## Friday, October 25, 2013

### The smallest natural number that can not be described by a phrase shorter than one hundred letters

What is the shortest natural number that can not be described by a phrase shorter than one hundred letters?  This is a paradox, because I AM describing it in a phrase shorter than one hundred letters.

Can there be a number that can not be described in one hundred letters or fewer?  There must be.  There can only be 26^100 (about 3.1429 x 10^141, or three sexquadragintillion) phrases with one hundred letters.  Which is an awful lot.  There aren't even that many atoms in the universe, according to the scientists. But there are aleph-null natural numbers.

For example:  five sexquadragintillion, seven hundred four octatrigintillion, three septentrigintillion, four hundred seventy eight duotrigintillion, sixty untrigintillion, five hundred thirty eight trigintillion, sixty seven octavigintillion, ninteen septenvigintillion, seven hundred six duovigintillion, twelve.

So what is the smallest number number whose description must exceed one hundred letters?  I an not curious enough to bother figuring it out.

names of large numbers:  ten power