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.
(In reply to re(3): This is my Guess...(factorials of fractions).....
by Ravi Raja)
Ravi, did you read the beginning of the post? I did not say that 1/(9261!) is close to 1, I said that (1/9261)! is close to 1. That is, using the definition of x!=Γ(x+1), when you take the fraction 1/9261, which itself is quite close to zero, and apply this generalized factorial function to that small number, the result is close to one, and that this is analogous to 0! itself being 1. It is you who have mistakenly stated that 1/(9261!) = (1/9261)!. It is the latter of this pair that I am saying is close to 1. The former is certainly close to zero, as you say.
What I said, copied:
In the case of (1/9261)!, the result comes out as approximately .999937683957. This is very close to 1 (one), as would be expected since 0! is defined as 1 (one) and 1/9261 is very close to zero.
Posted by Charlie
on 2003-04-14 03:45:58