Name: bomb basic 2009-10-17 5:21
Hey Science & Math, I'm new to this board. Forgive me ahead of time if I fail to make this idea complete or concise enough because I've only completed college algebra. I don't think I could transcribe this paradigm into an algebraic function as I know my maths because of the required iteration but I feel there should be something to express this process algebraically so it can be integrated with the rest of the formalized system. Anyways here is the pattern/process:
[2|3]?0 = [2|3]^0 = 1
2?1 = 2^2 = 4
3?1 = 3^3 = 9
2?2 = 2^(2^2) = 16
3?2 = 3^(3^3) = 7,625,597,484,987
2?3 = 2^(2^(2^2) = 65,536
3?3 = 3^(3^(3^3) = ??????? (calculation 404)
..So I was wondering if there was any operation that signifies and simplifies recursively raising the base number by powers of itself?
Alternatively maybe a pattern for this function could be established or derived from the previous one if what I'm looking for doesn't exist yet:
a. ? symbol independent from previous batch of processes
3?2 = (3^3)^3) = 19,683
3?3 = (3^3)^3)^3) = 7,625,597,484,987
b. implied function; a variant with respect to both former batches of processes
3?-2 = (3^3)^3) = 19,683
3?-3 = (3^3)^3)^3) = 7,625,597,484,987
However, with this batch when integrated with the first I come across this unintuitive dilemma which I'm currently trying to sort out (help with straightening this up would be appreciated too >=)):
3?2 = 3^(3^3) = 3?-3 = (3^3)^3)^3 = x
3?2 = 3^27 = 3?-3 = 19,683^3 = x
3?2 = 3?-3 = x = >:[
I really want to try my best to formalize this but I realize how daunting the task is for my current education level. Thanks for reading.
[2|3]?0 = [2|3]^0 = 1
2?1 = 2^2 = 4
3?1 = 3^3 = 9
2?2 = 2^(2^2) = 16
3?2 = 3^(3^3) = 7,625,597,484,987
2?3 = 2^(2^(2^2) = 65,536
3?3 = 3^(3^(3^3) = ??????? (calculation 404)
..So I was wondering if there was any operation that signifies and simplifies recursively raising the base number by powers of itself?
Alternatively maybe a pattern for this function could be established or derived from the previous one if what I'm looking for doesn't exist yet:
a. ? symbol independent from previous batch of processes
3?2 = (3^3)^3) = 19,683
3?3 = (3^3)^3)^3) = 7,625,597,484,987
b. implied function; a variant with respect to both former batches of processes
3?-2 = (3^3)^3) = 19,683
3?-3 = (3^3)^3)^3) = 7,625,597,484,987
However, with this batch when integrated with the first I come across this unintuitive dilemma which I'm currently trying to sort out (help with straightening this up would be appreciated too >=)):
3?2 = 3^(3^3) = 3?-3 = (3^3)^3)^3 = x
3?2 = 3^27 = 3?-3 = 19,683^3 = x
3?2 = 3?-3 = x = >:[
I really want to try my best to formalize this but I realize how daunting the task is for my current education level. Thanks for reading.