Hope (verb)

  1. To cherish a desire with anticipation.
  2. To want something to happen or be true.
  3. To desire with expectation of obtainment or fulfillment.
  4. To expect with confidence

Phrase “hope against hope” means to hope without any basis for expecting fulfillment.

The emotion of Hope is found in the Triple Heater meridian in the Fire element.

Definition from Dictionary by Merriam-Webster.