DOI: 10.36347/sjpms

Pages: 140-143

Firstly, this paper gives the conditions of the existence of four kinds of unilateral limits and limit values for monotone function; points out the relationship between the existence of four kinds of unilateral limits and sequence limit, and weakens the conditions of Heine theorem. Secondly, it demonstrates that the discontinuity points of monotone functions are the discontinuity points of the first kind, and their number is countable at most within a interval. Finally, it gives the relationship between upper and lower limits of bounded sequence and monotone function and bounded sequence, and provides corresponding application examples. Keywords: monotone function; limit; discontinuity point