# 2**2**2**2**2 wrong? Bug?

Wayne Brehaut wbrehaut at mcsnet.ca
Fri Jul 13 21:31:22 CEST 2007

```On Wed, 11 Jul 2007 21:37:00 -0400, "Terry Reedy" <tjreedy at udel.edu>
wrote:

>
>"Evan Klitzke" <evan at yelp.com> wrote in message
>news:cfb58d850707111747x4b83cb88wcaf45437e8e14511 at mail.gmail.com...
>| On 7/11/07, Gabriel Genellina <gagsl-py2 at yahoo.com.ar> wrote:
>| > Just for curiosity: This helps to find the answer to the problem "Which
>is
>| > the largest number that can be written with only 3 digits?"
>| > Some people stop at 999, others try 99**9 and 9**99, and the winner is
>| > 9**9**9, or:
>| >
>| > |   9
>| > |  9
>| > | 9
>| >
>| > Sorry, couldn't resist.
>|
>| But you can append ! (i.e. factorial) indefinitely without adding any
>| digits to make the number arbitrarily large ;-)
>
>But as Gabriel showed, 9**9**9 in standard math pen-and-paper or
>chalk-and-blackboard notation, not the squished computer linear imitation
>thereof, uses three nines and nothing else ;-)

Since no base was specified:

(hex) F**F**F > (dec) 9**9**9

and we could use BASE-64 numbers (immediately coming to mind if we
ever drove a CDC CYBER machine), where:

(base-64) del**del**del >  (hex) F**F**F > (dec) 9**9**9

Then someone who had read the Busy Beaver reference would introduce
base-BB2, or (where we assume the digits base-BB2 are 0, 1, ...,
BB2(???)):

BB2(11111) ** BB2(11111) ** BB2(11111)

and so on, ad infinitum--as the bard said
(http://www-groups.dcs.st-and.ac.uk/~history/Quotations/De_Morgan.html):

Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.

wwwayne
===
"Come along son, and put your whip away.  That horse is dead!"
--- Wise Old Man

>tjr
>
>

```