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1550s, "act of setting off" (on a journey, etc.), from off + set (adj.). Meaning "something 'set off' against something else, a counterbalance" is from 1769; the verb in this sense is from 1792. As a type of printing, in which the inked impression is first made on a rubber roller then transferred to paper, it is recorded from 1906.
A shoot that develops laterally at the base of a plant, often rooting to form a new plant. Many succulents and cacti are propagated by removing offsets and planting them elsewhere. See more at vegetative reproduction.
An index or position in an array, string, or block of memory usually a non-negative integer.
E.g. the Perl function splice(ARRAY, OFFSET, LENGTH, LIST) replaces LENGTH elements starting at index OFFSET in array with LIST, where offset zero means the start of the array.
For an Intel x86 processor with a segmented address space the offset is the position of a byte relative to the start of the segment.