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The phrase "acknowledges an error" is correct and usable in written English.
You can use it when discussing a situation where someone admits to making a mistake or recognizes a fault in their actions or statements.
Example: "The report acknowledges an error in the initial calculations, which has since been corrected."
Alternatives: "admits a mistake" or "recognizes an error."
Exact(2)
We also make allowances if the politician or interest group acknowledges an error was made.
In "Plan of Attack" Woodward acknowledges an error of his own: he admits he should have pushed The Washington Post to publish a front-page article about the flimsiness of the intelligence on W.M.D. I was Washington bureau chief for The Times while this was happening, and I failed to push hard enough for an almost identical, skeptical article, written by James Risen.
Similar(58)
We also acknowledge an error in the specification of a utility function in our previous paper.
Mr. Allen took responsibility for the original ad and acknowledged an "error in the scripting".
Still, he would come to acknowledge an error in his email.
Harwood posted a tweet two weeks ago acknowledging an error in his comparison of how the richest and poorest would fare.
After 25 minutes in the couple's home, the officials appeared to acknowledge an error had been made and retreated, leaving Qu terrified and Watkinson in tears.
The Metropolitan Museum of Art has acknowledged an error that was pointed out by a seventh-grade boy from West Hartford, Conn., in a 6th-century map of the Byzantine Empire.
His wilful refusal to acknowledge an error of judgement in a delicate area of professional responsibility will return to haunt him.
Calvin wrote: "His wilful refusal to acknowledge an error of judgement in a delicate area of professional responsibility will return to haunt him.
During her recent confirmation hearings, she had to acknowledge an error understating her income on federal disclosure forms by tens of millions of dollars.
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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