# Can there be fractional hyper operators and if so how to they function? [duplicate]

If we call addition (and subtraction as they are the same) the first hyperoperator, multiplication (and division) the second, exponentiation (radicals, indices and logarithms) the third, then tetration the fourth and so on, we then have a definition of a hyperoperator.

My question is:

Is there a way to have a fractional hyperoperator such as an operation half way between addition and subtraction which would be the 1 + 1/2’th hyperoperator.