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The phrase "improve without" is grammatically correct and can be used in written English. It is typically used to indicate that something has improved or been achieved without the use of a particular action or object. Example: The team was able to improve their performance without any additional training.
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What's more, there is a practical advantage to their doing so: you can't improve without knowing where you need improvement.
How would you help them improve without a judgement?
Finally, mathematics teaching will not improve without leadership.
This could not have happened and cannot continue to improve without support.
They improve without fanfare and frequently without much help from the mental health system.
They will try to improve without their two most productive hitters, Vinny Castilla and Jeromy Burnitz.
The NHS - or, indeed, any healthcare system - will not be able to improve without better information.
Democrats are pressing Mr. Bush to dedicate more money to education, arguing that schools cannot improve without the resources.
Certainly, if things are to improve without an increase in spending, greater public service efficiency is going to be vital.
Black respondents in our surveys, meanwhile, report believing that outcomes for blacks can improve without affecting outcomes for white Americans.
…But, at the same time, don't expect to improve without spending more, at least in the short term.
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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