arbitrate

verb3

1. •
   To make a judgment (on a dispute) as an arbitrator or arbiter

   • There shall your swords and lances arbitrate / The swelling difference of your settled hate. — 1595
2. •
   To submit (a dispute) to such judgment
3. •
   (rare) To assign an arbitrary value to, or otherwise determine arbitrarily.

   • We wish to show f is continuous. Arbitrate epsilon greater than zero...