From casual description of Turing Machine to the density of uncomputable functions
Defining the machine by describing it In Sipser’s Introduction to the theory of computation, a alternative way of defining a Turing machine (other than defining the formal 7-tuple, which is a PITA) - by its “description”. Example (from the proof of $A_{TM}$ is deciable): M = “On input <B, w>, where B is a DFA and w is a string: 1. Simulate B on input w. 2. If the simulation ends in an accept state, accept ....