This defines the term “computable”, but it doesn’t give you a sense of what things can be computed. Defining a term is entirely different from the above promise.

At the level you’re describing Turing machines, it’s also not clear that readers would have a precise notion of what an algorithm is. At no point (unless I missed it) do you explain that any algorithm is supposed to be implementable as a Turing machine, or the assumption of what is otherwise known as the Church–Turing thesis.