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Disinterested or Uninterested?
They are not the same. Disinterested means impartial or neutral; uninterested means bored or lacking interest.
Example: A good teacher should be disinterested but certainly not uninterested.

Farther or Further?
Farther refers to physical distances.
Example: Indiana is farther than I thought.
Further refers to quantity, time, or degree.
Example: They progressed further on their research.