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The phrase "a fundamental error in" is correct and usable in written English.
It can be used when discussing a significant mistake or flaw in a particular context, such as an argument, analysis, or process.
Example: "The report contained a fundamental error in its calculations, leading to incorrect conclusions."
Alternatives: "a critical mistake in" or "a major flaw in".
Exact(13)
We made a fundamental error in presenting that world".
He believes the Conservatives – who are in part advised by his own Democratic campaign colleague Jim Messina – made a fundamental error in underestimating Miliband.
He contended that Republicans out to roll back the welfare state made a fundamental error in thinking that politicians and their actions drive history.
I think I probably felt I'd made a fundamental error in agreeing to do that movie even though it was the part and the film that everyone wanted to do.
Prison experts said officials appeared to have made a fundamental error in placing a vulnerable inmate like Mr. Geoghan, 68, in the same protective custody unit as Mr. Druce.
"I think they are committing a fundamental error in thinking that the policies we are following are weakening France, when in fact these policies are strengthening it," he told Europe 1.
Similar(45)
Labour is making a fundamental error, however, in assuming that these young protesters want or need anybody to "be our voice".
A fundamental error relation inherent in the Gauss divergence theorem provided the basis for studying the truncation error of the finite volume method with cell center formulation for a model steady convective equation.
Mr. Litan's column conveniently omits any mention of a second fundamental error in the study that I point out in my blog.
The three listed companies combined have done less than $3m-worth of business in their entire history; not coincidentally, their total valuation has fallen by over $1.2 billion since going public (see chart 7).Their troubles are rooted in a fundamental error.
"Moving to Phoenix without a stadium deal in place was a fundamental error that should never have happened," says Marc Ganis, president of SportsCorp, a Chicago consulting firm.
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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