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naught
come to naught
To be totally unsuccessful or amount to nothing. Our efforts to keep the farm came to naught in the end. All those hours I spent researching my graduate thesis have come to naught.
come to nothing
and come to naughtto amount to nothing; to be worthless. So all my hard work comes to nothing. Yes, the whole project comes to naught.
(all) for naught
(slightly formal) without achievement or result
Marge's time in jail wasn't all for naught – she earned a college degree while she was there. Usage notes: sometimes, in less formal use, nothing is substituted for naught: I would hate to think that what we'd tried to do was all for nothing.
Etymology: based on the literal meaning of naught (zero or nothing)
come to nothing
Also, come to naught. Fail, as in All his efforts have come to nothing, or The last round of peace talks came to naught. The first term dates from the mid-1500s, the variant from the early 1600s.