How large is the set of all Turing machines? How large is the set of all Turing machines? I am confident it is infinitely large, but what kind of infinitely large is its size?

By an informal argument, Turing machines roughly correspond to programs written in some programming language. Each program is a finite string in ASCII or unicode or binary (or another finite alphabet of some kind). 
We might imagine writing a naive program that outputs all possible strings in lexographical order, running the compiler on each one, and throwing it out if there's an error. This program will ultimately list out every program (albeit, "hello world" would take a very long time to produce). Thus, we have a program which enumerates all programs. The set of all turing machines is countable.
