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Make the least of these digits (Posted on 2003-04-13) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Alan    
Rating: 3.0000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Amateurs! | Comment 58 of 67 |
(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 ()! .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:
en.wikipedia.org/wiki/tetration


  Posted by Cory Taylor on 2006-02-01 13:40:13

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