08/14/2007, 11:36 PM
Hm, I dont know. There is also the thing that one usually dont need for example a hyper-25-root. The most used number is 4, everything above probably then works in the same scheme. So perhaps we best stay with the established hyper power, hyper exponential, hyper root and hyper log (or similar super prefix).
andydude Wrote:and provisions should be made for the lesser and mixed hyper-operators, like those based on left-associative or right-associative iteration or left-right and right-left associative iteration. Since these only appear after hyper-3, I would imagine a logical way to name these would be to assign hyper-R = hyper-4 hyper-RR = hyper-5, hyper-RRR = hyper-6 since they all depend on right-associative iteration, and perhaps hyper-L, hyper-LL, and hyper-LLL for the "lower" or "hypo"-operator sequence. Using this terminology, we can refer to all of the above, for example, as hyper-LR-power, hyper-LR-ational, hyper-LR-root, hyper-LR-log, and so on.Not to forget the balanced bracketing, for example \( {}^4x=(x^x)^{x^x} \), perhaps denote with a B(alanced) or M(iddle). There are however several different types of balanced bracketing.
Quote:This works well for the hyper-operators based on simple iteration, but not for your Binary-Tree hyper-operators. How would that work for the Binary-Tree hyper-operators?Oh they are designed for containing all bracketings. Every binary tree encodes a bracketing. So one dont need to care about left bracketing or right bracketing, the bracketing is simply performed as it is encoded in the first operand, which is a binary tree. Thatswhy there is a natural sequence of hyper operations, not prefering a certain bracketing over others.