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.fr: poursuite perpétuelle
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A continuous state of physically chasing or being chased by someone or something.fr: poursuite constante
examples
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The artist dedicated his life to the perpetual pursuit of perfection.
L'artiste a consacré sa vie à la poursuite perpétuelle de la perfection.
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The prey lived in a state of perpetual pursuit by predators.
La proie vivait dans un état de poursuite constante par les prédateurs.