Integer-valued function
In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain. Floor and ceiling functions are examples of an integer-valued function of a real variable, but on real numbers and generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful. Any such function on a connected space either has discontinuities or is constant. On the other hand, on discrete and other totally disconnected spaces integer-valued functions have roughly the same importance as real-valued functions have on non-discrete spaces. Any function with natural, or non-negative integer values is a partial case of integer-valued function. (Wikipedia).
