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to try to be more successful than someone or something elseIt's difficult for a small supermarket to compete against/with the big supermarkets.
Both girls compete for their father's attention.
figurative Turn the music down - I'm not competing against/with that noise (= I can't/won't try to speak louder than that music)!
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to take part in a race or competitionAre you competing in the 100 metres?
The two athletes are competing for the gold medal.