 Here the first equation—called the base clause—defines the value of the function when the exponent is 0. And the second clause—called the recursive clause—uses the value of the function when the exponent is \(n\) to define the value when the exponent is \(n + 1\). This is perfectly legitimate, according to the traditional account, because a theorem of Peano Arithmetic establishes that the above definition is equivalent to one in normal  form.[10]  Recursive definitions are circular in their format, and indeed it is this circularity that renders them perspicuous. But the circularity is entirely on the surface, as the existence of normal forms shows. See the discussion of circular definitions below.