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tetration

Tetration (also exponential map, hyperpower, power tower, super-exponentiation, and hyper4) is iterated exponentiation, the first hyper operator after exponentiation. The portmanteau word tetration was coined by Reuben Louis Goodstein from tetra- (four) and iteration. Tetration is used for the notation of very large numbers. Tetration follows exponentiation in the sequence:

1. addition

2. multiplication

3. exponentiation

4. tetration

where each operation is defined by iterating the previous one.

Multiplication (a x b) can be thought of as B instances of A added together, and consequently exponentiation (ab) can be thought of as B instances of A multiplied together. So a step further can be taken, and tetration (ba) can be thought of as B instances of A exponentiated together.

Source: Wikipedia.

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