Integer-valued function

In other words, it is a function that assigns an integer to each member of its domain.

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.

They also have similar uses in geometric group theory, where length function represents the concept of norm, and word metric represents the concept of metric.

Gödel numbering, defined on well-formed formulae of some formal language, is a natural-valued function.

In computer programming, many functions return values of integer type due to simplicity of implementation.

The floor function on real numbers. Its discontinuities are pictured with white discs outlines with blue circles.