You can use the digits 1,2,and 3 once only and any mathematical symbols you are aware of, but no symbol is to be used more than once. The challenge is to see if you can make the smallest positive number.
Special rules: You cannot use Euler's number or pi or infinity.
Special thanks to: Rhonda Wendel for Make the most of these digits and for the problem text which was slightly altered.
I've only briefly skimmed the responses, but I did not see anyone bring up tetration, pentation, or hexation.
If multiplication is defined as repeated addition,
and exponentiation is defined as repeated multiplcation,
then tetration is defined as repeated exponentiation,
pentation is defined as repeated tetration,
and hexation is defined as repeated pentation.
Multiplication: 2*3 = 6
Exponentiation: 2**3 = 8
Tetration: 2***3 = 134217728
Pentation: 2****3 = 2417851639229258349412352
Hexation: 2*****3 = 1.4134776518227074636666380005943e+73
Once you're aware of these math procedures, then go back and apply the trig functions, factorials, etc. to make the result a truly infinitessimal value.
Posted by Erik O.
on 2004-06-10 23:08:01