Transcription
Succession, addition, multiplication, exponentiation, tetration, pentation, hexation. These are hyper operations, which are natural extensions of basic arithmetic. Addition is repeated succession, multiplication is repeated addition, exponentiation is repeated multiplication.
So, it follows that tetration is repeated exponentiation. But, how do we use this? Well, let's take three tetrated to four. This means we have three to the power of three four times. But, the exponents calculate downwards, meaning our exponential is exponentially increasing.
But, we can go further with pentation, which is repeated tetration. In fact, there's a generalized notation which allows us to say repeat the previous operation. This can use up arrow notation, where one arrow represents exponentiation, two arrows represent tetration, and so on.
But, what is this used for? Addition is adding things, multiplication is splitting things, exponentiation models real life, but tetration isn't a physical model. In fact, its only real use is to represent gargantuan numbers. Take for example, Graham's number. The only meaningful representation uses this notation, and even then, it's in the form of an algorithm. So, that's why you probably haven't heard half of