What is the meaning of persevering?

verb

• Be persistent, refuse to stop.
  • usage: "he persisted to call me every night"; "The child persisted and kept asking questions"
  • synonyms: persevere, persist, hang in, hang on, hold on

adjective

• Quietly and steadily persevering especially in detail or exactness)
  • usage: "a diligent (or patient) worker"; "with persevering (or patient. industry she revived the failing business"
  • synonyms: diligent