Gödel's Theorem in a nutshell: Introduction

• Let C(n) be a computation that acts upon or depends upon a natural number n i.e C(n) is the action of some Turing Machine on the number n. For example from (A) and (B) we could define a C(n) as

  

• Define a computational procedure or algorithm , A, which when it terminates provides us with the demonstration or proof that C(n) does not ever stop. We require that A is sound.
• For A to apply to all computations generally we label all computations with subscripts consisting of the natural numbers. i.e

  

  and refer to as the qth computation applied to the particular natural number n.