Daegu , (대구, 大邱, literally 'large hill') formerly spelled Taegu, and officially known as the Daegu Metropolitan City, is a city in South Korea, the fourth largest after Seoul, Busan, and Incheon, and the third largest metropolitan area in the nation with over 2.5 million residents. Daegu is the capital and principal city of the surrounding Gyeongsangbuk-do province, although it is not legally part of it. The two areas combined are often referred to as Daegu-Gyeongbuk, with a total population of over 5 million.