Understanding the reason behind the μ (mu) operator

Question

• What is the purpose of the $\mu$ operator?
• Is there a real world example?
• Is it correct that it can create partial functions out of total functions and it makes a function $g$ with k parameters out of a function $f$ with $k+1$ parameters?

Answer 1

Adding the μ-operator to the five primitive recursive operators makes it possible to define all computable functions. It is well explained in wikipedia.