Yes, I meant O(log N log log N ...). Oops. Sincerely, Adam P. Goucher ----- Original Message ----- From: Robert Munafo To: math-fun Cc: Adam P. Goucher Sent: Wednesday, October 12, 2011 10:45 PM Subject: Re: [math-fun] Zillions It looks like you're using Greek. It is more common to use Latin, following Chuquet and the standard dictionary words like "tredecillion" and "vigintillion". "duotrigintillion" for 10^99 is pretty standard ([1] and [2]). For 10^600, [1] gives "novenonagintacentillion" and [2] gives "cennovemnonagintillion". Broken up to show they are made from the same pieces: nove-nonaginta-cent-illion and cen-novem-nonagint-illion. I don't see your O(N log N log log N...) claim. The name of 2^32=4294967296 is not twice as long as the name of 2^31=2147483648. It seems the first N should be removed: O(log N log log N ...) - Robert [1] Conway and Guy, "The Book of Numbers", ISBN 0-387-97993-X or my own web page, http://mrob.com/pub/math/largenum.html#conway-wechsler [2] http://isthe.com/cgi-bin/number.cgi On Wed, Oct 12, 2011 at 16:31, Adam P. Goucher <apgoucher@gmx.com> wrote: Anyway, why are we using 10^66 as the highest named power of 1000? Can't we call 10^99 a 'dotriacontillion', for example? That system extends up to 10^600 ('enneanonacontahectillion') quite easily. It appears that any similar systematic naming of all integers must surely use recursion, resulting in a number N having a representation of length: O(N log N log log N log log log N ... 2^log* N) -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com