Could someone explain the following definition of a Turing Machine?
A Turing Machine $M$ is defined formally by a tuple $(\Sigma, Q, \delta)$
Where $\Sigma$ is a finite set representing the number of symbols that $M$'s tape can contain. We assume $\Sigma$ to contain a blank symbol as well as a start symbol. We call $\Sigma$ the alphabet of $M$.
And a finite set $Q$ of possible states of $M$'s register can be in. We assume that $\exists q_{start}, q_{halt} \in Q$
And $\delta$ is a function $\delta : Q \times \Sigma^k \to Q \times \Sigma^{k-1} \times \{L,S,R \}^k$
Anyone have any consensus on the definition?