The claim that the Z3 computer was Turing-complete is not true. There is a paper arguing for it, but a detailed reading of it shows that this is an extremely far-fetched and somewhat disingenuous stretch. (The disingenuous part is because any fixed-function calculator could then be claimed to be "Turing-complete", not just the Z3). The central point of the Church-Turing thesis is that a finite set of instructions, given an unlimited memory to work with, can perform any calculation we can imagine (where the "can imagine" part makes the thesis philosophical). The "finite set of instructions" is indispensable, however, since if the instructions are unlimited, you can simply encode any answer you want into them. The "Turing" mode of Z3, which was of course never used, involves a program which essentially scales in length with the total number of calculations it will perform - or even the exponential of that number, if there are many branches - which is not a good model of a Turing machine.
Of course, no computer is a true Turing machine, since the memory is always limited, but our computers are a useful physical approximation of a Turing machine because a small program can compute using a large memory. The Z3 is not that type of a device at all.
Of course, no computer is a true Turing machine, since the memory is always limited, but our computers are a useful physical approximation of a Turing machine because a small program can compute using a large memory. The Z3 is not that type of a device at all.