can anyone explain this concept to me? and help me out in figuring out the answer? as I don't quite get it yet but any help will do, thank you
There exists two really cool primitive recursive functions: T(z, x1, x2, ..., xn, y) returns 0 if z is an encoding of a Turing Machine, and its computation with inputs x1, ... xn encodes to y. The function returns 1 otherwise. U(y) returns the result of the computation y.
Goal:Use these two functions and the µ(mu) operator to get a definition of a function f(x1, x2, ...xn) which returns the output of the TM encoded by z
what I have so far:
using these two functions and the µ operator we can then generate a definition for the function f(x1,x2, ...xn) that returns the output of the TM encoded by z such that we have a TM that we can define as T(n) where this computes the number of primes which are less than or equal n. z = 0 which is the number of primes found, y = 1 which is for each y we test whether it is prime, while k <= n:, j = 1 are the possible divisors of y, d = 0 the number of divisors of k found, while j <= n: if y % j == 0:, d = d + 1, j = j + 1, if d== 2:, z= z+1,y=y+1, then return z which is the output of the TM encoded by z
