Applications of general arrow notation?
I don't know where to put this, so I put it here cause it is so advanced...
Anyway, for those who knows what arrow notation is, I have some questions, and for those who don't know what it is, here's a brief explanaition:
The arrow notation is used to apply an operation multiple times ( times) at variable with variable . For example, means that operation is applied times at , with itself. So since is defined as multiplication, means power since is multiplicated times with itself.
All this also means that . For example, .
This can go on forever, meaning that can grov from 1 to 2, from 2 to 3 and so on, creating new operators all the time. For example
This can create very big numbers if we continue developing the operators. This is an very interesting invention made by Donald Knuth, but what is it good for? I recently saw an application of when reading about power towers.