Let <math>f:\mathbb{N}\to\mathbb{N}</math> be the function defined by:
:<math>f(\#_{\mathcal{A}}) = \#[\mathcal{A}(^{\circ}\#_{\mathcal{A}})]</math>It’s defining “f” to be a function such that, for each possible formula with one free variable, it evaluates to the godel number of plugging that formula’s own godel number into its free variable. like saying, for each expression function A of one operand, f(A) = A(A) . f passes its parameter to its parameter, and returns the result. expressions are encoded as godel numbers.
