The Sorites Paradox

The word "sorites" derives from the Greek word for heap. The paradox of the heap arises when one considers a heap of sand, from which grains are individually removed. Is it still a heap when only one grain remains? If not, when did it change from a heap to a non-heap?

This is something I´ve been thinking of a lot during the last months. There are some things that change into others very quickly; if you drop a glass, it breaks into pieces, and can´t be considered a glass anymore. But there´re other changes that are way smoother. 

In the Serengeti plein one can see granite formations like the ones in these pictures. They are called Kopjes; which can be translated as "little heads". It´s a swahili word that comes from the Afrikaans. These granite rocks used to be the core of a former hill. The hill disappeared due to the effect of erosion, but the rock remains. When did the hill became a rock?

This idea is directly related to the concept of identity. Does identity actually exist?