from C's and LISP's 0-based indexing of arrays. Hardware people also tend to start counting at 0 instead of 1; this is natural since, e.g., the 256 states of 8 bits correspond to the binary numbers 0, 1, ..., 255 and the digital devices known as `counters' count in this way.Hackers and computer scientists often like to call the first chapter of a publication `chapter 0', especially if it is of an introductory nature (one of the classic instances was in the First Edition of K&R). In recent years this trait has also been observed among many pure mathematicians (who have an independent tradition of numbering from 0). Zero-based numbering tends to reduce fencepost errors, though it cannot eliminate them entirely.