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general::
Phrase(s): Have a nice day. [and] Have a good day.; Have a nice one.; Have a good one.
Cliché an expression said when parting or saying good-bye. (This is now quite hackneyed, and many people are annoyed by it.) • Clerk: Thank you. Tom: Thank you. Clerk: Have a nice day. • Bob: See you, man! John: Bye, Bob. Have a good one!
McGrawhill's American Idioms And Phrasal Verbs
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general::
Also, have a good day;have a good one. A cordial goodbye to you. For example, Thanks for the order, have a nice day, or See you next week?? have a good day, or The car's ready for youhave a good one. These expressions have become synonymous with a polite farewell. The first originated about 1920 but, like the variants, became widespread only after 1950.
American Heritage Idioms