Abstract:It’s of vital importance to get a proper understanding of the concept of limit in the learning of mathematical analysis. However, the teaching of limit has long become one of the lingering headaches in the teaching of advanced mathematics. An analysis of the historical development from the perspectives of origin, evolvement and formation tells us three key points deserve our attention, namely, the setting up of a correspondent concept of infinity, athletics and the mastery of the methodology in these concepts, centering on which an annotation is made of the puzzles that arise from the formation of the limit concept.