perpetual pursuit
definitions
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The continuous and never-ending effort to achieve, find, or attain something, typically an abstract concept like happiness, truth, or excellence.ru: вечное стремление
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A continuous state of physically chasing or being chased by someone or something.ru: постоянная погоня
examples
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The artist dedicated his life to the perpetual pursuit of perfection.
Художник посвятил свою жизнь вечному стремлению к совершенству.
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The prey lived in a state of perpetual pursuit by predators.
Добыча жила в состоянии постоянной погони хищников.