Undespairing means not giving up hope, remaining optimistic or persistent even in the face of difficulty. There are several synonyms for undespairing, including hopeful, determined, resolute, indefatigable, persevering, and dogged. These words carry a positive connotation, highlighting the resilience and tenacity of a person who refuses to give up. Other synonyms include steadfast, unyielding, undaunted, and unflagging, emphasizing the idea of remaining strong and true to one's goals and beliefs despite challenging circumstances. These words all convey a sense of strength and conviction, inspiring us to keep pushing forward and never lose hope, no matter how tough things may seem.