Assume that a computable function is formalized as a Turing machine that

can be represented as a finite length string from a finite alphabet. Thus, any string

over this alphabet is simply defined to be a Turing machine. Is the set of all Turing

machines countable? If so$,$ give a listing $(1-1$ map with the integers$)$ of all Turing

machines. Note, such a listing is called an $$effective enumeration.$$ If not, explain

why the set of all Turing machines is not countable.