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.

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

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.

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This article uses material from the Wikipedia article Integer-valued function, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.