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A model for generally thinking about mathematical algorithms, using formal logic. It consists of a theoretical endless tape (memory tape), where each cell contains a binary number (0/1); a read/write head which can move left or right and manipulate the cells, and a set of instructions - control unit. The machine halts when it reaches an end state - tries to leave the tape (go left from memory cell 0), or when it encounters a situation with no defined rule.

"Turing complete" is mark used for computer systems that are complete enough to calculate anything, they do not have to resemble a turing machine.