Since zero is the lowest value of an unsigned integer, which is one of the most fundamental types in programming and hardware design, it is often natural to count from zero rather than one, especially when the integer is actually an index or offset, as used when addressing hardware and arrays.
Hackers, computer scientists and pure mathematicians 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).
Zero-based numbering tends to reduce fencepost errors, though it cannot eliminate them entirely.
Logically, the next item after the zeroth should be the "oneth" but this is never used.
[Dijkstra, "Why Numbering Should Start at Zero" http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html].
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Nearby terms: zero assignment « zero-content « Zero Insertion Force « zeroth » ZEST » ZetaLisp » zetta-