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 Amateurs!
by Erik O.)
The trick with these "notations" is that they use repeated "symbols".
The best I can do is find a notation for tetration that wont use any
symbols, so I can have (³²)! .1, or some such construction, but the
higher superfunctions notations wont work under the problem
constraints. I recall having seen once, in the far distant past,
a notation for these operations using geometric shapes (triangle for
tetration, square for pentation etc.) but I can't find a reference for
it when searching. This notation would allow for, essentially,
epsilon (a circle would be the infinitely orders superpower, which
could be created with the 23 and be the bottom of the fraction with the
1 on top - now lets not debate the relative sizes dofferent epsilons...)
The challenge once these operators is brought in is in the comparison
of the numbers to determine their relative smallness. At the
magnitude that will be achieved with them, even multiple orders of
magnitude are difficult to detect...
Wikepedia reference for the notations at: