3^..2)..^3 {3)3^..2)..^3 } >3^27
^ . { . { . { . } } levels
^ . { . { . { . >27 }
^ . { . { . { . } levels}
<<<<.....BAYS { ..< ......levels < .....levels } }
{ { { } }
{ { { } }
\________________________________________________/ }
| }
>>>>>>>>>>>>>>>>>>>>>>>>| }
^ }
^ }
^ 1)27 { {1)27 {1)27 } }
^ 2)3^..1)..^3 { {2)3^..1)..^3 {2)3^..1)..^3 } }
^ 3)3^..2)..^3 {.. {3)3^..2)..^3 {3)3^..2)..^3 } }
^ . { . { . { . >27 }
^ . { . { . { . } levels}
^ . { . { . { . } }
<<<......Bays { ..< ......levels < ......levels} }
{ { { } }
\________________________________________________/ }
| }
27 bays }

Notes:Reads from right to left, bottom to top with the final amount of arrows top left. Why start with 27? I calculated this using Robert Munafo's c3(N):chain: function at http://home.earthlink.net/~mrob/pub/math/ln-notes1.html

The top of each "bay" should really read 1)27
2)3^..^3 with 1) arrows,in other words 27 arrows and so forth on down the bay vertically.

Thanks to Munafo's function above,I was able to make a rough estimate of 3->3->2->4 and worked from there. One thing about 3->3->2->2->2 is,three steps into the expansion,it changes into a 4-number notation similiar to 3->3->2->4 and I worked from there.
Having said all this,the construction above may very well be wrong.I would appreciate anyone posting if they find an error (or errors!).One thing for sure,3->3->2->2->2 is one "BIG NUMBER"!




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.