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What does "run after" mean?

    Also, chase after.
  1. Follow, pursue with haste, as in Our dog loves to run after the mail truck, or The children were chasing after the geese in the park. [c. 1300]
  2. Seek the company or attention of, especially aggressively. For example, He's run after her for a year, but she just ignores him. [Early 1500s]

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