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"imprudent, not discrete" (early 15c.) and indiscrete "not containing distinct parts" (c.1600) are both from Latin indiscretus "unseparated; indistinguishable, not known apart," the former via an Old French or Medieval Latin secondary sense. From in- "not" (see in- (1)) + discreet. Related: Indiscreetly; indiscreetness.