integer (n.)

"a whole number" (as opposed to a fraction), 1570s, from Latin integer (adj.) "intact, whole, complete," figuratively, "untainted, upright," literally "untouched," from in- "not" (see in- (1)) + root of tangere "to touch," from PIE root *tag- "to touch, handle," from PIE root *tag- "to touch, handle." The word was used earlier in English as an adjective in the Latin sense, "whole, entire" (c. 1500).

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