Off-by-one Error
An off-by-one error (OBOE) is a logic error involving the discrete equivalent of a boundary condition. It often occurs in computer programming when an iterative loop iterates one time too many or too few. This problem could arise when a programmer makes mistakes such as using "is less than or equal to" where "is less than" should have been used in a comparison or fails to take into account that a sequence starts at zero rather than one (as with array indices in many languages). This can also occur in a mathematical context.
Read more about Off-by-one Error: Looping Over Arrays, Fencepost Error, Security Implications
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“Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus “theoretically,” is to use language in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.”
—Charles Sanders Peirce (1839–1914)