The floor function on real numbers. Its discontinuities are pictured with white discs outlines with blue circles.
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.
The floor and ceiling functions are examples of integer-valued functions 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 an integer-valued function.
Z of integers. Since the latter is an ordered ring, the functions form a partially ordered ring:| View original on Wikipedia | Back | FazBrowse Home |