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The phrase "without having reached" is correct and commonly used in written English.
One example usage could be: "She was disappointed that she couldn't go on the trip without having reached her savings goal." This sentence means that she was unable to go on the trip because she had not yet saved enough money.
Exact(12)
He is the only Yankee to have his uniform number retired without having reached a World Series.
Last year, around one in five children left primary school without having reached a sufficient standard in reading and writing.
Here, watching Ms. Mullova play from a score, you sensed that she was thoroughly reconsidering a canonical work without having reached any firm conclusions.
Jurors in the Arthur Andersen criminal trial began deliberations this morning but left the courtroom at the end of the day without having reached a verdict.
Leinster, winner of the Heineken Cup — rugby's answer to soccer's Champions League — for the past two seasons and three of the past four, is on the verge of elimination without having reached the playoff stage.
On Oct. 17, 2006, without having reached Mr. Adams, much less received his consent, the city issued a demolition permit for the house of God, at 2223 Lizardi Street.
Similar(48)
To put Kerber's run in perspective, here is a look at the 10 unseeded players who made the semifinals of the U.S. Open in the Open Era without previously having reached the quarterfinals or better of any other Grand Slam tournament.
While he was alive, he also held the record for the fastest ascent without oxygen, having reached the top in under 17 hours.
Allison is the only Atlantic tropical storm to have its name retired without ever having reached hurricane strength.
Soon afterwards, he finally learned that the Duke of Albany had lost the larger part of his army to attrition and desertion, and had returned to France without ever having reached Naples.
At high forward speeds, the precession is usually too slow, contributing to an uncontrolled bike's tendency to understeer and eventually fall over without ever having reached the upright position.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com