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.

Here is the smallest number that I could get using the digits 1, 2 and 3 only:

[(.1)]^[(2)^(3!)]!

Which is equal to (.1) raised to the power of (64!) (factorial of 64). Since (3!) = 6 and [(2)^(3!)] = 64 and therefore [(2)^(3!)]! = (64)!. This will give us a number which will contain (64!), that is, (factorial 64) zeros between the 'Decimal Point' and the digit 1(One), and this I believe is the "SMALLEST" of all the numbers yet obtained/derived using the digits 1, 2 and 3 only.

Does anybody else agree with me ?