 There are two important things to notice about the Turing machine setup. The first concerns the definition of the machine itself, namely that the machine’s tape is potentially infinite. This corresponds to an assumption that the memory of the machine is (potentially) infinite. The second concerns the definition of Turing computable, namely that a function will be Turing computable if there exists a set of instructions that will result in a Turing machine computing the function regardless of the amount of time it takes. One can think of this as assuming the availability of potentially infinite time to complete the computation.